1
00:00:05,150 --> 00:00:12,160
Well, nice to meet you, folks. If only you actually said I wouldn't tell you about classical in quantum black holes.
2
00:00:12,160 --> 00:00:17,180
It's an incredibly exciting subject. And so let me get started.
3
00:00:17,180 --> 00:00:23,780
So black holes. Of course, one of the most awe inspiring objects in the universe.
4
00:00:23,780 --> 00:00:30,230
They imply the end of spacetime as we know it. And also appear to imply deep paradoxes.
5
00:00:30,230 --> 00:00:37,970
When we try to meld quantum mechanics with gravitation in particular, it's by context.
6
00:00:37,970 --> 00:00:45,890
And as I said, there's actually, in fact, been significant progress, both observational and theoretical, in black hole physics in the past four years.
7
00:00:45,890 --> 00:00:47,840
I want to tell you about these exciting developments.
8
00:00:47,840 --> 00:00:54,920
And my message is going to be that the black holes should be thought of as like the hydrogen atom, the 21st century.
9
00:00:54,920 --> 00:01:00,880
By studying this particular system, I think we can learn a great deal about what quantum gravity is.
10
00:01:00,880 --> 00:01:10,140
And in fact, about other subjects, too. For instance, information theory and how it very surprisingly might connect with gravity.
11
00:01:10,140 --> 00:01:14,730
So let me get started. So let me tell you a little bit about classical black holes.
12
00:01:14,730 --> 00:01:20,040
So we now know that astrophysical black holes exist and behave to a very good
13
00:01:20,040 --> 00:01:24,850
approximation the way that Einstein classical generals who he said they should.
14
00:01:24,850 --> 00:01:30,930
And at least the exterior, we should emphasise that we only have information about the exterior of.
15
00:01:30,930 --> 00:01:39,390
So Carswell Schwarzschild in 1915 was the first person who wrote down actually immediately after Einstein's general theory relativity appeared,
16
00:01:39,390 --> 00:01:46,020
he wrote, and the first solution and the solution, in fact, was the black hole solution.
17
00:01:46,020 --> 00:01:54,930
Sadly, while fighting and dying were war one. And so his solution has a property that has an event horizon, a black hole event horizon,
18
00:01:54,930 --> 00:01:58,270
not that they realised really was property at the time, but it's there.
19
00:01:58,270 --> 00:02:03,370
And his solution and a crucial aspect of what I will tell you about later.
20
00:02:03,370 --> 00:02:08,970
And I hope you can see my point here is that the size of the black hole, the short shield radius,
21
00:02:08,970 --> 00:02:16,550
the radius of event horizon is twice Newton's constant times the black hole mass oversea square.
22
00:02:16,550 --> 00:02:20,680
OK, so this property. So I want you to remember that the short, short rate is the size.
23
00:02:20,680 --> 00:02:25,880
The event horizon goes linearly with a black hole mass.
24
00:02:25,880 --> 00:02:31,970
And so to give you an idea about what this says, Schwarzschild radius is for various objects for a solar mass,
25
00:02:31,970 --> 00:02:36,980
black hole, short radius is just under three kilometres.
26
00:02:36,980 --> 00:02:50,400
So if he crushed adiabatic lee the sun down to two point nine two kilometres, it would go inside its event horizon and form a black hole.
27
00:02:50,400 --> 00:02:58,410
Instantly, if we maintained a constant distance from the sun, so we stay here on the earth, our current distance away from the sun,
28
00:02:58,410 --> 00:03:04,950
and we did this idea that it crash crushing the force of gravity here on earth that we feel from the sun wouldn't change.
29
00:03:04,950 --> 00:03:09,450
It's not like suddenly the black hole will strength. It causes gravity to come much stronger.
30
00:03:09,450 --> 00:03:14,550
The reason why the strength of gravity is so much stronger at the black hole event horizon is just
31
00:03:14,550 --> 00:03:23,460
because we concentrated a tremendous amount of mass and energy in a very tiny volume indeed.
32
00:03:23,460 --> 00:03:26,400
And it's because we can approach much more closely.
33
00:03:26,400 --> 00:03:30,660
So, of course, usually when we go to the sun, you're going to get close to the sun as the surface of the sun.
34
00:03:30,660 --> 00:03:37,160
But here we crush it down to three kilometres. And that's the reason why the gravitational affective of a black hole is much larger.
35
00:03:37,160 --> 00:03:42,720
It's because we are concentrating it so much. So anyway, that was a solar mass black hole.
36
00:03:42,720 --> 00:03:48,210
We also know there exist supermassive black holes in the centre of almost all galaxies.
37
00:03:48,210 --> 00:03:52,640
And these have masses somewhere between the range of ten to the six to 10 to the nine solar masses.
38
00:03:52,640 --> 00:03:57,030
And therefore, correspondingly, they have a size which is quite large.
39
00:03:57,030 --> 00:04:01,660
They have sizes which have older tend to the six to 10 to the nine kilometres.
40
00:04:01,660 --> 00:04:10,500
And so, for instance, if you fell in into a galactic centre, supermassive black hole, you don't immediately die as you cross the event horizon.
41
00:04:10,500 --> 00:04:13,380
Actually, you don't notice anything particular happening to you.
42
00:04:13,380 --> 00:04:18,000
In fact, it takes you quite a few minutes until you reach the singularity and finally die.
43
00:04:18,000 --> 00:04:22,110
So you can live. So an observer, according to our current theories,
44
00:04:22,110 --> 00:04:27,660
understanding black holes can live for quite a long time inside a black hole and could make measurements.
45
00:04:27,660 --> 00:04:31,240
So it's interesting question to ask. What would such an observer see?
46
00:04:31,240 --> 00:04:36,400
And maybe we can discuss that later on in the question, not secessions.
47
00:04:36,400 --> 00:04:40,270
We can also consider a hypothetical Blackhall investment earth mass,
48
00:04:40,270 --> 00:04:43,780
and if you crush us into a black hole, it would have size just under one centimetre.
49
00:04:43,780 --> 00:04:53,190
So this gives you an idea of the sizes of some possible black holes actually physically realised and possible hypothetical ones.
50
00:04:53,190 --> 00:04:58,020
So what does the solution look like in equations? Well, we're talking about General Hibito.
51
00:04:58,020 --> 00:05:02,400
You have to talk about the spacetime distances. Nature, geometry.
52
00:05:02,400 --> 00:05:07,050
So here we have the S squared is a spacetime distance between events.
53
00:05:07,050 --> 00:05:14,610
And this is given by this expression involves four coordinates. Two of them are just the normal angular corners D, Theta, Theta and Phi.
54
00:05:14,610 --> 00:05:23,900
And this is just saying that everywhere there's a normal one. Spherical behaviour circle, symmetry, behaviour of the system where.
55
00:05:23,900 --> 00:05:27,520
That's the area of a given sphere is four pi R-squared.
56
00:05:27,520 --> 00:05:36,780
So this is this here. But now we have this issue here where we have this second term here gives you the fact that as you approach she horizon,
57
00:05:36,780 --> 00:05:44,670
this denominator here is going to zero. So this factor here, there's an infinity that's appearing here at Times Square.
58
00:05:44,670 --> 00:05:49,940
And this is telling you you get radial length contraction as the Iraq horizon is approach.
59
00:05:49,940 --> 00:05:58,310
The other hand, this first term here, this factor, this is also going to zero as you approach to RSS, I guess you go to we will see Horizon.
60
00:05:58,310 --> 00:06:04,280
This is saying that according to a static external observer, right far away from the black hole,
61
00:06:04,280 --> 00:06:10,000
that as time dilation, as the horizon at a shorter radius of approach.
62
00:06:10,000 --> 00:06:14,540
Right. So so there's both time dilation and radial length contraction.
63
00:06:14,540 --> 00:06:20,440
Mr. Secretary. Well, that's in equations. And of course, you can study this.
64
00:06:20,440 --> 00:06:27,680
Great, Lena. I want to emphasise that the more longstanding of classical black holes is due to record a number of people.
65
00:06:27,680 --> 00:06:30,650
Wheeler, who coined the name Black Holes,
66
00:06:30,650 --> 00:06:38,340
which will see libraries as somewhat inappropriate name and thanks Kruskal occur Thone Hawking and especially our own Roger Penrose.
67
00:06:38,340 --> 00:06:44,270
And I think Roger made the greatest contributions to modern sounding of classical my calls.
68
00:06:44,270 --> 00:06:49,730
So what are these awe inspiring objects look like? Well, here they are.
69
00:06:49,730 --> 00:06:54,770
Here's a lovely little Etsy baby black hole. You can purchase for the low, low price of just 10 pounds.
70
00:06:54,770 --> 00:07:01,040
Here's a baby black hole accretion disc for astrophysical black holes have accretion discs.
71
00:07:01,040 --> 00:07:08,210
You can get these things with adoption certificates. That's lovely. Here is a different picture of what a black hole looks like.
72
00:07:08,210 --> 00:07:15,050
We can take this geometry. And of course, it's very hard for me to represent the geometry of this situation in two dimensions.
73
00:07:15,050 --> 00:07:19,640
But let me try. So this is a picture of radius and time.
74
00:07:19,640 --> 00:07:24,370
He? S each of these points you should think of as a particular four dimensional thing,
75
00:07:24,370 --> 00:07:29,060
as a as a two sphere sort of living about every one of these things.
76
00:07:29,060 --> 00:07:35,060
And what I want, I emphasise is as this is the exterior. This white region is the exterior geometry of the black hole.
77
00:07:35,060 --> 00:07:37,230
And then we have this horizon.
78
00:07:37,230 --> 00:07:47,270
And the crucial thing is as you go inside your eyes and in fact, Space-Time itself is not really static inside the horizon.
79
00:07:47,270 --> 00:07:53,980
The reason is, is because you don't get a hint of this from this thing as you go are is less than our.
80
00:07:53,980 --> 00:07:59,180
Notice that this term here changes sign. And this thing here changes sign.
81
00:07:59,180 --> 00:08:06,710
So that means now there is an overall negative sign in front of the R-squared and there is no real positive sign in front of the D.T. squared.
82
00:08:06,710 --> 00:08:12,170
And that means this now becomes a spatial like coordinate. And this is the temporal called note here.
83
00:08:12,170 --> 00:08:17,730
So, in fact, there's a definite different a Kornet system where you see this having better.
84
00:08:17,730 --> 00:08:24,460
But you get a hint about what's going on here. And the idea is that, in fact, the radio corner becomes a temporal coordinate.
85
00:08:24,460 --> 00:08:32,730
So, in fact, as you're going on with this thing, in fact, space time itself is dynamical here.
86
00:08:32,730 --> 00:08:36,900
And is dragging you towards the singularity as you go down.
87
00:08:36,900 --> 00:08:47,370
So as you see this picture being animated here. Well, as I emphasised before passing the horizon, nothing special happens to you.
88
00:08:47,370 --> 00:08:50,810
There's no infinite forces. You don't necessarily get ripped apart.
89
00:08:50,810 --> 00:08:58,680
The horizon of freely falling observer just thinks the horizon is very much like empty Minkowski space.
90
00:08:58,680 --> 00:09:07,590
In fact, the only place where something truly singular and terrible happens to you is here, right at the singularity are equal zero in these corners.
91
00:09:07,590 --> 00:09:13,050
But we should be wary about this because in fact, the classical solution.
92
00:09:13,050 --> 00:09:17,820
And in fact, Einstein's classical generals, hefty itself is not reliable here.
93
00:09:17,820 --> 00:09:25,830
So I want to emphasise to you that you that even though the singularity is predicted by classical general relativity,
94
00:09:25,830 --> 00:09:30,150
we know the theory is not really self-consistent here.
95
00:09:30,150 --> 00:09:35,070
So we believe that itself consistently describes exterior geometry and near the horizon.
96
00:09:35,070 --> 00:09:40,040
But once we start approaching the singularity, we don't know what that physics is.
97
00:09:40,040 --> 00:09:48,660
So, of course, the subject of active research I'm trying to understand. So here's another picture of what a black hole looks like.
98
00:09:48,660 --> 00:09:53,280
And so here we have radius again. So here is a star collapsing to form a black hole.
99
00:09:53,280 --> 00:09:59,410
And here we have an event horizon forming. And so the crucial thing about the event horizon is here.
100
00:09:59,410 --> 00:10:03,120
Here is drawn are light cones. So this.
101
00:10:03,120 --> 00:10:13,140
So what happens is light rise, quote unquote, ingoing or outgoing light rays have to be there on the edge of this light cone here.
102
00:10:13,140 --> 00:10:17,190
And material objects, massive objects always travel less than the speed of light.
103
00:10:17,190 --> 00:10:23,880
So I always have to travel with inside the light cone. So signals can only be sent in in these angles here.
104
00:10:23,880 --> 00:10:28,010
So this one here is ingoing light. Right. And would go into the.
105
00:10:28,010 --> 00:10:33,500
We go back into the black hole. But this one here would escape to infinity.
106
00:10:33,500 --> 00:10:37,580
But there's this distortion of space time in the black hole background.
107
00:10:37,580 --> 00:10:39,710
And what happens is the light cones tip over.
108
00:10:39,710 --> 00:10:48,920
So once you go to the event horizon, now you see right at the event horizon, the outgoing light rays actually go right along the horizon.
109
00:10:48,920 --> 00:10:53,360
All material objects inevitably go get dragged into the singularity.
110
00:10:53,360 --> 00:10:58,010
That's the only possibility. And ingoing light rays, of course, go very quickly.
111
00:10:58,010 --> 00:11:06,860
So it's this tipping over the light cones force you to go to the singularity is another way of saying that inside the event horizon,
112
00:11:06,860 --> 00:11:11,190
forward in time becomes radially inward.
113
00:11:11,190 --> 00:11:13,570
All right. So that's the thing.
114
00:11:13,570 --> 00:11:19,600
But there's another thing here, which is, again, a freely falling observer, a freely falling observer going through this system.
115
00:11:19,600 --> 00:11:26,410
I mean, we'll go through the rent rising, hit the singularity. But nothing special happens is really falling observer.
116
00:11:26,410 --> 00:11:31,750
She through force, through the horizon. It's just the usual finite tidal forces.
117
00:11:31,750 --> 00:11:35,780
You always get when you're in the external gravitational fields.
118
00:11:35,780 --> 00:11:39,520
All right. So there will be tidal forces on this person who is a tiny black hole.
119
00:11:39,520 --> 00:11:45,220
These tidal forces might be strong enough to rip the person apart, spike spaghetti for her.
120
00:11:45,220 --> 00:11:52,360
But otherwise, it's a large black hole like a galactic centre, black hole falling through horizon of such an object gain.
121
00:11:52,360 --> 00:11:56,950
Nothing special happens in the observable survive. A human would survive.
122
00:11:56,950 --> 00:12:01,960
And only when you finally get to the singularity, which should be destroyed.
123
00:12:01,960 --> 00:12:06,400
And so I emphasise, if we go back to the metric,
124
00:12:06,400 --> 00:12:12,040
it looked like there was apparently singular behaviour in this metric near our equals, our s, and that's why.
125
00:12:12,040 --> 00:12:21,190
And in fact, took roughly 45 years or so before people took black hole solutions seriously, they thought.
126
00:12:21,190 --> 00:12:26,350
In fact, this wasn't sensible. This only could be used as if it was a mathematical artefact.
127
00:12:26,350 --> 00:12:34,330
But later on, it was realised. In fact, there's nothing singular about this solution apart from right at the Singularity Arkos zero.
128
00:12:34,330 --> 00:12:38,260
In fact, this apparent singular behaviour, the short geometric, is just a natural supporters.
129
00:12:38,260 --> 00:12:43,750
It's like longitude. If you're at the north and south poles, it's a corner that breaks down.
130
00:12:43,750 --> 00:12:50,000
It's not truly physics breaks down at the event horizon. So that was that.
131
00:12:50,000 --> 00:13:00,760
Now. We now know to a very, very high degree of confidence that supermassive astroparticle black holes exist in galactic centres of most galaxies.
132
00:13:00,760 --> 00:13:05,860
And so here is a little movie, which I hope now plays.
133
00:13:05,860 --> 00:13:13,590
So this is pointing towards our galactic centre and it's starting over a whole bunch of years, the motion of the stars.
134
00:13:13,590 --> 00:13:17,140
And what you see here is a right at the galactic centre.
135
00:13:17,140 --> 00:13:26,050
This is a tiny distance, 10 light days that the stars are orbiting around a very massive, very centrally concentrated object.
136
00:13:26,050 --> 00:13:32,670
In fact, there was a Nobel prise shared with Roger Penrose this year in 2020,
137
00:13:32,670 --> 00:13:37,210
where these two teams, led by these two investigators, independently show.
138
00:13:37,210 --> 00:13:41,590
By measuring the trajectories of these seven stars. Right. Close to the likely centre.
139
00:13:41,590 --> 00:13:43,470
They're not they're not perfectly on ellipses.
140
00:13:43,470 --> 00:13:50,450
In fact, there are general relativistic effects exactly of the kind predicted by General 50 in the background of a black hole.
141
00:13:50,450 --> 00:13:54,520
The slight distorting these lipsett. So this is a confirmation.
142
00:13:54,520 --> 00:14:01,940
You have a supermassive black hole with a guy with a very high degree of confidence at our collective centre.
143
00:14:01,940 --> 00:14:07,880
So recently we have a direct image of a supermassive black hole, not in our galaxy fate in M80 seven.
144
00:14:07,880 --> 00:14:13,220
This is from the Event Horizon Telescope in 2019. And here is the shadow, the event horizon.
145
00:14:13,220 --> 00:14:19,280
And here is the accretion disk. So just like that little Etsy toy you can buy here.
146
00:14:19,280 --> 00:14:26,870
What the light is coming from the accretion disk is the black hole. And here is the shadow of the event horizon.
147
00:14:26,870 --> 00:14:33,770
So we now know there's a whole range of black holes. And in fact, we have another way of looking at black holes, not just visibly,
148
00:14:33,770 --> 00:14:40,700
but we also now here in the sense the sound of black holes merging through gravitational waves.
149
00:14:40,700 --> 00:14:45,420
So, again, I hope you can just click on this thing. Sometimes it's worth.
150
00:14:45,420 --> 00:14:50,040
Do you hear that sound, doesn't hear the sound? I hope so.
151
00:14:50,040 --> 00:14:54,030
It's so that is the sound. It was picked up in the gravitational wave detectors,
152
00:14:54,030 --> 00:15:00,540
the advanced liger collaboration that they have two sell at Hanford and Livingston in the United States.
153
00:15:00,540 --> 00:15:08,340
And this is the sound, the final chirp as the two black holes, two very supermassive black hole, actually, not supermassive.
154
00:15:08,340 --> 00:15:16,380
Very massive. Multiple solar masses are rotating together and finally colliding and they merge.
155
00:15:16,380 --> 00:15:19,200
And during that final seconds there,
156
00:15:19,200 --> 00:15:25,260
the energy released in gravitational waves far exceeds the energy produced by all the suns in all the galaxies in the universe.
157
00:15:25,260 --> 00:15:34,110
It's an extraordinary three or four solar masses worth of mass are being converted to energy, almost alling and gravitational waves.
158
00:15:34,110 --> 00:15:39,240
And so now we've seen dozens, actually hundreds of black hole mergers.
159
00:15:39,240 --> 00:15:43,710
And so this is merger tree of how black holes of urging, merging and evolving.
160
00:15:43,710 --> 00:15:45,060
And of course, it's nice. Let's see thing.
161
00:15:45,060 --> 00:15:52,800
And the nice thing about this is let's see cartoon you see here is, in fact, it shows these two black holes will be rotating around to each other.
162
00:15:52,800 --> 00:15:58,710
The final black hole produces a highly spinning black hole. So it's not a short, tall black hole, but the astroparticle black holes.
163
00:15:58,710 --> 00:16:06,010
We have a highly rotating just for simplicity in this Coke. I'm going to focus just on short term black holes, non rotating black holes.
164
00:16:06,010 --> 00:16:13,980
Okay. So the summary is, is we know there's a wide variety of black holes exist in our universe.
165
00:16:13,980 --> 00:16:19,740
And they're very well described by Einstein's by this virtual solution or the curse solution.
166
00:16:19,740 --> 00:16:25,530
It's generalised the rotating generalisation in external region.
167
00:16:25,530 --> 00:16:29,070
So my interest, though, is quantum black holes.
168
00:16:29,070 --> 00:16:34,440
That's what I want to tell you about. So the classical theory of black holes is extraordinarily rich.
169
00:16:34,440 --> 00:16:45,720
But the world is really quantum mechanical. And so we need to study what the behaviour of quantum mechanics, what a quantum behaviour, black holes is.
170
00:16:45,720 --> 00:16:50,430
And what we are going to find is even more remarkable in the classical case.
171
00:16:50,430 --> 00:17:01,750
And it apparently leads to deep paradoxes and these deep, dark paradoxes, rather like the birth of the early history of quantum mechanics itself.
172
00:17:01,750 --> 00:17:05,520
The thinking about these paradoxes and understanding how they're resolved is
173
00:17:05,520 --> 00:17:10,450
guiding us towards a much better understanding of aspects of quantum gravity.
174
00:17:10,450 --> 00:17:16,630
So I would emphasise it's been significant progress in the last years, and I will tell you a little bit about what the significant progress is.
175
00:17:16,630 --> 00:17:27,450
All right. Next slide. So the first thing to realise is the most basic quantum facts about a black hole is hawking radiation.
176
00:17:27,450 --> 00:17:32,600
So let me tell you about why what hawking radiation is and why it exists.
177
00:17:32,600 --> 00:17:38,520
So in relativistic quantum mechanics, sometimes we call quantum field theory empty space, quote unquote.
178
00:17:38,520 --> 00:17:43,080
The vacuum is full of quantum fluctuations of all fields and particles.
179
00:17:43,080 --> 00:17:52,020
So it's not a static. You shouldn't really think it is an empty thing. So here is actually a precision numerical evaluation of the vacuum of QC day.
180
00:17:52,020 --> 00:17:57,420
This is on a five Fermi cubed lattice.
181
00:17:57,420 --> 00:18:04,680
And this is a a time loop of it. And here we just have one realisation show we spoke to Super posed a different
182
00:18:04,680 --> 00:18:08,350
quantum superposition and we have different positions of what the vacuum is doing.
183
00:18:08,350 --> 00:18:12,870
This is one realisation. And you see this thing is fluctuating like crazy.
184
00:18:12,870 --> 00:18:15,180
We're getting fluctuations of scales that you see.
185
00:18:15,180 --> 00:18:23,030
There's a typical sort of scale here that set by the scale of QCT, its self, which is Voda itself about one Fermi.
186
00:18:23,030 --> 00:18:27,720
Right. Or 200. I mean, the Lambda QCT. So.
187
00:18:27,720 --> 00:18:32,590
And instantly this is verified, these cutey deep precision calculations.
188
00:18:32,590 --> 00:18:38,580
And now give you quite accurate description of the low lying masons and baritones and various other states, other properties.
189
00:18:38,580 --> 00:18:44,720
We know this is true. We know quantum motivations are there for many reasons. This is one demonstration.
190
00:18:44,720 --> 00:18:51,260
So what about hawking radiation? Well, so here we have space time and here's a black hole.
191
00:18:51,260 --> 00:18:58,170
And as I emphasised, at least near the horizon, it's just like empty Minkowski space.
192
00:18:58,170 --> 00:19:02,550
So we have these positive and negative energy, virtual particle fluctuations happening everywhere.
193
00:19:02,550 --> 00:19:08,790
We have them happening outside the black hole. We have them happening certainly in the region anterior to the black hole.
194
00:19:08,790 --> 00:19:11,500
As long as we're not very close to the singularity, we don't know what's going on.
195
00:19:11,500 --> 00:19:18,710
Singularity, but certainly in the region around the horizon, we have these virtual particle fluctuations.
196
00:19:18,710 --> 00:19:25,740
I won't ever size the particles antiparticles here, but is the crucial thing is whether they're positive or negative energy overall.
197
00:19:25,740 --> 00:19:31,370
These things have zero energy. All right. And there is a correlation between their energies such.
198
00:19:31,370 --> 00:19:36,290
They start off in the vacuum, go back to the vacuum, constantly doing this.
199
00:19:36,290 --> 00:19:42,560
Well, if you have one of these fluctuations in the vicinity of the rise in the black hole,
200
00:19:42,560 --> 00:19:52,280
there's a quantum mechanical tunnelling process that allows the positive energy guy here in red, which could be a particle or an antiparticle.
201
00:19:52,280 --> 00:19:57,620
So I don't know, you'd get confused. It's not always that particles come out of the black and antiparticles go in.
202
00:19:57,620 --> 00:20:03,440
It can be either particles or antiparticles can escape. The crucial thing is whether they're positive energy or not.
203
00:20:03,440 --> 00:20:15,080
So rarely is tunnelling process allows a positive energy particle or antiparticle to a state to infinity while its negative energy sibling.
204
00:20:15,080 --> 00:20:21,980
And this is negative energy from the perspective of some distant observer particle or antiparticle is captured by the black hole.
205
00:20:21,980 --> 00:20:27,440
And therefore, because it's negative, energy reduces the black hole mass. So the end effect of this is the black hole.
206
00:20:27,440 --> 00:20:33,540
Mass has gone down slightly and its energy has been radiated away to infinity a little bit.
207
00:20:33,540 --> 00:20:39,190
And I like to experts here, this is sort of sometimes given as an intuitive picture of hawking radiation,
208
00:20:39,190 --> 00:20:42,420
that this tunnelling picture of organisation can be made precise.
209
00:20:42,420 --> 00:20:49,340
And he has an interesting advantage over Hawking's original calculation that actually explicitly shows the black hole mass is reducing.
210
00:20:49,340 --> 00:20:55,610
In fact, in Hawking's calculation on deficit of it maybe is that it's on a static background where the
211
00:20:55,610 --> 00:20:59,540
black hole mass is not reducing these tunnelling way of thinking about hawking radiation. In fact,
212
00:20:59,540 --> 00:21:09,600
shows the black hole mass is being reduced and its it is being reduced by this sort of inflow of negative energy from the distant observers suspect.
213
00:21:09,600 --> 00:21:15,000
So the end result of this is physical black holes are never truly black.
214
00:21:15,000 --> 00:21:18,480
In fact, they produce thermal radiation, all climatically allowed modes.
215
00:21:18,480 --> 00:21:25,540
And here is a little cartoon. So I went inside dominantly for black holes. It would be gravitons, photons or maybe neutrinos.
216
00:21:25,540 --> 00:21:29,730
But in fact, in fact, all kinematics available modes are allowed. So amazing.
217
00:21:29,730 --> 00:21:30,770
End result is black.
218
00:21:30,770 --> 00:21:40,200
Was a thermal system with a temperature gain is seen by a far away static observer t hawking and the hawking temperature here it is goes like h bar.
219
00:21:40,200 --> 00:21:45,360
It's a quantum effect. C cubed over eight pi. Newton's constant.
220
00:21:45,360 --> 00:21:53,550
K Boltzmann. If we want normal temperature, normal kelvin units and then one over the massive black hole we put in for instance a massive black on KG.
221
00:21:53,550 --> 00:21:59,280
Imagine we had a kg sized black hole. That's a logically consistent thing to consider though.
222
00:21:59,280 --> 00:22:03,930
Hypothetical, and since we've never observed such a thing, it would actually have a very high temperature.
223
00:22:03,930 --> 00:22:10,380
Ten to twenty three, Kelvin. So it's not like this is a small temperature, at least if we have a small black hole.
224
00:22:10,380 --> 00:22:12,720
This is a very large temperature for a small black hole.
225
00:22:12,720 --> 00:22:17,780
On the other hand, because astrophysical black holes are so massive, solar mass for solar mass.
226
00:22:17,780 --> 00:22:26,710
My call. It's ten to the minus seven Kelvin. So that means that we're never going to observe, at least for astrophysical black holes.
227
00:22:26,710 --> 00:22:29,330
The Hawking temperature satellite.
228
00:22:29,330 --> 00:22:38,570
But if you start off with a black hole, let's say you start a full black hole, which is in between a kilogram and a solar mass.
229
00:22:38,570 --> 00:22:47,450
Well, it would start radiating energy. It was mass will work with we all juice and therefore its temperature will rise.
230
00:22:47,450 --> 00:22:53,510
And there's a runaway process here. So that's important to bear in mind.
231
00:22:53,510 --> 00:22:59,030
I want you to remember that for Lytro. So Blackhall Hawking radiation has never been observed.
232
00:22:59,030 --> 00:23:04,340
But we have a high degree of confidence. That's true. We now know many ways it could be theoretically derived.
233
00:23:04,340 --> 00:23:07,760
And it solves some otherwise troubling aspects of classical black hole physics.
234
00:23:07,760 --> 00:23:10,640
Let me tell you a little bit by one of these quite troubling aspects.
235
00:23:10,640 --> 00:23:16,670
So one of these is associated with a second law of thermodynamics, which, of course, is that the change in entropy,
236
00:23:16,670 --> 00:23:22,490
in a physical process should be greater than zero or equal reserve if it's reversible.
237
00:23:22,490 --> 00:23:30,560
So Fleckenstein argued that to say the second law one must sign and I want to emphasise is a finite end to black holes.
238
00:23:30,560 --> 00:23:40,580
Otherwise, one could systematically reduce the entropy of the universe by throwing in matter with entropy greater than zero, which then disappears.
239
00:23:40,580 --> 00:23:47,540
All right. And if you do not assign any entropy to the black hole, then you reduce systematically the entropy of the universe.
240
00:23:47,540 --> 00:23:52,550
By doing this process, by just quantity recycling this process, you could use it with universe.
241
00:23:52,550 --> 00:24:01,870
This is a pretty bad thing. So Berenstein suggested, in fact, that the entropy of a black hole is fine.
242
00:24:01,870 --> 00:24:04,010
Entropy should be proportional to the area.
243
00:24:04,010 --> 00:24:10,010
The black hole and Hawking's calculation of the temperature confirm this because the first laws were seven.
244
00:24:10,010 --> 00:24:13,460
Amik says d e equals temperature times D.
245
00:24:13,460 --> 00:24:18,620
S with the E is the change in the energy. The S is the change in the entropy.
246
00:24:18,620 --> 00:24:22,970
And we now have a formula for the temperature due to Hawking and we know the energy.
247
00:24:22,970 --> 00:24:30,050
Here is the massive black hole time C squared. And if you put this N, you put the formula in for your tea.
248
00:24:30,050 --> 00:24:34,400
Hawking arrived earlier and you put in what you just take the derivative.
249
00:24:34,400 --> 00:24:39,620
This thing, d.A. So it's just the M C squared. You can then find what the change of D.
250
00:24:39,620 --> 00:24:46,430
S is D. S and integrate that up. And what you find is you find this expression for the entropy of a black hole.
251
00:24:46,430 --> 00:24:51,200
It goes. This is called the either the black hole entropy or the Berenstein Hawking entropy.
252
00:24:51,200 --> 00:24:56,480
It goes like CS cubed on G Newton one over H bar.
253
00:24:56,480 --> 00:24:59,300
And then the area, the black hole on four.
254
00:24:59,300 --> 00:25:06,710
In fact, this combination of units here, this defines the planked length squared or the one over the Planck link squared.
255
00:25:06,710 --> 00:25:10,430
Another better way of writing this is one quarter of IE.
256
00:25:10,430 --> 00:25:15,710
The area of the black hole event horizon over the Planck Link Square.
257
00:25:15,710 --> 00:25:19,910
I want out I want you to notice this Planck length squared is Planck length is incredibly tiny,
258
00:25:19,910 --> 00:25:23,360
is approximately ten to the minus 33 centimetres and black.
259
00:25:23,360 --> 00:25:27,120
Oh, of course. Black hole of enterprises. Well, that macroscopic things there.
260
00:25:27,120 --> 00:25:31,340
You know, kilometres squared or much bigger banks.
261
00:25:31,340 --> 00:25:34,830
All right. Or much bigger for supermassive black holes.
262
00:25:34,830 --> 00:25:38,890
Now, I want to emphasise to you that here. Notice isn't one over H bar here.
263
00:25:38,890 --> 00:25:46,460
So that means the classical limit. Each bar goes to zero. The entropy of a black hole in the classical limit will be infinite.
264
00:25:46,460 --> 00:25:50,510
And this is why you can constantly keep highlighting entropy there in this process. Why should you?
265
00:25:50,510 --> 00:25:59,310
Homer Simpson falling into a black hole. So this should remind you of the catastrophe of plis pre plank classical black body radiation spectrum.
266
00:25:59,310 --> 00:26:08,210
The fact that the quantum effects actually make finite insensible what will be an infinity in the classical theory.
267
00:26:08,210 --> 00:26:11,450
That's very interesting. So that's one way of thinking about this.
268
00:26:11,450 --> 00:26:16,430
Well, one way of thinking about the meaning of this entropic formula that the entropy goes like one quarter.
269
00:26:16,430 --> 00:26:25,130
The area over Delplanque squared is as one cubitt sorry, one cubic per for Planck areas for the arisan.
270
00:26:25,130 --> 00:26:28,640
So here is the event rising, divided up in little things.
271
00:26:28,640 --> 00:26:37,700
And there's a cubit, you know, either zero one basically on average, one for every two or four triangles or Planck areas here.
272
00:26:37,700 --> 00:26:46,460
So this is a very, very rich and complicated system, has an enormous number of cubits.
273
00:26:46,460 --> 00:26:51,710
Let me tell you about that. Well, the entropy if you put in this formula for a solar mass black hole,
274
00:26:51,710 --> 00:26:59,060
you find the entropy is a vote would attend to the 77 times the mass of the black hole over M Solar Square.
275
00:26:59,060 --> 00:27:08,210
That means the entropy of a single solar mass black hole is roughly equal to that of the entropy of all the stars in the entire universe.
276
00:27:08,210 --> 00:27:13,130
In fact, because these guys like mass squared and we know there exist supermassive black holes,
277
00:27:13,130 --> 00:27:21,860
the entropy of a super a single supermassive black hole exceeds the entropy of everything else in the universe.
278
00:27:21,860 --> 00:27:24,980
So that's an extraordinary statement.
279
00:27:24,980 --> 00:27:31,970
Another way of thinking about this very large entropy is quantum black holes of thermal systems with a huge number of microstates member.
280
00:27:31,970 --> 00:27:36,380
If we take member Boltzmann's famous Formula S is.
281
00:27:36,380 --> 00:27:41,600
Well, let's forget in place of constant Essy was log W with W's number of microstates.
282
00:27:41,600 --> 00:27:46,610
The system, which says high then exponentially therefore misses a number of states,
283
00:27:46,610 --> 00:27:52,070
is approximately exponential of this century and this century is already huge.
284
00:27:52,070 --> 00:27:58,580
So the number of states of a black hole, a low lying state, so black hole is incredibly large.
285
00:27:58,580 --> 00:28:05,180
It's bigger than Google, vastly bigger than a Google.
286
00:28:05,180 --> 00:28:12,470
So this has some comments. Well, the information content of the universe appears to be hugely dominated by black holes.
287
00:28:12,470 --> 00:28:18,890
That's a remarkable statement. We don't understand well, these microstates of black holes, exactly what these microstates are.
288
00:28:18,890 --> 00:28:24,650
There's some progress in string theory, but aren't sending is certainly not complete.
289
00:28:24,650 --> 00:28:28,850
Very interesting. Late this Entropia respected site hawking entropy or the black hole.
290
00:28:28,850 --> 00:28:34,400
Entropy is not extensive. It goes with area, not volume.
291
00:28:34,400 --> 00:28:37,700
It doesn't go with mass either. Goes like mass squared because it area.
292
00:28:37,700 --> 00:28:43,820
This leads the idea of the holographic principle which motivates mouther signer's actually
293
00:28:43,820 --> 00:28:50,630
very specific and concrete thing called A.D.s CFT duality for certain space times.
294
00:28:50,630 --> 00:28:58,310
So this holographic principle says basically that the infinite information content of a region goes like the area,
295
00:28:58,310 --> 00:29:06,830
the bounds the region rather than the region itself. So there's far less degrees of freedom than you might think in in a theory.
296
00:29:06,830 --> 00:29:10,760
This is an incredibly rich area that deserves an entire morning in itself.
297
00:29:10,760 --> 00:29:15,230
I don't have a size that we understand holography reasonably well, inequitably curved space time.
298
00:29:15,230 --> 00:29:21,790
We don't understand Flatt's white space a lot graphy currently.
299
00:29:21,790 --> 00:29:28,640
So that's already something remark. We got out of black holes. But let me turn to some other implications for creation.
300
00:29:28,640 --> 00:29:35,150
Well, since hawking temperature increases and decreases black holes and explosively evaporate
301
00:29:35,150 --> 00:29:39,800
by runaway hawking radiation and the end temperature of hawking evaporation,
302
00:29:39,800 --> 00:29:44,870
a black hole is almost planking is incredibly high temperature.
303
00:29:44,870 --> 00:29:48,650
So this means that hawking reparation is quite extraordinary.
304
00:29:48,650 --> 00:29:53,630
Every particle in nature with mass less than implant overwrite pi.
305
00:29:53,630 --> 00:29:59,990
So that's about 10 to the 18 G.V. can be produced even if it's completely decoupled from the standard model.
306
00:29:59,990 --> 00:30:03,770
And the reason is nothing. Hisam gravity. This is not using evaporation.
307
00:30:03,770 --> 00:30:09,020
Occupation doesn't depend upon a particle being charged or colour charge or anything like that.
308
00:30:09,020 --> 00:30:11,750
Having company Salmo nothing hisam gravity.
309
00:30:11,750 --> 00:30:18,450
Therefore Hawking evaporation is a scan over all of creation, even things that are hidden from the standard model.
310
00:30:18,450 --> 00:30:24,700
So this way you can produce, for instance, dark matter or even start a hot phase of the big bang.
311
00:30:24,700 --> 00:30:27,600
And so I've been investigating these issues with my students.
312
00:30:27,600 --> 00:30:33,570
These are three of my very good graduate students here at Oxford and Olivier Rudan and Hannah.
313
00:30:33,570 --> 00:30:36,820
Two of them, I think, are in some of the breakout sessions. We have to talk, too.
314
00:30:36,820 --> 00:30:45,390
So this leads to what could be observable signatures and hawking radiation, hiding in dark matter and in gravitational waves.
315
00:30:45,390 --> 00:30:51,260
Adam, very sadly and of course, whole Steven himself.
316
00:30:51,260 --> 00:30:59,080
We've got see this. But if we'd seen Hawking radiation, he would have been able to win his very well-deserved Nobel prise.
317
00:30:59,080 --> 00:31:07,650
So this is quite incredible. Why was Ms. I'm surprised. Yes, there's this possible observable signatures hawking radiation, but there's more.
318
00:31:07,650 --> 00:31:15,860
Right. Adam, coking evaporation applies a remarkable consequence that many for the theory, including gravity,
319
00:31:15,860 --> 00:31:21,770
there are non spies and non spacetime global symmetries or with violated this approximate at best.
320
00:31:21,770 --> 00:31:24,290
So let me just quickly describe this mean what this means.
321
00:31:24,290 --> 00:31:30,080
This means you can't have exactly to generate physically distinct states without him such internal symmetries.
322
00:31:30,080 --> 00:31:34,190
You can't have an exact quote. Zack Clay. Every potential surface.
323
00:31:34,190 --> 00:31:44,450
Let me just explain why this is true. Well, we know Emmi Novia taught us that if you have a symmetry, you have global challenges.
324
00:31:44,450 --> 00:31:49,910
So if you if you slightly violate this symmetry, that means the global charges are not conserved.
325
00:31:49,910 --> 00:31:55,040
So one example of this would be the non conservation of barrier number, for instance,
326
00:31:55,040 --> 00:32:00,140
snapping not normal Yousafzai Baren number with some you won global symmetry with this must be violated.
327
00:32:00,140 --> 00:32:09,470
So here's the argument of why it's true. Go back to Zelda, which so imagine you start forming a black out of a large initial number of neutrons.
328
00:32:09,470 --> 00:32:12,680
So you crush these neutrons to form a black hole,
329
00:32:12,680 --> 00:32:20,930
but then it hawking evaporates and is hawking radiation is independent of whether your initial state is a barrier on the balance or anti baryonic.
330
00:32:20,930 --> 00:32:26,060
It only cares about the mass spin in charge of these states, not whether they're baren anti barium.
331
00:32:26,060 --> 00:32:33,140
So at most the final state has plus or minus root end of of Barry on charge here.
332
00:32:33,140 --> 00:32:37,340
The blue there's one, the three blue and one reds is one net state.
333
00:32:37,340 --> 00:32:42,530
Here we started out with a lot. So you lose Barry a number in this process.
334
00:32:42,530 --> 00:32:47,450
So global symmetries are violated by hawking evaporation.
335
00:32:47,450 --> 00:32:50,810
Now, there's a we don't extend exactly how this works.
336
00:32:50,810 --> 00:32:55,490
And for generations in particular, we don't sign a form and summarise the global symmetry value interactions.
337
00:32:55,490 --> 00:32:59,150
But there's progress, again, by by groups involving me,
338
00:32:59,150 --> 00:33:03,200
but other people as well around the world and progress, recent progress being made on this issue.
339
00:33:03,200 --> 00:33:07,460
That's interesting. So I'm almost done. Let me make a few final words.
340
00:33:07,460 --> 00:33:14,090
So one issue I haven't spoken about is if quantum mechanics and black holes are, in fact inconsistent with each other.
341
00:33:14,090 --> 00:33:21,140
And this was the view of Stephen Hawking himself for many years, though I would say not for the last five years, his life might still be Roger.
342
00:33:21,140 --> 00:33:25,190
Roger Penrose is you. So what is the reason for this?
343
00:33:25,190 --> 00:33:32,960
Well, hawking evaporation of black holes appears to allow for quantum mechanical, pure states to evolve to mixed states.
344
00:33:32,960 --> 00:33:39,580
If so, this would be of would violate a fundamental axiom of quantum mechanics and imply information loss.
345
00:33:39,580 --> 00:33:47,480
But in the last two years, there's been major progress on this issue and a consistent calculational framework is now emerging.
346
00:33:47,480 --> 00:33:56,900
So there's a whole bunch of papers from people for the Institute of Arts today, from Stanford, from M.I.T., from other places as well.
347
00:33:56,900 --> 00:34:02,780
And what is their basic idea? Notice that some very exciting things here, replica wormholes in the black hole interior.
348
00:34:02,780 --> 00:34:06,920
This is trying to understand in a real way what is the physics of the interior?
349
00:34:06,920 --> 00:34:12,170
What observers who fall through the arisan would sees is crucial in understanding these issues.
350
00:34:12,170 --> 00:34:18,080
And you're having some very interesting things like wormholes appear, other kinds of solutions possibly to Einstein's equations.
351
00:34:18,080 --> 00:34:28,180
So the basic idea, and this is true for experts, is that Hawking's calculation of this thermal effect is thermal density matrix was never exact.
352
00:34:28,180 --> 00:34:32,280
In fact, we always knew that it had his calculation had loop effects there.
353
00:34:32,280 --> 00:34:39,710
But in fact, the paradox was, is all these local quantum field theory loop corrections don't help solve the paradox.
354
00:34:39,710 --> 00:34:48,030
It turns out you can show. But now it's been realised. There are new tiny non perturb two effects, which are Suckley non-local.
355
00:34:48,030 --> 00:34:54,860
All right. And that's the crucial thing. They're very tiny. They go like E to the minus area, the black hole over Delplanque Square.
356
00:34:54,860 --> 00:34:56,510
They're incredibly tiny.
357
00:34:56,510 --> 00:35:03,620
So you may say, how can these incredibly tiny effects make a difference and somehow change mixed states, what looks like a mixed state or pure state?
358
00:35:03,620 --> 00:35:07,600
And the answer is, if you compute the radiation, the entropy of the radiation is coming out.
359
00:35:07,600 --> 00:35:13,640
So some other states of the eigenvalues of this density matrix and these eigenvalues
360
00:35:13,640 --> 00:35:17,810
now shifted by exponentially small amounts because of these tiny corrections.
361
00:35:17,810 --> 00:35:20,890
But there's an exponentially large number of states here.
362
00:35:20,890 --> 00:35:26,240
Remember, emphasised before that the black hole was an he let excellent large number of states.
363
00:35:26,240 --> 00:35:32,540
So there's exponentially larger number of terms times, exponentially small corrections to each one of these terms.
364
00:35:32,540 --> 00:35:41,180
And this can lead to an order, one modification. And in fact, there are demonstrations in simple cases that this purifies the final radiation.
365
00:35:41,180 --> 00:35:49,110
So leads to pure state to pure state evolution, meaning that quantum mechanics is consistent with black holes.
366
00:35:49,110 --> 00:35:56,410
So I want to finish there with a statement, the quantum mechanics, black holes is even more remarkable than you might have thought.
367
00:35:56,410 --> 00:36:01,440
He's guiding us towards a better understanding of quantum gravity, and I emphasise information as well.
368
00:36:01,440 --> 00:36:05,490
And so I think is very good reason to believe that black holes are quantum black holes.
369
00:36:05,490 --> 00:36:09,600
And think about the hypernatremia 21st century. So I'll stop there.
370
00:36:09,600 --> 00:36:15,373
Thank you.
00:00:05,150 --> 00:00:12,160
Well, nice to meet you, folks. If only you actually said I wouldn't tell you about classical in quantum black holes.
2
00:00:12,160 --> 00:00:17,180
It's an incredibly exciting subject. And so let me get started.
3
00:00:17,180 --> 00:00:23,780
So black holes. Of course, one of the most awe inspiring objects in the universe.
4
00:00:23,780 --> 00:00:30,230
They imply the end of spacetime as we know it. And also appear to imply deep paradoxes.
5
00:00:30,230 --> 00:00:37,970
When we try to meld quantum mechanics with gravitation in particular, it's by context.
6
00:00:37,970 --> 00:00:45,890
And as I said, there's actually, in fact, been significant progress, both observational and theoretical, in black hole physics in the past four years.
7
00:00:45,890 --> 00:00:47,840
I want to tell you about these exciting developments.
8
00:00:47,840 --> 00:00:54,920
And my message is going to be that the black holes should be thought of as like the hydrogen atom, the 21st century.
9
00:00:54,920 --> 00:01:00,880
By studying this particular system, I think we can learn a great deal about what quantum gravity is.
10
00:01:00,880 --> 00:01:10,140
And in fact, about other subjects, too. For instance, information theory and how it very surprisingly might connect with gravity.
11
00:01:10,140 --> 00:01:14,730
So let me get started. So let me tell you a little bit about classical black holes.
12
00:01:14,730 --> 00:01:20,040
So we now know that astrophysical black holes exist and behave to a very good
13
00:01:20,040 --> 00:01:24,850
approximation the way that Einstein classical generals who he said they should.
14
00:01:24,850 --> 00:01:30,930
And at least the exterior, we should emphasise that we only have information about the exterior of.
15
00:01:30,930 --> 00:01:39,390
So Carswell Schwarzschild in 1915 was the first person who wrote down actually immediately after Einstein's general theory relativity appeared,
16
00:01:39,390 --> 00:01:46,020
he wrote, and the first solution and the solution, in fact, was the black hole solution.
17
00:01:46,020 --> 00:01:54,930
Sadly, while fighting and dying were war one. And so his solution has a property that has an event horizon, a black hole event horizon,
18
00:01:54,930 --> 00:01:58,270
not that they realised really was property at the time, but it's there.
19
00:01:58,270 --> 00:02:03,370
And his solution and a crucial aspect of what I will tell you about later.
20
00:02:03,370 --> 00:02:08,970
And I hope you can see my point here is that the size of the black hole, the short shield radius,
21
00:02:08,970 --> 00:02:16,550
the radius of event horizon is twice Newton's constant times the black hole mass oversea square.
22
00:02:16,550 --> 00:02:20,680
OK, so this property. So I want you to remember that the short, short rate is the size.
23
00:02:20,680 --> 00:02:25,880
The event horizon goes linearly with a black hole mass.
24
00:02:25,880 --> 00:02:31,970
And so to give you an idea about what this says, Schwarzschild radius is for various objects for a solar mass,
25
00:02:31,970 --> 00:02:36,980
black hole, short radius is just under three kilometres.
26
00:02:36,980 --> 00:02:50,400
So if he crushed adiabatic lee the sun down to two point nine two kilometres, it would go inside its event horizon and form a black hole.
27
00:02:50,400 --> 00:02:58,410
Instantly, if we maintained a constant distance from the sun, so we stay here on the earth, our current distance away from the sun,
28
00:02:58,410 --> 00:03:04,950
and we did this idea that it crash crushing the force of gravity here on earth that we feel from the sun wouldn't change.
29
00:03:04,950 --> 00:03:09,450
It's not like suddenly the black hole will strength. It causes gravity to come much stronger.
30
00:03:09,450 --> 00:03:14,550
The reason why the strength of gravity is so much stronger at the black hole event horizon is just
31
00:03:14,550 --> 00:03:23,460
because we concentrated a tremendous amount of mass and energy in a very tiny volume indeed.
32
00:03:23,460 --> 00:03:26,400
And it's because we can approach much more closely.
33
00:03:26,400 --> 00:03:30,660
So, of course, usually when we go to the sun, you're going to get close to the sun as the surface of the sun.
34
00:03:30,660 --> 00:03:37,160
But here we crush it down to three kilometres. And that's the reason why the gravitational affective of a black hole is much larger.
35
00:03:37,160 --> 00:03:42,720
It's because we are concentrating it so much. So anyway, that was a solar mass black hole.
36
00:03:42,720 --> 00:03:48,210
We also know there exist supermassive black holes in the centre of almost all galaxies.
37
00:03:48,210 --> 00:03:52,640
And these have masses somewhere between the range of ten to the six to 10 to the nine solar masses.
38
00:03:52,640 --> 00:03:57,030
And therefore, correspondingly, they have a size which is quite large.
39
00:03:57,030 --> 00:04:01,660
They have sizes which have older tend to the six to 10 to the nine kilometres.
40
00:04:01,660 --> 00:04:10,500
And so, for instance, if you fell in into a galactic centre, supermassive black hole, you don't immediately die as you cross the event horizon.
41
00:04:10,500 --> 00:04:13,380
Actually, you don't notice anything particular happening to you.
42
00:04:13,380 --> 00:04:18,000
In fact, it takes you quite a few minutes until you reach the singularity and finally die.
43
00:04:18,000 --> 00:04:22,110
So you can live. So an observer, according to our current theories,
44
00:04:22,110 --> 00:04:27,660
understanding black holes can live for quite a long time inside a black hole and could make measurements.
45
00:04:27,660 --> 00:04:31,240
So it's interesting question to ask. What would such an observer see?
46
00:04:31,240 --> 00:04:36,400
And maybe we can discuss that later on in the question, not secessions.
47
00:04:36,400 --> 00:04:40,270
We can also consider a hypothetical Blackhall investment earth mass,
48
00:04:40,270 --> 00:04:43,780
and if you crush us into a black hole, it would have size just under one centimetre.
49
00:04:43,780 --> 00:04:53,190
So this gives you an idea of the sizes of some possible black holes actually physically realised and possible hypothetical ones.
50
00:04:53,190 --> 00:04:58,020
So what does the solution look like in equations? Well, we're talking about General Hibito.
51
00:04:58,020 --> 00:05:02,400
You have to talk about the spacetime distances. Nature, geometry.
52
00:05:02,400 --> 00:05:07,050
So here we have the S squared is a spacetime distance between events.
53
00:05:07,050 --> 00:05:14,610
And this is given by this expression involves four coordinates. Two of them are just the normal angular corners D, Theta, Theta and Phi.
54
00:05:14,610 --> 00:05:23,900
And this is just saying that everywhere there's a normal one. Spherical behaviour circle, symmetry, behaviour of the system where.
55
00:05:23,900 --> 00:05:27,520
That's the area of a given sphere is four pi R-squared.
56
00:05:27,520 --> 00:05:36,780
So this is this here. But now we have this issue here where we have this second term here gives you the fact that as you approach she horizon,
57
00:05:36,780 --> 00:05:44,670
this denominator here is going to zero. So this factor here, there's an infinity that's appearing here at Times Square.
58
00:05:44,670 --> 00:05:49,940
And this is telling you you get radial length contraction as the Iraq horizon is approach.
59
00:05:49,940 --> 00:05:58,310
The other hand, this first term here, this factor, this is also going to zero as you approach to RSS, I guess you go to we will see Horizon.
60
00:05:58,310 --> 00:06:04,280
This is saying that according to a static external observer, right far away from the black hole,
61
00:06:04,280 --> 00:06:10,000
that as time dilation, as the horizon at a shorter radius of approach.
62
00:06:10,000 --> 00:06:14,540
Right. So so there's both time dilation and radial length contraction.
63
00:06:14,540 --> 00:06:20,440
Mr. Secretary. Well, that's in equations. And of course, you can study this.
64
00:06:20,440 --> 00:06:27,680
Great, Lena. I want to emphasise that the more longstanding of classical black holes is due to record a number of people.
65
00:06:27,680 --> 00:06:30,650
Wheeler, who coined the name Black Holes,
66
00:06:30,650 --> 00:06:38,340
which will see libraries as somewhat inappropriate name and thanks Kruskal occur Thone Hawking and especially our own Roger Penrose.
67
00:06:38,340 --> 00:06:44,270
And I think Roger made the greatest contributions to modern sounding of classical my calls.
68
00:06:44,270 --> 00:06:49,730
So what are these awe inspiring objects look like? Well, here they are.
69
00:06:49,730 --> 00:06:54,770
Here's a lovely little Etsy baby black hole. You can purchase for the low, low price of just 10 pounds.
70
00:06:54,770 --> 00:07:01,040
Here's a baby black hole accretion disc for astrophysical black holes have accretion discs.
71
00:07:01,040 --> 00:07:08,210
You can get these things with adoption certificates. That's lovely. Here is a different picture of what a black hole looks like.
72
00:07:08,210 --> 00:07:15,050
We can take this geometry. And of course, it's very hard for me to represent the geometry of this situation in two dimensions.
73
00:07:15,050 --> 00:07:19,640
But let me try. So this is a picture of radius and time.
74
00:07:19,640 --> 00:07:24,370
He? S each of these points you should think of as a particular four dimensional thing,
75
00:07:24,370 --> 00:07:29,060
as a as a two sphere sort of living about every one of these things.
76
00:07:29,060 --> 00:07:35,060
And what I want, I emphasise is as this is the exterior. This white region is the exterior geometry of the black hole.
77
00:07:35,060 --> 00:07:37,230
And then we have this horizon.
78
00:07:37,230 --> 00:07:47,270
And the crucial thing is as you go inside your eyes and in fact, Space-Time itself is not really static inside the horizon.
79
00:07:47,270 --> 00:07:53,980
The reason is, is because you don't get a hint of this from this thing as you go are is less than our.
80
00:07:53,980 --> 00:07:59,180
Notice that this term here changes sign. And this thing here changes sign.
81
00:07:59,180 --> 00:08:06,710
So that means now there is an overall negative sign in front of the R-squared and there is no real positive sign in front of the D.T. squared.
82
00:08:06,710 --> 00:08:12,170
And that means this now becomes a spatial like coordinate. And this is the temporal called note here.
83
00:08:12,170 --> 00:08:17,730
So, in fact, there's a definite different a Kornet system where you see this having better.
84
00:08:17,730 --> 00:08:24,460
But you get a hint about what's going on here. And the idea is that, in fact, the radio corner becomes a temporal coordinate.
85
00:08:24,460 --> 00:08:32,730
So, in fact, as you're going on with this thing, in fact, space time itself is dynamical here.
86
00:08:32,730 --> 00:08:36,900
And is dragging you towards the singularity as you go down.
87
00:08:36,900 --> 00:08:47,370
So as you see this picture being animated here. Well, as I emphasised before passing the horizon, nothing special happens to you.
88
00:08:47,370 --> 00:08:50,810
There's no infinite forces. You don't necessarily get ripped apart.
89
00:08:50,810 --> 00:08:58,680
The horizon of freely falling observer just thinks the horizon is very much like empty Minkowski space.
90
00:08:58,680 --> 00:09:07,590
In fact, the only place where something truly singular and terrible happens to you is here, right at the singularity are equal zero in these corners.
91
00:09:07,590 --> 00:09:13,050
But we should be wary about this because in fact, the classical solution.
92
00:09:13,050 --> 00:09:17,820
And in fact, Einstein's classical generals, hefty itself is not reliable here.
93
00:09:17,820 --> 00:09:25,830
So I want to emphasise to you that you that even though the singularity is predicted by classical general relativity,
94
00:09:25,830 --> 00:09:30,150
we know the theory is not really self-consistent here.
95
00:09:30,150 --> 00:09:35,070
So we believe that itself consistently describes exterior geometry and near the horizon.
96
00:09:35,070 --> 00:09:40,040
But once we start approaching the singularity, we don't know what that physics is.
97
00:09:40,040 --> 00:09:48,660
So, of course, the subject of active research I'm trying to understand. So here's another picture of what a black hole looks like.
98
00:09:48,660 --> 00:09:53,280
And so here we have radius again. So here is a star collapsing to form a black hole.
99
00:09:53,280 --> 00:09:59,410
And here we have an event horizon forming. And so the crucial thing about the event horizon is here.
100
00:09:59,410 --> 00:10:03,120
Here is drawn are light cones. So this.
101
00:10:03,120 --> 00:10:13,140
So what happens is light rise, quote unquote, ingoing or outgoing light rays have to be there on the edge of this light cone here.
102
00:10:13,140 --> 00:10:17,190
And material objects, massive objects always travel less than the speed of light.
103
00:10:17,190 --> 00:10:23,880
So I always have to travel with inside the light cone. So signals can only be sent in in these angles here.
104
00:10:23,880 --> 00:10:28,010
So this one here is ingoing light. Right. And would go into the.
105
00:10:28,010 --> 00:10:33,500
We go back into the black hole. But this one here would escape to infinity.
106
00:10:33,500 --> 00:10:37,580
But there's this distortion of space time in the black hole background.
107
00:10:37,580 --> 00:10:39,710
And what happens is the light cones tip over.
108
00:10:39,710 --> 00:10:48,920
So once you go to the event horizon, now you see right at the event horizon, the outgoing light rays actually go right along the horizon.
109
00:10:48,920 --> 00:10:53,360
All material objects inevitably go get dragged into the singularity.
110
00:10:53,360 --> 00:10:58,010
That's the only possibility. And ingoing light rays, of course, go very quickly.
111
00:10:58,010 --> 00:11:06,860
So it's this tipping over the light cones force you to go to the singularity is another way of saying that inside the event horizon,
112
00:11:06,860 --> 00:11:11,190
forward in time becomes radially inward.
113
00:11:11,190 --> 00:11:13,570
All right. So that's the thing.
114
00:11:13,570 --> 00:11:19,600
But there's another thing here, which is, again, a freely falling observer, a freely falling observer going through this system.
115
00:11:19,600 --> 00:11:26,410
I mean, we'll go through the rent rising, hit the singularity. But nothing special happens is really falling observer.
116
00:11:26,410 --> 00:11:31,750
She through force, through the horizon. It's just the usual finite tidal forces.
117
00:11:31,750 --> 00:11:35,780
You always get when you're in the external gravitational fields.
118
00:11:35,780 --> 00:11:39,520
All right. So there will be tidal forces on this person who is a tiny black hole.
119
00:11:39,520 --> 00:11:45,220
These tidal forces might be strong enough to rip the person apart, spike spaghetti for her.
120
00:11:45,220 --> 00:11:52,360
But otherwise, it's a large black hole like a galactic centre, black hole falling through horizon of such an object gain.
121
00:11:52,360 --> 00:11:56,950
Nothing special happens in the observable survive. A human would survive.
122
00:11:56,950 --> 00:12:01,960
And only when you finally get to the singularity, which should be destroyed.
123
00:12:01,960 --> 00:12:06,400
And so I emphasise, if we go back to the metric,
124
00:12:06,400 --> 00:12:12,040
it looked like there was apparently singular behaviour in this metric near our equals, our s, and that's why.
125
00:12:12,040 --> 00:12:21,190
And in fact, took roughly 45 years or so before people took black hole solutions seriously, they thought.
126
00:12:21,190 --> 00:12:26,350
In fact, this wasn't sensible. This only could be used as if it was a mathematical artefact.
127
00:12:26,350 --> 00:12:34,330
But later on, it was realised. In fact, there's nothing singular about this solution apart from right at the Singularity Arkos zero.
128
00:12:34,330 --> 00:12:38,260
In fact, this apparent singular behaviour, the short geometric, is just a natural supporters.
129
00:12:38,260 --> 00:12:43,750
It's like longitude. If you're at the north and south poles, it's a corner that breaks down.
130
00:12:43,750 --> 00:12:50,000
It's not truly physics breaks down at the event horizon. So that was that.
131
00:12:50,000 --> 00:13:00,760
Now. We now know to a very, very high degree of confidence that supermassive astroparticle black holes exist in galactic centres of most galaxies.
132
00:13:00,760 --> 00:13:05,860
And so here is a little movie, which I hope now plays.
133
00:13:05,860 --> 00:13:13,590
So this is pointing towards our galactic centre and it's starting over a whole bunch of years, the motion of the stars.
134
00:13:13,590 --> 00:13:17,140
And what you see here is a right at the galactic centre.
135
00:13:17,140 --> 00:13:26,050
This is a tiny distance, 10 light days that the stars are orbiting around a very massive, very centrally concentrated object.
136
00:13:26,050 --> 00:13:32,670
In fact, there was a Nobel prise shared with Roger Penrose this year in 2020,
137
00:13:32,670 --> 00:13:37,210
where these two teams, led by these two investigators, independently show.
138
00:13:37,210 --> 00:13:41,590
By measuring the trajectories of these seven stars. Right. Close to the likely centre.
139
00:13:41,590 --> 00:13:43,470
They're not they're not perfectly on ellipses.
140
00:13:43,470 --> 00:13:50,450
In fact, there are general relativistic effects exactly of the kind predicted by General 50 in the background of a black hole.
141
00:13:50,450 --> 00:13:54,520
The slight distorting these lipsett. So this is a confirmation.
142
00:13:54,520 --> 00:14:01,940
You have a supermassive black hole with a guy with a very high degree of confidence at our collective centre.
143
00:14:01,940 --> 00:14:07,880
So recently we have a direct image of a supermassive black hole, not in our galaxy fate in M80 seven.
144
00:14:07,880 --> 00:14:13,220
This is from the Event Horizon Telescope in 2019. And here is the shadow, the event horizon.
145
00:14:13,220 --> 00:14:19,280
And here is the accretion disk. So just like that little Etsy toy you can buy here.
146
00:14:19,280 --> 00:14:26,870
What the light is coming from the accretion disk is the black hole. And here is the shadow of the event horizon.
147
00:14:26,870 --> 00:14:33,770
So we now know there's a whole range of black holes. And in fact, we have another way of looking at black holes, not just visibly,
148
00:14:33,770 --> 00:14:40,700
but we also now here in the sense the sound of black holes merging through gravitational waves.
149
00:14:40,700 --> 00:14:45,420
So, again, I hope you can just click on this thing. Sometimes it's worth.
150
00:14:45,420 --> 00:14:50,040
Do you hear that sound, doesn't hear the sound? I hope so.
151
00:14:50,040 --> 00:14:54,030
It's so that is the sound. It was picked up in the gravitational wave detectors,
152
00:14:54,030 --> 00:15:00,540
the advanced liger collaboration that they have two sell at Hanford and Livingston in the United States.
153
00:15:00,540 --> 00:15:08,340
And this is the sound, the final chirp as the two black holes, two very supermassive black hole, actually, not supermassive.
154
00:15:08,340 --> 00:15:16,380
Very massive. Multiple solar masses are rotating together and finally colliding and they merge.
155
00:15:16,380 --> 00:15:19,200
And during that final seconds there,
156
00:15:19,200 --> 00:15:25,260
the energy released in gravitational waves far exceeds the energy produced by all the suns in all the galaxies in the universe.
157
00:15:25,260 --> 00:15:34,110
It's an extraordinary three or four solar masses worth of mass are being converted to energy, almost alling and gravitational waves.
158
00:15:34,110 --> 00:15:39,240
And so now we've seen dozens, actually hundreds of black hole mergers.
159
00:15:39,240 --> 00:15:43,710
And so this is merger tree of how black holes of urging, merging and evolving.
160
00:15:43,710 --> 00:15:45,060
And of course, it's nice. Let's see thing.
161
00:15:45,060 --> 00:15:52,800
And the nice thing about this is let's see cartoon you see here is, in fact, it shows these two black holes will be rotating around to each other.
162
00:15:52,800 --> 00:15:58,710
The final black hole produces a highly spinning black hole. So it's not a short, tall black hole, but the astroparticle black holes.
163
00:15:58,710 --> 00:16:06,010
We have a highly rotating just for simplicity in this Coke. I'm going to focus just on short term black holes, non rotating black holes.
164
00:16:06,010 --> 00:16:13,980
Okay. So the summary is, is we know there's a wide variety of black holes exist in our universe.
165
00:16:13,980 --> 00:16:19,740
And they're very well described by Einstein's by this virtual solution or the curse solution.
166
00:16:19,740 --> 00:16:25,530
It's generalised the rotating generalisation in external region.
167
00:16:25,530 --> 00:16:29,070
So my interest, though, is quantum black holes.
168
00:16:29,070 --> 00:16:34,440
That's what I want to tell you about. So the classical theory of black holes is extraordinarily rich.
169
00:16:34,440 --> 00:16:45,720
But the world is really quantum mechanical. And so we need to study what the behaviour of quantum mechanics, what a quantum behaviour, black holes is.
170
00:16:45,720 --> 00:16:50,430
And what we are going to find is even more remarkable in the classical case.
171
00:16:50,430 --> 00:17:01,750
And it apparently leads to deep paradoxes and these deep, dark paradoxes, rather like the birth of the early history of quantum mechanics itself.
172
00:17:01,750 --> 00:17:05,520
The thinking about these paradoxes and understanding how they're resolved is
173
00:17:05,520 --> 00:17:10,450
guiding us towards a much better understanding of aspects of quantum gravity.
174
00:17:10,450 --> 00:17:16,630
So I would emphasise it's been significant progress in the last years, and I will tell you a little bit about what the significant progress is.
175
00:17:16,630 --> 00:17:27,450
All right. Next slide. So the first thing to realise is the most basic quantum facts about a black hole is hawking radiation.
176
00:17:27,450 --> 00:17:32,600
So let me tell you about why what hawking radiation is and why it exists.
177
00:17:32,600 --> 00:17:38,520
So in relativistic quantum mechanics, sometimes we call quantum field theory empty space, quote unquote.
178
00:17:38,520 --> 00:17:43,080
The vacuum is full of quantum fluctuations of all fields and particles.
179
00:17:43,080 --> 00:17:52,020
So it's not a static. You shouldn't really think it is an empty thing. So here is actually a precision numerical evaluation of the vacuum of QC day.
180
00:17:52,020 --> 00:17:57,420
This is on a five Fermi cubed lattice.
181
00:17:57,420 --> 00:18:04,680
And this is a a time loop of it. And here we just have one realisation show we spoke to Super posed a different
182
00:18:04,680 --> 00:18:08,350
quantum superposition and we have different positions of what the vacuum is doing.
183
00:18:08,350 --> 00:18:12,870
This is one realisation. And you see this thing is fluctuating like crazy.
184
00:18:12,870 --> 00:18:15,180
We're getting fluctuations of scales that you see.
185
00:18:15,180 --> 00:18:23,030
There's a typical sort of scale here that set by the scale of QCT, its self, which is Voda itself about one Fermi.
186
00:18:23,030 --> 00:18:27,720
Right. Or 200. I mean, the Lambda QCT. So.
187
00:18:27,720 --> 00:18:32,590
And instantly this is verified, these cutey deep precision calculations.
188
00:18:32,590 --> 00:18:38,580
And now give you quite accurate description of the low lying masons and baritones and various other states, other properties.
189
00:18:38,580 --> 00:18:44,720
We know this is true. We know quantum motivations are there for many reasons. This is one demonstration.
190
00:18:44,720 --> 00:18:51,260
So what about hawking radiation? Well, so here we have space time and here's a black hole.
191
00:18:51,260 --> 00:18:58,170
And as I emphasised, at least near the horizon, it's just like empty Minkowski space.
192
00:18:58,170 --> 00:19:02,550
So we have these positive and negative energy, virtual particle fluctuations happening everywhere.
193
00:19:02,550 --> 00:19:08,790
We have them happening outside the black hole. We have them happening certainly in the region anterior to the black hole.
194
00:19:08,790 --> 00:19:11,500
As long as we're not very close to the singularity, we don't know what's going on.
195
00:19:11,500 --> 00:19:18,710
Singularity, but certainly in the region around the horizon, we have these virtual particle fluctuations.
196
00:19:18,710 --> 00:19:25,740
I won't ever size the particles antiparticles here, but is the crucial thing is whether they're positive or negative energy overall.
197
00:19:25,740 --> 00:19:31,370
These things have zero energy. All right. And there is a correlation between their energies such.
198
00:19:31,370 --> 00:19:36,290
They start off in the vacuum, go back to the vacuum, constantly doing this.
199
00:19:36,290 --> 00:19:42,560
Well, if you have one of these fluctuations in the vicinity of the rise in the black hole,
200
00:19:42,560 --> 00:19:52,280
there's a quantum mechanical tunnelling process that allows the positive energy guy here in red, which could be a particle or an antiparticle.
201
00:19:52,280 --> 00:19:57,620
So I don't know, you'd get confused. It's not always that particles come out of the black and antiparticles go in.
202
00:19:57,620 --> 00:20:03,440
It can be either particles or antiparticles can escape. The crucial thing is whether they're positive energy or not.
203
00:20:03,440 --> 00:20:15,080
So rarely is tunnelling process allows a positive energy particle or antiparticle to a state to infinity while its negative energy sibling.
204
00:20:15,080 --> 00:20:21,980
And this is negative energy from the perspective of some distant observer particle or antiparticle is captured by the black hole.
205
00:20:21,980 --> 00:20:27,440
And therefore, because it's negative, energy reduces the black hole mass. So the end effect of this is the black hole.
206
00:20:27,440 --> 00:20:33,540
Mass has gone down slightly and its energy has been radiated away to infinity a little bit.
207
00:20:33,540 --> 00:20:39,190
And I like to experts here, this is sort of sometimes given as an intuitive picture of hawking radiation,
208
00:20:39,190 --> 00:20:42,420
that this tunnelling picture of organisation can be made precise.
209
00:20:42,420 --> 00:20:49,340
And he has an interesting advantage over Hawking's original calculation that actually explicitly shows the black hole mass is reducing.
210
00:20:49,340 --> 00:20:55,610
In fact, in Hawking's calculation on deficit of it maybe is that it's on a static background where the
211
00:20:55,610 --> 00:20:59,540
black hole mass is not reducing these tunnelling way of thinking about hawking radiation. In fact,
212
00:20:59,540 --> 00:21:09,600
shows the black hole mass is being reduced and its it is being reduced by this sort of inflow of negative energy from the distant observers suspect.
213
00:21:09,600 --> 00:21:15,000
So the end result of this is physical black holes are never truly black.
214
00:21:15,000 --> 00:21:18,480
In fact, they produce thermal radiation, all climatically allowed modes.
215
00:21:18,480 --> 00:21:25,540
And here is a little cartoon. So I went inside dominantly for black holes. It would be gravitons, photons or maybe neutrinos.
216
00:21:25,540 --> 00:21:29,730
But in fact, in fact, all kinematics available modes are allowed. So amazing.
217
00:21:29,730 --> 00:21:30,770
End result is black.
218
00:21:30,770 --> 00:21:40,200
Was a thermal system with a temperature gain is seen by a far away static observer t hawking and the hawking temperature here it is goes like h bar.
219
00:21:40,200 --> 00:21:45,360
It's a quantum effect. C cubed over eight pi. Newton's constant.
220
00:21:45,360 --> 00:21:53,550
K Boltzmann. If we want normal temperature, normal kelvin units and then one over the massive black hole we put in for instance a massive black on KG.
221
00:21:53,550 --> 00:21:59,280
Imagine we had a kg sized black hole. That's a logically consistent thing to consider though.
222
00:21:59,280 --> 00:22:03,930
Hypothetical, and since we've never observed such a thing, it would actually have a very high temperature.
223
00:22:03,930 --> 00:22:10,380
Ten to twenty three, Kelvin. So it's not like this is a small temperature, at least if we have a small black hole.
224
00:22:10,380 --> 00:22:12,720
This is a very large temperature for a small black hole.
225
00:22:12,720 --> 00:22:17,780
On the other hand, because astrophysical black holes are so massive, solar mass for solar mass.
226
00:22:17,780 --> 00:22:26,710
My call. It's ten to the minus seven Kelvin. So that means that we're never going to observe, at least for astrophysical black holes.
227
00:22:26,710 --> 00:22:29,330
The Hawking temperature satellite.
228
00:22:29,330 --> 00:22:38,570
But if you start off with a black hole, let's say you start a full black hole, which is in between a kilogram and a solar mass.
229
00:22:38,570 --> 00:22:47,450
Well, it would start radiating energy. It was mass will work with we all juice and therefore its temperature will rise.
230
00:22:47,450 --> 00:22:53,510
And there's a runaway process here. So that's important to bear in mind.
231
00:22:53,510 --> 00:22:59,030
I want you to remember that for Lytro. So Blackhall Hawking radiation has never been observed.
232
00:22:59,030 --> 00:23:04,340
But we have a high degree of confidence. That's true. We now know many ways it could be theoretically derived.
233
00:23:04,340 --> 00:23:07,760
And it solves some otherwise troubling aspects of classical black hole physics.
234
00:23:07,760 --> 00:23:10,640
Let me tell you a little bit by one of these quite troubling aspects.
235
00:23:10,640 --> 00:23:16,670
So one of these is associated with a second law of thermodynamics, which, of course, is that the change in entropy,
236
00:23:16,670 --> 00:23:22,490
in a physical process should be greater than zero or equal reserve if it's reversible.
237
00:23:22,490 --> 00:23:30,560
So Fleckenstein argued that to say the second law one must sign and I want to emphasise is a finite end to black holes.
238
00:23:30,560 --> 00:23:40,580
Otherwise, one could systematically reduce the entropy of the universe by throwing in matter with entropy greater than zero, which then disappears.
239
00:23:40,580 --> 00:23:47,540
All right. And if you do not assign any entropy to the black hole, then you reduce systematically the entropy of the universe.
240
00:23:47,540 --> 00:23:52,550
By doing this process, by just quantity recycling this process, you could use it with universe.
241
00:23:52,550 --> 00:24:01,870
This is a pretty bad thing. So Berenstein suggested, in fact, that the entropy of a black hole is fine.
242
00:24:01,870 --> 00:24:04,010
Entropy should be proportional to the area.
243
00:24:04,010 --> 00:24:10,010
The black hole and Hawking's calculation of the temperature confirm this because the first laws were seven.
244
00:24:10,010 --> 00:24:13,460
Amik says d e equals temperature times D.
245
00:24:13,460 --> 00:24:18,620
S with the E is the change in the energy. The S is the change in the entropy.
246
00:24:18,620 --> 00:24:22,970
And we now have a formula for the temperature due to Hawking and we know the energy.
247
00:24:22,970 --> 00:24:30,050
Here is the massive black hole time C squared. And if you put this N, you put the formula in for your tea.
248
00:24:30,050 --> 00:24:34,400
Hawking arrived earlier and you put in what you just take the derivative.
249
00:24:34,400 --> 00:24:39,620
This thing, d.A. So it's just the M C squared. You can then find what the change of D.
250
00:24:39,620 --> 00:24:46,430
S is D. S and integrate that up. And what you find is you find this expression for the entropy of a black hole.
251
00:24:46,430 --> 00:24:51,200
It goes. This is called the either the black hole entropy or the Berenstein Hawking entropy.
252
00:24:51,200 --> 00:24:56,480
It goes like CS cubed on G Newton one over H bar.
253
00:24:56,480 --> 00:24:59,300
And then the area, the black hole on four.
254
00:24:59,300 --> 00:25:06,710
In fact, this combination of units here, this defines the planked length squared or the one over the Planck link squared.
255
00:25:06,710 --> 00:25:10,430
Another better way of writing this is one quarter of IE.
256
00:25:10,430 --> 00:25:15,710
The area of the black hole event horizon over the Planck Link Square.
257
00:25:15,710 --> 00:25:19,910
I want out I want you to notice this Planck length squared is Planck length is incredibly tiny,
258
00:25:19,910 --> 00:25:23,360
is approximately ten to the minus 33 centimetres and black.
259
00:25:23,360 --> 00:25:27,120
Oh, of course. Black hole of enterprises. Well, that macroscopic things there.
260
00:25:27,120 --> 00:25:31,340
You know, kilometres squared or much bigger banks.
261
00:25:31,340 --> 00:25:34,830
All right. Or much bigger for supermassive black holes.
262
00:25:34,830 --> 00:25:38,890
Now, I want to emphasise to you that here. Notice isn't one over H bar here.
263
00:25:38,890 --> 00:25:46,460
So that means the classical limit. Each bar goes to zero. The entropy of a black hole in the classical limit will be infinite.
264
00:25:46,460 --> 00:25:50,510
And this is why you can constantly keep highlighting entropy there in this process. Why should you?
265
00:25:50,510 --> 00:25:59,310
Homer Simpson falling into a black hole. So this should remind you of the catastrophe of plis pre plank classical black body radiation spectrum.
266
00:25:59,310 --> 00:26:08,210
The fact that the quantum effects actually make finite insensible what will be an infinity in the classical theory.
267
00:26:08,210 --> 00:26:11,450
That's very interesting. So that's one way of thinking about this.
268
00:26:11,450 --> 00:26:16,430
Well, one way of thinking about the meaning of this entropic formula that the entropy goes like one quarter.
269
00:26:16,430 --> 00:26:25,130
The area over Delplanque squared is as one cubitt sorry, one cubic per for Planck areas for the arisan.
270
00:26:25,130 --> 00:26:28,640
So here is the event rising, divided up in little things.
271
00:26:28,640 --> 00:26:37,700
And there's a cubit, you know, either zero one basically on average, one for every two or four triangles or Planck areas here.
272
00:26:37,700 --> 00:26:46,460
So this is a very, very rich and complicated system, has an enormous number of cubits.
273
00:26:46,460 --> 00:26:51,710
Let me tell you about that. Well, the entropy if you put in this formula for a solar mass black hole,
274
00:26:51,710 --> 00:26:59,060
you find the entropy is a vote would attend to the 77 times the mass of the black hole over M Solar Square.
275
00:26:59,060 --> 00:27:08,210
That means the entropy of a single solar mass black hole is roughly equal to that of the entropy of all the stars in the entire universe.
276
00:27:08,210 --> 00:27:13,130
In fact, because these guys like mass squared and we know there exist supermassive black holes,
277
00:27:13,130 --> 00:27:21,860
the entropy of a super a single supermassive black hole exceeds the entropy of everything else in the universe.
278
00:27:21,860 --> 00:27:24,980
So that's an extraordinary statement.
279
00:27:24,980 --> 00:27:31,970
Another way of thinking about this very large entropy is quantum black holes of thermal systems with a huge number of microstates member.
280
00:27:31,970 --> 00:27:36,380
If we take member Boltzmann's famous Formula S is.
281
00:27:36,380 --> 00:27:41,600
Well, let's forget in place of constant Essy was log W with W's number of microstates.
282
00:27:41,600 --> 00:27:46,610
The system, which says high then exponentially therefore misses a number of states,
283
00:27:46,610 --> 00:27:52,070
is approximately exponential of this century and this century is already huge.
284
00:27:52,070 --> 00:27:58,580
So the number of states of a black hole, a low lying state, so black hole is incredibly large.
285
00:27:58,580 --> 00:28:05,180
It's bigger than Google, vastly bigger than a Google.
286
00:28:05,180 --> 00:28:12,470
So this has some comments. Well, the information content of the universe appears to be hugely dominated by black holes.
287
00:28:12,470 --> 00:28:18,890
That's a remarkable statement. We don't understand well, these microstates of black holes, exactly what these microstates are.
288
00:28:18,890 --> 00:28:24,650
There's some progress in string theory, but aren't sending is certainly not complete.
289
00:28:24,650 --> 00:28:28,850
Very interesting. Late this Entropia respected site hawking entropy or the black hole.
290
00:28:28,850 --> 00:28:34,400
Entropy is not extensive. It goes with area, not volume.
291
00:28:34,400 --> 00:28:37,700
It doesn't go with mass either. Goes like mass squared because it area.
292
00:28:37,700 --> 00:28:43,820
This leads the idea of the holographic principle which motivates mouther signer's actually
293
00:28:43,820 --> 00:28:50,630
very specific and concrete thing called A.D.s CFT duality for certain space times.
294
00:28:50,630 --> 00:28:58,310
So this holographic principle says basically that the infinite information content of a region goes like the area,
295
00:28:58,310 --> 00:29:06,830
the bounds the region rather than the region itself. So there's far less degrees of freedom than you might think in in a theory.
296
00:29:06,830 --> 00:29:10,760
This is an incredibly rich area that deserves an entire morning in itself.
297
00:29:10,760 --> 00:29:15,230
I don't have a size that we understand holography reasonably well, inequitably curved space time.
298
00:29:15,230 --> 00:29:21,790
We don't understand Flatt's white space a lot graphy currently.
299
00:29:21,790 --> 00:29:28,640
So that's already something remark. We got out of black holes. But let me turn to some other implications for creation.
300
00:29:28,640 --> 00:29:35,150
Well, since hawking temperature increases and decreases black holes and explosively evaporate
301
00:29:35,150 --> 00:29:39,800
by runaway hawking radiation and the end temperature of hawking evaporation,
302
00:29:39,800 --> 00:29:44,870
a black hole is almost planking is incredibly high temperature.
303
00:29:44,870 --> 00:29:48,650
So this means that hawking reparation is quite extraordinary.
304
00:29:48,650 --> 00:29:53,630
Every particle in nature with mass less than implant overwrite pi.
305
00:29:53,630 --> 00:29:59,990
So that's about 10 to the 18 G.V. can be produced even if it's completely decoupled from the standard model.
306
00:29:59,990 --> 00:30:03,770
And the reason is nothing. Hisam gravity. This is not using evaporation.
307
00:30:03,770 --> 00:30:09,020
Occupation doesn't depend upon a particle being charged or colour charge or anything like that.
308
00:30:09,020 --> 00:30:11,750
Having company Salmo nothing hisam gravity.
309
00:30:11,750 --> 00:30:18,450
Therefore Hawking evaporation is a scan over all of creation, even things that are hidden from the standard model.
310
00:30:18,450 --> 00:30:24,700
So this way you can produce, for instance, dark matter or even start a hot phase of the big bang.
311
00:30:24,700 --> 00:30:27,600
And so I've been investigating these issues with my students.
312
00:30:27,600 --> 00:30:33,570
These are three of my very good graduate students here at Oxford and Olivier Rudan and Hannah.
313
00:30:33,570 --> 00:30:36,820
Two of them, I think, are in some of the breakout sessions. We have to talk, too.
314
00:30:36,820 --> 00:30:45,390
So this leads to what could be observable signatures and hawking radiation, hiding in dark matter and in gravitational waves.
315
00:30:45,390 --> 00:30:51,260
Adam, very sadly and of course, whole Steven himself.
316
00:30:51,260 --> 00:30:59,080
We've got see this. But if we'd seen Hawking radiation, he would have been able to win his very well-deserved Nobel prise.
317
00:30:59,080 --> 00:31:07,650
So this is quite incredible. Why was Ms. I'm surprised. Yes, there's this possible observable signatures hawking radiation, but there's more.
318
00:31:07,650 --> 00:31:15,860
Right. Adam, coking evaporation applies a remarkable consequence that many for the theory, including gravity,
319
00:31:15,860 --> 00:31:21,770
there are non spies and non spacetime global symmetries or with violated this approximate at best.
320
00:31:21,770 --> 00:31:24,290
So let me just quickly describe this mean what this means.
321
00:31:24,290 --> 00:31:30,080
This means you can't have exactly to generate physically distinct states without him such internal symmetries.
322
00:31:30,080 --> 00:31:34,190
You can't have an exact quote. Zack Clay. Every potential surface.
323
00:31:34,190 --> 00:31:44,450
Let me just explain why this is true. Well, we know Emmi Novia taught us that if you have a symmetry, you have global challenges.
324
00:31:44,450 --> 00:31:49,910
So if you if you slightly violate this symmetry, that means the global charges are not conserved.
325
00:31:49,910 --> 00:31:55,040
So one example of this would be the non conservation of barrier number, for instance,
326
00:31:55,040 --> 00:32:00,140
snapping not normal Yousafzai Baren number with some you won global symmetry with this must be violated.
327
00:32:00,140 --> 00:32:09,470
So here's the argument of why it's true. Go back to Zelda, which so imagine you start forming a black out of a large initial number of neutrons.
328
00:32:09,470 --> 00:32:12,680
So you crush these neutrons to form a black hole,
329
00:32:12,680 --> 00:32:20,930
but then it hawking evaporates and is hawking radiation is independent of whether your initial state is a barrier on the balance or anti baryonic.
330
00:32:20,930 --> 00:32:26,060
It only cares about the mass spin in charge of these states, not whether they're baren anti barium.
331
00:32:26,060 --> 00:32:33,140
So at most the final state has plus or minus root end of of Barry on charge here.
332
00:32:33,140 --> 00:32:37,340
The blue there's one, the three blue and one reds is one net state.
333
00:32:37,340 --> 00:32:42,530
Here we started out with a lot. So you lose Barry a number in this process.
334
00:32:42,530 --> 00:32:47,450
So global symmetries are violated by hawking evaporation.
335
00:32:47,450 --> 00:32:50,810
Now, there's a we don't extend exactly how this works.
336
00:32:50,810 --> 00:32:55,490
And for generations in particular, we don't sign a form and summarise the global symmetry value interactions.
337
00:32:55,490 --> 00:32:59,150
But there's progress, again, by by groups involving me,
338
00:32:59,150 --> 00:33:03,200
but other people as well around the world and progress, recent progress being made on this issue.
339
00:33:03,200 --> 00:33:07,460
That's interesting. So I'm almost done. Let me make a few final words.
340
00:33:07,460 --> 00:33:14,090
So one issue I haven't spoken about is if quantum mechanics and black holes are, in fact inconsistent with each other.
341
00:33:14,090 --> 00:33:21,140
And this was the view of Stephen Hawking himself for many years, though I would say not for the last five years, his life might still be Roger.
342
00:33:21,140 --> 00:33:25,190
Roger Penrose is you. So what is the reason for this?
343
00:33:25,190 --> 00:33:32,960
Well, hawking evaporation of black holes appears to allow for quantum mechanical, pure states to evolve to mixed states.
344
00:33:32,960 --> 00:33:39,580
If so, this would be of would violate a fundamental axiom of quantum mechanics and imply information loss.
345
00:33:39,580 --> 00:33:47,480
But in the last two years, there's been major progress on this issue and a consistent calculational framework is now emerging.
346
00:33:47,480 --> 00:33:56,900
So there's a whole bunch of papers from people for the Institute of Arts today, from Stanford, from M.I.T., from other places as well.
347
00:33:56,900 --> 00:34:02,780
And what is their basic idea? Notice that some very exciting things here, replica wormholes in the black hole interior.
348
00:34:02,780 --> 00:34:06,920
This is trying to understand in a real way what is the physics of the interior?
349
00:34:06,920 --> 00:34:12,170
What observers who fall through the arisan would sees is crucial in understanding these issues.
350
00:34:12,170 --> 00:34:18,080
And you're having some very interesting things like wormholes appear, other kinds of solutions possibly to Einstein's equations.
351
00:34:18,080 --> 00:34:28,180
So the basic idea, and this is true for experts, is that Hawking's calculation of this thermal effect is thermal density matrix was never exact.
352
00:34:28,180 --> 00:34:32,280
In fact, we always knew that it had his calculation had loop effects there.
353
00:34:32,280 --> 00:34:39,710
But in fact, the paradox was, is all these local quantum field theory loop corrections don't help solve the paradox.
354
00:34:39,710 --> 00:34:48,030
It turns out you can show. But now it's been realised. There are new tiny non perturb two effects, which are Suckley non-local.
355
00:34:48,030 --> 00:34:54,860
All right. And that's the crucial thing. They're very tiny. They go like E to the minus area, the black hole over Delplanque Square.
356
00:34:54,860 --> 00:34:56,510
They're incredibly tiny.
357
00:34:56,510 --> 00:35:03,620
So you may say, how can these incredibly tiny effects make a difference and somehow change mixed states, what looks like a mixed state or pure state?
358
00:35:03,620 --> 00:35:07,600
And the answer is, if you compute the radiation, the entropy of the radiation is coming out.
359
00:35:07,600 --> 00:35:13,640
So some other states of the eigenvalues of this density matrix and these eigenvalues
360
00:35:13,640 --> 00:35:17,810
now shifted by exponentially small amounts because of these tiny corrections.
361
00:35:17,810 --> 00:35:20,890
But there's an exponentially large number of states here.
362
00:35:20,890 --> 00:35:26,240
Remember, emphasised before that the black hole was an he let excellent large number of states.
363
00:35:26,240 --> 00:35:32,540
So there's exponentially larger number of terms times, exponentially small corrections to each one of these terms.
364
00:35:32,540 --> 00:35:41,180
And this can lead to an order, one modification. And in fact, there are demonstrations in simple cases that this purifies the final radiation.
365
00:35:41,180 --> 00:35:49,110
So leads to pure state to pure state evolution, meaning that quantum mechanics is consistent with black holes.
366
00:35:49,110 --> 00:35:56,410
So I want to finish there with a statement, the quantum mechanics, black holes is even more remarkable than you might have thought.
367
00:35:56,410 --> 00:36:01,440
He's guiding us towards a better understanding of quantum gravity, and I emphasise information as well.
368
00:36:01,440 --> 00:36:05,490
And so I think is very good reason to believe that black holes are quantum black holes.
369
00:36:05,490 --> 00:36:09,600
And think about the hypernatremia 21st century. So I'll stop there.
370
00:36:09,600 --> 00:36:15,373
Thank you.
