Classical and Quantum Black Holes の全文書き起こし

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.