1 00:00:00,000 --> 00:00:05,209 So black holes exist and they are an important part of the constitution of 2 00:00:05,209 --> 00:00:10,485 galaxies and they are the end point of stellar evolution for mass of stars and 3 00:00:10,485 --> 00:00:14,693 most of them we don't see. But if they happen to have a bindery 4 00:00:14,693 --> 00:00:18,300 partner we can detect the accretion discs around them. 5 00:00:18,300 --> 00:00:23,982 Okay, what can we say about these objects from understanding GR. 6 00:00:23,982 --> 00:00:27,571 What do people's studies tell us. the black holes 7 00:00:27,571 --> 00:00:31,654 we've been considering have been the simplest, spherically symmetric, 8 00:00:31,654 --> 00:00:35,677 non-rotating, simple objects. how complicated can black holes get? 9 00:00:35,677 --> 00:00:39,040 Well, they can get complicated, but it turns out not very. 10 00:00:39,040 --> 00:00:43,543 there's a beautiful theory known colloquially as the Black Hole No Hair 11 00:00:43,543 --> 00:00:48,347 theorem, or a black hole has no hair. it turns out that in the collapse from a 12 00:00:48,347 --> 00:00:52,250 star to a black hole, all of the properties of the stars are lost. 13 00:00:52,250 --> 00:00:54,867 The chemical composition makes no difference. 14 00:00:54,867 --> 00:00:58,649 The temperature is gone, the shape of something that collapsed is 15 00:00:58,649 --> 00:01:01,267 gone. All of those features are radiated away 16 00:01:01,267 --> 00:01:05,281 as gravitational waves or energy. All that information is gone in the 17 00:01:05,281 --> 00:01:08,190 collapse. Black holes are completely characterized 18 00:01:08,190 --> 00:01:11,564 by three numbers. Tell me three properties of a black hole, 19 00:01:11,564 --> 00:01:15,288 and I can exactly describe, that is all there is to say about it. 20 00:01:15,288 --> 00:01:19,535 We said that stars are by and large described by mass, but the stars also 21 00:01:19,535 --> 00:01:23,665 have magnetic fields, and rate of rotation, and [INAUDIBLE], chemical 22 00:01:23,665 --> 00:01:27,310 composition, and metallicity, and age. No such thing for a black hole. 23 00:01:27,310 --> 00:01:30,060 A black hole is completely characterized by its mass, 24 00:01:30,060 --> 00:01:32,406 its angular momentum and its electric charge. 25 00:01:32,406 --> 00:01:34,647 Now, electric charge is expected to be zero. 26 00:01:34,647 --> 00:01:36,993 Why would a black hole carry an electric charge? 27 00:01:36,993 --> 00:01:39,600 Everything in the universe is pretty much neutral. 28 00:01:39,600 --> 00:01:42,937 we know that its mass. We can measure if something's orbiting 29 00:01:42,937 --> 00:01:45,283 it. Angular momentum is expected to be rather 30 00:01:45,283 --> 00:01:47,525 large. Remember, this is a collapsed neutron 31 00:01:47,525 --> 00:01:49,714 stars. These neutron stars we saw are in a 32 00:01:49,714 --> 00:01:52,217 collapsed core. When it collapsed to a neutron star, it 33 00:01:52,217 --> 00:01:54,824 carried enough angular momentum to drive a pulsar. 34 00:01:54,824 --> 00:01:57,430 We expect most black holes to be rotating rapidly. 35 00:01:57,430 --> 00:02:01,793 the Schwarzchild example that was the topic of the simulations we've been doing 36 00:02:01,793 --> 00:02:04,922 was a simplified case with vanishing angular momentum. 37 00:02:04,922 --> 00:02:08,572 Angular momentum makes it a lot more complicated to understand, 38 00:02:08,572 --> 00:02:12,165 but that's all there is. There's only that one extra parameter. 39 00:02:12,165 --> 00:02:16,510 The second thing is, we discussed this very special, spherical symmetric case, 40 00:02:16,510 --> 00:02:20,670 and we found the singularity. Maybe that's a artifact of the symmetry 41 00:02:20,670 --> 00:02:24,469 of the situation. This was a real consideration when the 42 00:02:24,469 --> 00:02:27,238 black hole solutions were first discovered. 43 00:02:27,238 --> 00:02:30,974 work of Hawking and Penrose shows that no, this is real. 44 00:02:30,974 --> 00:02:36,577 general relativity is a theory which when you start with an initially smooth and 45 00:02:36,577 --> 00:02:41,600 reasonable un, non singular space time you can prove that within a finite time 46 00:02:41,600 --> 00:02:46,108 in the future, or possibly in a finite time in the past, you had actual 47 00:02:46,108 --> 00:02:49,522 singularities. General relatively produces singularities 48 00:02:49,522 --> 00:02:54,067 starting from non-singular initial conditions, and then it doesn't know what 49 00:02:54,067 --> 00:02:55,981 to do, which means that relativity as a theory 50 00:02:55,981 --> 00:03:00,407 is intrinsically incomplete. We know that we don't have the final word 51 00:03:00,407 --> 00:03:05,431 on gravity, and some of us are trying to do better, but at the moment this is what 52 00:03:05,431 --> 00:03:08,146 we have. Do we need to care about what happens at 53 00:03:08,146 --> 00:03:10,873 the singularity? Well, again we will never see what 54 00:03:10,873 --> 00:03:15,237 happens at the singularity, at the center of the black hole, because we don't see 55 00:03:15,237 --> 00:03:18,510 anything inside the horizon. There's this light like-surface 56 00:03:18,510 --> 00:03:22,656 surrounding it, and light cannot escape, so in some sense maybe we don't care. 57 00:03:22,656 --> 00:03:26,619 there is a conjecture called the cosmic censorship conjecture, 58 00:03:26,619 --> 00:03:31,032 which is our model of base, which says that all singularities are hidden inside 59 00:03:31,032 --> 00:03:33,323 horizons, which means, things that are not 60 00:03:33,323 --> 00:03:36,675 described by the equations might be going on in your theory. 61 00:03:36,675 --> 00:03:41,145 But they're going on in places, that have no causal effect on anything that's 62 00:03:41,145 --> 00:03:44,330 happening outside. We could go there and investigate them, 63 00:03:44,330 --> 00:03:48,758 though we'd never come back to tell, but they will never influence anything 64 00:03:48,758 --> 00:03:51,711 about us. The inside of a black hole has no impact 65 00:03:51,711 --> 00:03:54,722 on the exterior of a black hole. Nothing can escape, 66 00:03:54,722 --> 00:03:57,911 not even light. so this is the cosmic censorship 67 00:03:57,911 --> 00:04:01,041 hypothesis. there are indications that it may fail 68 00:04:01,041 --> 00:04:05,732 and that there maybe such things violating it, as singularities not hidden 69 00:04:05,732 --> 00:04:09,546 behind horizons. Those would be naked similarities, and 70 00:04:09,546 --> 00:04:14,831 there is recent evidence that such things are in fact possible in reasonable 71 00:04:14,831 --> 00:04:18,979 gravitational theories, but we of course have not observed any. 72 00:04:18,979 --> 00:04:25,816 in the realm of fantasy, let's look again at this image of the black hole that I 73 00:04:25,816 --> 00:04:31,526 showed you, where you remember that I described this is the outside of the 74 00:04:31,526 --> 00:04:35,230 black hole. This as the inside of the black hole. 75 00:04:35,230 --> 00:04:40,000 This was the singularity, and this was the horizon. 76 00:04:40,000 --> 00:04:44,725 This was the line r equals r Schwarzschild, which was lake like, in 77 00:04:44,725 --> 00:04:49,177 fact, and yeah well this is the black hole, this is the outside. 78 00:04:49,177 --> 00:04:54,870 What is the rest of this? and, this region, and I should note, 79 00:04:54,870 --> 00:04:59,534 this, description, is a description that is valid for a region just outside the 80 00:04:59,534 --> 00:05:01,491 horizon. That's why I was using it. 81 00:05:01,491 --> 00:05:05,522 But it's obtained by ignoring completely the fact that there's a star. 82 00:05:05,522 --> 00:05:10,186 you're basically using the solution to the part of Einstein's equations where 83 00:05:10,186 --> 00:05:12,720 you set the energy and momentum bit to zero. 84 00:05:12,720 --> 00:05:15,492 Which is true, everywhere outside the star. 85 00:05:15,492 --> 00:05:20,310 So those are the equations you solve to describe everything except where 86 00:05:20,310 --> 00:05:23,808 materials are. Most of space is free of matter and 87 00:05:23,808 --> 00:05:25,524 energy. It's mostly vacuum. 88 00:05:25,524 --> 00:05:31,068 And so we use those equations and then you, you get that solution, you can 89 00:05:31,068 --> 00:05:35,160 extend that solution. So in real life there would be a big fat 90 00:05:35,160 --> 00:05:39,676 star over here and while you could hit the singularity, just like most of the 91 00:05:39,676 --> 00:05:44,211 matter in the star is, all of this stuff down here and to the left would be 92 00:05:44,211 --> 00:05:47,463 complete fantasy. But let's imagine, we've drawn a valid 93 00:05:47,463 --> 00:05:52,467 solution to Einstein's equations anyway. we don't know how to create such a thing, 94 00:05:52,467 --> 00:05:56,399 but what does this look like. Well so there's this region out here 95 00:05:56,399 --> 00:06:00,092 which is the outside. There's this region out in here which is 96 00:06:00,092 --> 00:06:03,190 the black hole. There's this region in here which is 97 00:06:03,190 --> 00:06:06,228 interesting. Notice that you can't get into that 98 00:06:06,228 --> 00:06:09,870 region no matter what you do. Remember time moves this way. 99 00:06:09,870 --> 00:06:13,400 you would have to be moving faster than light. 100 00:06:13,400 --> 00:06:17,487 To tip through this light cone. This is what's called a white hole. 101 00:06:17,487 --> 00:06:21,513 Everything can only come out of it, nothing can ever fall into it. 102 00:06:21,513 --> 00:06:24,300 It's a time reversed version of a black hole. 103 00:06:24,300 --> 00:06:29,184 And this region out here, it turns out, looks a lot like this region out here. 104 00:06:29,184 --> 00:06:34,069 So there is another asymptotic region. And away from the black hole, it looks 105 00:06:34,069 --> 00:06:36,640 quite reasonable. Like normal space time. 106 00:06:36,640 --> 00:06:39,532 And so, remembering that time runs vertically. 107 00:06:39,532 --> 00:06:43,581 You now have this great description of two regions, which, 108 00:06:43,581 --> 00:06:47,695 outside, the outsides, that look like the outside of a black hole, 109 00:06:47,695 --> 00:06:51,423 which are disjoint, right? They, they don't touch each other. 110 00:06:51,423 --> 00:06:57,277 Except at this, one point. they actually intersect, and this one 111 00:06:57,277 --> 00:07:01,640 point is just, too short. The, the, length of time that these two 112 00:07:01,640 --> 00:07:06,643 universes are connected, if you want, is just too short for a light beam to get 113 00:07:06,643 --> 00:07:10,364 from here to here. A light beam sort of that can travel the 114 00:07:10,364 --> 00:07:15,239 boundary from one to the other. but, this is the idea for what is called a 115 00:07:15,239 --> 00:07:18,190 wormhole. A small deformation of this leads to 116 00:07:18,190 --> 00:07:23,002 something called the Einstein-Rosen Bridge, where there is a sort of finite 117 00:07:23,002 --> 00:07:28,070 time where the space time on the right, space time on the left are connected. 118 00:07:28,070 --> 00:07:31,817 that is the origin of the idea of worm holes. 119 00:07:31,817 --> 00:07:38,229 You can imagine that somewhere in our space time is a horizon, and there is a 120 00:07:38,229 --> 00:07:45,256 sort of a, a length of time during which by going through that region of strong 121 00:07:45,256 --> 00:07:48,137 curvature. You could come out and go completely 122 00:07:48,137 --> 00:07:53,104 different universe or into a part of our own universe that is very far you could 123 00:07:53,104 --> 00:07:58,070 imagine sort of our universe bending over and a wormhole cutting through or some 124 00:07:58,070 --> 00:08:00,400 such nonsense. And at the moment 125 00:08:00,400 --> 00:08:05,319 we don't have any, working solutions. So the Einstein-Rosen Bridge has been 126 00:08:05,319 --> 00:08:09,088 shown to be unstable, Any perturbation anywhere, would, 127 00:08:09,088 --> 00:08:12,985 collapse it down, People have been working on various ways 128 00:08:12,985 --> 00:08:16,946 to modify the solutions to get wormholes that are both stable. 129 00:08:16,946 --> 00:08:22,759 And last long enough for, at least a, a photon or a particle to get through and 130 00:08:22,759 --> 00:08:27,230 maybe something macroscopic. that has not happened, but there is no 131 00:08:27,230 --> 00:08:30,638 theorem that I know of, that precludes its existence, 132 00:08:30,638 --> 00:08:35,946 and so maybe there are solutions to the equations that generate wormholes, and 133 00:08:35,946 --> 00:08:38,522 maybe, maybe, there are actually wormholes out 134 00:08:38,522 --> 00:08:42,327 there. I cannot exclude that, and then what's on the other side could 135 00:08:42,327 --> 00:08:46,245 be a different universe, could be a different part of our own universe. 136 00:08:46,245 --> 00:08:50,162 Going through a wormhole would be an exciting thing to think about. 137 00:08:50,162 --> 00:08:54,583 I didn't want to leave you without them. And then the last thing I wanted to 138 00:08:54,583 --> 00:08:59,228 discuss is quantum issues of black holes. And so it's a result again due to Hawking 139 00:08:59,228 --> 00:09:02,810 that quantum effects, the quantum fluctuations near a horizon 140 00:09:02,810 --> 00:09:07,905 violate this idea that a black hole produces no energy and in fact a black 141 00:09:07,905 --> 00:09:11,498 hole does emit radiation. It's called Hawking radiation. 142 00:09:11,498 --> 00:09:16,071 It's not a property of general relativity which is a classical theory. 143 00:09:16,071 --> 00:09:20,905 It's a property of the quantum fields, electromagnetic fields and electron 144 00:09:20,905 --> 00:09:26,392 fields and whatever other fields you have in your theory fluctuating near, in the 145 00:09:26,392 --> 00:09:30,442 presence of the large curvatures at black holes horizon. 146 00:09:30,442 --> 00:09:33,195 And That means that a black hole radiates, 147 00:09:33,195 --> 00:09:38,089 and Hawking's calculation of the black hole radiation led him to, later figure 148 00:09:38,089 --> 00:09:41,230 out that a black hole radiates black body radiation. 149 00:09:41,230 --> 00:09:45,459 A black hole has a temperature. The thermodynamics of a black hole was 150 00:09:45,459 --> 00:09:48,903 later developed. It's, quite a developed art, but it's a 151 00:09:48,903 --> 00:09:51,803 weird object. The temperature of a black body, 152 00:09:51,803 --> 00:09:55,669 decreases with its mass, of a black hole, decreases with its mass. 153 00:09:55,669 --> 00:09:59,778 It's inversely proportional to its mass. Bigger black holes are cold. 154 00:09:59,778 --> 00:10:02,980 Smaller black holes, less massive black holes, are hot. 155 00:10:02,980 --> 00:10:06,490 So, smaller black holes, that means, radiate more. 156 00:10:06,490 --> 00:10:11,451 This is very strange because when a black hole radiates of course a the energy came 157 00:10:11,451 --> 00:10:16,117 from the black holes mass so the black hole become loses mass, becomes a little 158 00:10:16,117 --> 00:10:18,833 bit smaller and therefore a little bit hotter. 159 00:10:18,833 --> 00:10:23,027 A black hole is one of those weird objects with negative specific heat. 160 00:10:23,027 --> 00:10:27,018 As it loses heat, it heats up. Typically, objects lose energy and they 161 00:10:27,018 --> 00:10:29,998 cool. A black hole heats as it loses energy. 162 00:10:29,998 --> 00:10:33,620 So as it loses energy it heats more, it loses, it radiates more. 163 00:10:33,620 --> 00:10:36,892 Remember T to the fourth, it heats more, it radiates more. 164 00:10:36,892 --> 00:10:40,865 So the end of a black holes life would be a very dramatic explosion. 165 00:10:40,865 --> 00:10:45,188 In fact the title of Hawking's paper was Cosmic Explosions, because he was 166 00:10:45,188 --> 00:10:50,095 thinking about, maybe we should go look for these black holes that at the end of 167 00:10:50,095 --> 00:10:54,594 their life produce these very explosive, high temperature, large amounts of 168 00:10:54,594 --> 00:10:59,172 radiation and black holes can completely disappear, evaporate. 169 00:10:59,172 --> 00:11:04,407 That's not a big worry it turns out. the expected lifetime of a five solar 170 00:11:04,407 --> 00:11:09,250 mass black hole is on the order of the ten to the 62 years, given a universe 171 00:11:09,250 --> 00:11:13,902 that is ten to the ten or so years old. That's not yet a major concern. 172 00:11:13,902 --> 00:11:18,300 But if there are tiny black holes around, that therefore radiate more. 173 00:11:18,300 --> 00:11:21,167 We know about million solar mass black holes. 174 00:11:21,167 --> 00:11:25,119 Those last even longer. We know about stellar mass black holes. 175 00:11:25,119 --> 00:11:28,942 Those last too long, but if some mechanism produced two kilo 176 00:11:28,942 --> 00:11:32,513 black holes or proton mass black holes, those would 177 00:11:32,513 --> 00:11:37,360 evaporate much more rapidly. And the possibility of microscopic black 178 00:11:37,360 --> 00:11:43,283 holes, and their evaporation is something that people are studying in various, both 179 00:11:43,283 --> 00:11:48,938 theoretical, and at the LHC, even experimental level, to try to see if they 180 00:11:48,938 --> 00:11:53,919 can form a black hole and watch it evaporate essentially as part of their 181 00:11:53,919 --> 00:11:58,160 high energy collisions. So, this is the theory bit of the black 182 00:11:58,160 --> 00:11:58,497 hole.