1 00:00:19,390 --> 00:00:25,600 Welcome back to The Talk of the Morning, which is from Professor Andre Star, next. 2 00:00:25,600 --> 00:00:31,330 Andre got his undergraduate degree at Moscow State University and then pitched it New York 3 00:00:31,330 --> 00:00:38,780 University and then had postdocs and fellowships in the states at CERN in Canada and Southampton. 4 00:00:38,780 --> 00:00:48,730 And luckily for us, ended up in 2008 at Oxford, where he's professor of physics and the Rudolf Parr Centre and fellow at St. John's. 5 00:00:48,730 --> 00:00:53,230 Andre is from the particle physics group and he's interested in the application 6 00:00:53,230 --> 00:00:57,990 of string theory to quantum field theories and in particular in philosophy. 7 00:00:57,990 --> 00:01:01,930 And he's going to explain to us what to Locher fears. So thanks, Andre. 8 00:01:01,930 --> 00:01:05,950 Over to you. Thank you very much. 9 00:01:05,950 --> 00:01:17,570 So look me for a screen. And hopefully. 10 00:01:17,570 --> 00:01:21,020 If you could just confirm it when you don't get on Lowden's. Good. 11 00:01:21,020 --> 00:01:28,950 Thank you, everybody, for joining. So we'll talk a little bit about a slightly more exotic complications for hybrid of Lennix, 12 00:01:28,950 --> 00:01:33,380 which is fluid gravity, duality and hydatid mimics mix of black holes. 13 00:01:33,380 --> 00:01:38,960 So here is the outline of a book. We'll discuss a little bit relativistic, kind of mimics the foundations. 14 00:01:38,960 --> 00:01:46,520 So this of a subject and then turn to black holes. I will remind you what black holes are as solutions of Einstein's general relativity. 15 00:01:46,520 --> 00:01:54,410 And I will also remind you about black hole thermodynamics. Then we'll discuss what happens if you perturb black holes, all equilibrium. 16 00:01:54,410 --> 00:01:59,360 So out of equilibrium are described by a so-called black hole membrane paradigm. 17 00:01:59,360 --> 00:02:01,340 And I will discuss this in some detail. 18 00:02:01,340 --> 00:02:10,880 And then we will embed all of all this picture into the modern sort of modern theoretical framework, which is known as holographic duality. 19 00:02:10,880 --> 00:02:17,450 So this will bring us to a discussion of whether or not I'm just tocks equations can be discussed that in this holographic galaxy, 20 00:02:17,450 --> 00:02:22,460 as I Stine's equations of general relativity close to the horizon. So black holes. 21 00:02:22,460 --> 00:02:29,380 And we will finish by discussing some recent gravity inspired new advances in the relativistic hydroponics. 22 00:02:29,380 --> 00:02:34,720 So relativity credit remix is necessary when fluids and gases move of speeds, 23 00:02:34,720 --> 00:02:40,510 which are comparable to the speed of light in such situations, are not so uncommon. 24 00:02:40,510 --> 00:02:50,050 As Steve already mentioned in his stock. So first of all, of course, we have multiple applications in atavistic astrophysics, 25 00:02:50,050 --> 00:02:54,160 in particular, if accretion disks, black holes and stars and so on. 26 00:02:54,160 --> 00:03:00,910 But also here in URF, if you have high energy cosmic rays which are coming to Earth and striking the ordinary mantra, 27 00:03:00,910 --> 00:03:05,710 we produce zillions of particles and particles behave that in anemically. 28 00:03:05,710 --> 00:03:13,960 And they are described. His behaviour is described by relativistic hydrodynamics, as was shown by Fantome and Landow in 1950s. 29 00:03:13,960 --> 00:03:18,400 You can also do artificial experiments here on Earth in accelerators such as Rukun. 30 00:03:18,400 --> 00:03:24,460 LHC is also Steve mentioned in his first stock. Then you create the so-called coagulant plasma. 31 00:03:24,460 --> 00:03:29,470 And choirgirl plasma is a quantum strongly interacting fluid. 32 00:03:29,470 --> 00:03:33,640 So it is described by relativistic hydrodynamics, but not by kinetic fury. 33 00:03:33,640 --> 00:03:40,250 So this is sort of a rather interesting object to study. So in relativistic domain, we have new features. 34 00:03:40,250 --> 00:03:47,930 Again, Steve already mentioned this. But let me mention this again. So energy, momentum and mass are no longer separate quantities. 35 00:03:47,930 --> 00:03:51,990 They are tied together by formulas like this, one of which, of course, is equal terms. 36 00:03:51,990 --> 00:03:56,640 Two squared is the simple limit. But we also have momentum in the game. 37 00:03:56,640 --> 00:04:02,620 In more general. Second, and therefore it makes sense to go to different variables. 38 00:04:02,620 --> 00:04:08,560 So do not consider density of mass alone because mass can be converted to energy and vice versa. 39 00:04:08,560 --> 00:04:17,290 But to consider instead energy density as a basic variable and momentum density and as often happens in special relativity, 40 00:04:17,290 --> 00:04:21,310 you have to recast all these objects into four dimensional language, 41 00:04:21,310 --> 00:04:26,170 into the language of Mankowski spacetime, where every object will have four components. 42 00:04:26,170 --> 00:04:34,030 So here you have the object, which is known as the energy momentum denser in which the package is energy density and momentum density. 43 00:04:34,030 --> 00:04:41,620 And you have these indices, A and B running from zero to three as appropriate and special relativity. 44 00:04:41,620 --> 00:04:45,730 Another point in the relativistic systems is that the number of particles is no longer conserved. 45 00:04:45,730 --> 00:04:50,350 Right. For the same reason as this formula shows that you can if you have enough energy, 46 00:04:50,350 --> 00:04:54,970 you can create zillions of particles out of vacuum, particle antiparticle pairs. 47 00:04:54,970 --> 00:04:59,680 And so it doesn't make sense to talk about conserved quantity, which is a number of particles. 48 00:04:59,680 --> 00:05:05,050 But we can have other conserved quantities in the game, such as the only charge left on charge. 49 00:05:05,050 --> 00:05:11,050 And they are really concerned, but they have to be written in four dimensional language of special relativity. 50 00:05:11,050 --> 00:05:15,440 And so the main hero here, it would be the density of some sort of charge, for example. 51 00:05:15,440 --> 00:05:20,610 But you take charge and then the other components, the components of the current X, G, 52 00:05:20,610 --> 00:05:26,860 Y and Jay Z are tied together to this density of conserved charge in the conservation equation, which again, 53 00:05:26,860 --> 00:05:34,570 in four dimensional language, can you simply read them as a forward divergence of this for current J and conservation of origin, 54 00:05:34,570 --> 00:05:40,960 momentum is presented by the conservation of TAAB in the following equation here. 55 00:05:40,960 --> 00:05:49,600 So these are the conservation laws in the relativistic domain and these are the main building blocks of hatred of Lennix relativistic domain. 56 00:05:49,600 --> 00:05:52,840 So let me remind you again about foundations of hydrodynamics. Right? 57 00:05:52,840 --> 00:05:59,230 So if you wait, so suppose you have a system of two Mystikal, not many, many, many, many constituents. 58 00:05:59,230 --> 00:06:02,770 If you wait long enough, the system equilibrate, hopefully. 59 00:06:02,770 --> 00:06:07,990 Again, this is not guaranteed. But in most systems, we observe the equilibration. 60 00:06:07,990 --> 00:06:17,730 If you wait long, long for a long, long time, just before this equilibration on very large scales of space, 61 00:06:17,730 --> 00:06:23,620 the system will be characterised by time and space dependent densities of conserved charges. 62 00:06:23,620 --> 00:06:28,630 Because in thermal equilibrium, when you wait for infinity right for eternity, 63 00:06:28,630 --> 00:06:35,620 it is characterised by globally conserved charge of just a handful of globally conserved churches in thermal equilibrium. 64 00:06:35,620 --> 00:06:42,550 So if you just make one step back in time before everything has the calibrated, 65 00:06:42,550 --> 00:06:47,620 you will see that these conserved churches acquire dependence on space and time. 66 00:06:47,620 --> 00:06:50,920 But still, there are just handful of disconcert churches. Right. 67 00:06:50,920 --> 00:06:57,730 But these densities of conserved churches are the main fundamental degrees of freedom of hydrodynamic description. 68 00:06:57,730 --> 00:07:01,640 So this is this is the the key the key assumption, if you want, 69 00:07:01,640 --> 00:07:09,580 because it's sometimes very hard to derive either description from from fundamental principles such as Latron Children Donnell's. 70 00:07:09,580 --> 00:07:13,930 You can do it with kinetic beauty, but not a every fluid has a kinetic description. 71 00:07:13,930 --> 00:07:20,650 Of course, this is so. So let me add a little bit more to that. 72 00:07:20,650 --> 00:07:25,640 So we have fundamental degrees of freedom, which are densities of contempt charges. 73 00:07:25,640 --> 00:07:29,140 Now, what about the equations of motion? For me is density is often surcharges. 74 00:07:29,140 --> 00:07:35,170 So equations of motion come from conservation laws and the so-called constitutive relations. 75 00:07:35,170 --> 00:07:39,160 So let me explain. This is very simple example of the consideration of a charge. 76 00:07:39,160 --> 00:07:43,390 So suppose because you want to charge rent, but when a charge in four dimensions, 77 00:07:43,390 --> 00:07:48,520 the conservation law, as I mentioned earlier, is just a forward divergence equal to zero. 78 00:07:48,520 --> 00:07:55,090 So this is a microscopic law which holds all this. Now, but in the hydrodynamic regime. 79 00:07:55,090 --> 00:08:01,540 So this Jay here. Right, it has four components. Do not the density of charge and then J x j jay wages. 80 00:08:01,540 --> 00:08:10,150 These are components of the cut. But in the hydrodynamic regime, the only degree of freedom allowed is the density of conserved charge. 81 00:08:10,150 --> 00:08:18,820 J Not so. We have to have another equation which would express components of the current through these fundamental degree of freedom, 82 00:08:18,820 --> 00:08:22,210 which is the density of conserve charge. How can we do this? 83 00:08:22,210 --> 00:08:29,740 This is done in effective fury as the infinite series which is compatible before symmetries of the system. 84 00:08:29,740 --> 00:08:36,310 So what happens? So here we have a simple first term which says that if you have a gradient of the density of charge. 85 00:08:36,310 --> 00:08:40,120 Suppose the density of charge here is higher than here, then the current will flow. 86 00:08:40,120 --> 00:08:46,720 It will flow proportionally to the gradient. Right. So there's some coefficient of proportionality which happens to be diffusion constant. 87 00:08:46,720 --> 00:08:52,000 All right. And then you can have more and more terms added to the fired higher gradients. 88 00:08:52,000 --> 00:08:58,720 So this is known as the gradient expansion. If you combine these two equations, you will get the equations of motion in hydrodynamic reaching, 89 00:08:58,720 --> 00:09:03,570 which in this case is nothing but a diffusion equation with energy momentum. 90 00:09:03,570 --> 00:09:08,890 Denzel, it's a similar story. You have microscopic conservation law and then you have constitutive relation, 91 00:09:08,890 --> 00:09:13,900 which is an infinite serious in terms of gringo's more and more derivatives. 92 00:09:13,900 --> 00:09:20,590 So if you take term devout from K to serious with terms only containing loaded widgets at all. 93 00:09:20,590 --> 00:09:25,540 And combined with conservation law, you will get what is known as relativistic euler's equation. 94 00:09:25,540 --> 00:09:30,100 If you allow invis truncation, the first derivatives use only, but no second, which is the higher. 95 00:09:30,100 --> 00:09:34,030 And combined with this equation, you get them just getting to know your stocks equations. 96 00:09:34,030 --> 00:09:40,840 If you allow second order in derivatives, you get generalisation, often get stocks equations known as Biomet equations and so on. 97 00:09:40,840 --> 00:09:46,750 So in principle, this is the way to build the build hydrodynamics. So this is a scary formula. 98 00:09:46,750 --> 00:09:55,180 But let me just just freude for a second. It shows this first term, which contains only first derivatives and loving and nothing else. 99 00:09:55,180 --> 00:10:04,540 And what I would like to emphasise that for derivative structures of this complicated crocodile here is completely universal for any liquid to gas. 100 00:10:04,540 --> 00:10:10,580 It is absolutely universal. What is not universal is the set of these coefficients which multiply. 101 00:10:10,580 --> 00:10:14,980 It stands out to structures. These coefficients eight are cut, I love and so on. 102 00:10:14,980 --> 00:10:20,650 And no one is Transperth coefficients. And they corrected eiseley method of the fluid, the fury at hand. 103 00:10:20,650 --> 00:10:26,470 So for each fluid, they are different. They have to be computed from the microscopic underlying microscopic view. 104 00:10:26,470 --> 00:10:30,640 And this is what difference what what makes, for example, hydrodynamics of water. 105 00:10:30,640 --> 00:10:37,430 Different from the dynamics of formula plus. All right, so one important coefficient that is shared is Capozzi. 106 00:10:37,430 --> 00:10:42,560 So share viscosity can be understood as a measure of internal friction in the fluid on gas. 107 00:10:42,560 --> 00:10:47,600 So suppose you have two layers of fluid or gas moving to slightly different velocities. 108 00:10:47,600 --> 00:10:56,490 For example, top layer is a little bit faster than the lower level. Now, particles of both layers can penetrate these layers. 109 00:10:56,490 --> 00:11:00,200 From from from top to bottom and vice versa. They carry momentum. 110 00:11:00,200 --> 00:11:04,820 So this particle, for example, from its slow layer, can penetrate this one. 111 00:11:04,820 --> 00:11:09,650 Right. And it will carry a horizontal momentum of this, which will slow down the upper layer. 112 00:11:09,650 --> 00:11:13,640 And likewise, the particle from the upper layer can penetrate the lower layer. 113 00:11:13,640 --> 00:11:17,420 And it will speed it up because it will carry some momentum a bit. 114 00:11:17,420 --> 00:11:25,070 So if viscosity is a measure of how much this transfer of momentum is actually transferred by this bogus motion of particles. 115 00:11:25,070 --> 00:11:29,210 So this is internal friction. It's no different from when you when you have your poems. 116 00:11:29,210 --> 00:11:34,460 Right. And doing this right, you feel heat. So this is internal friction. No different from what is happening in here. 117 00:11:34,460 --> 00:11:38,840 And viscosity is a measure, quantitative measure of its internal friction. 118 00:11:38,840 --> 00:11:42,860 So now let us abandon abandon the reduced equity dynamics for a while. 119 00:11:42,860 --> 00:11:47,830 For a while, we come back to it and go to gravity and black holes. 120 00:11:47,830 --> 00:11:51,170 So we'll generate a little activity is a fury of classical gravity, classical meaning, 121 00:11:51,170 --> 00:11:56,270 not quite Einsteins equation determine the metric of space and time. 122 00:11:56,270 --> 00:12:00,050 And these equations philosophically so very often here and philosophically, 123 00:12:00,050 --> 00:12:08,900 they encode the following situation that if you have on the right hand side distribution of mass and energy encoded in energy momentum, 124 00:12:08,900 --> 00:12:14,240 Tenzer, then you can determine the geometry of spacetime. 125 00:12:14,240 --> 00:12:16,880 By solving this equation, because on the left hand side, 126 00:12:16,880 --> 00:12:22,610 you have objects such as symmetric cream on Tenzer and so on, which encode geometry of spacetime. 127 00:12:22,610 --> 00:12:33,100 So you have to solve this equations in order to determine the metric of spacetime, given the distribution of masses and energy in space and time. 128 00:12:33,100 --> 00:12:36,650 All right. So this is this is what Ben Stein's equations are doing now. 129 00:12:36,650 --> 00:12:41,270 This is similar to Maxwell's equations, where you have also left one side and Right-Hand side. 130 00:12:41,270 --> 00:12:45,950 On the right hand side, you have distributional charges and currents in space and time. 131 00:12:45,950 --> 00:12:51,680 And on the left hand side, you have electric and magnetic field encoded in this for potential, Amy. 132 00:12:51,680 --> 00:13:00,830 So if you have if you know, distribution of charges and currents in space and time, then you can compute electric and magnetic fields produced. 133 00:13:00,830 --> 00:13:08,030 So this is sort of kailasam. Now the main hero in science equations is of course symmetric Denzel. 134 00:13:08,030 --> 00:13:16,270 And let me remind you what it is. Right. So we have for example, if I got a theorem in two dimensions of flat space and two dimensions, 135 00:13:16,270 --> 00:13:23,090 then if I got a theorem tells us how to compute infinitesimal distance between points, let's say B and C, just use. 136 00:13:23,090 --> 00:13:29,540 This can be written more generally because this is the quadratic form which which has the X squared UI squared. 137 00:13:29,540 --> 00:13:32,160 But no crust term gets the way more generally. 138 00:13:32,160 --> 00:13:37,490 You can write down the distance between two points and one general space, for example, curved space or a sphere. 139 00:13:37,490 --> 00:13:42,530 And see where you do have of the organon terms. And these old diagonal terms. 140 00:13:42,530 --> 00:13:51,510 Do you want one? You want to do two, one and so on. They are they can be written conveniently in the form of a metrics, the metrics of entries. 141 00:13:51,510 --> 00:13:59,720 Do you want one. Do you want to. And so on. And these entries can also depend on space and time so they can be local in space of time. 142 00:13:59,720 --> 00:14:04,020 In this simple example. Right. We have a diagonal metric. Very, very simple. 143 00:14:04,020 --> 00:14:11,990 One, two. By two metrics. Which is just a unit metrics. But of course, it can be far more non-trivial that these components dependent on Excel. 144 00:14:11,990 --> 00:14:17,990 So an example of a flat Mankowski space, of course, is a metric line element of which is given by this expression. 145 00:14:17,990 --> 00:14:24,290 And we have time here entering the game because this is special relativity, the minus sign list if you want. 146 00:14:24,290 --> 00:14:31,880 This is the contents of special relativity. In one line. Right. And we have time joining in the spatial directions. 147 00:14:31,880 --> 00:14:37,250 And this is just a metric of ordinary Euclidean three space. Written in circle words. 148 00:14:37,250 --> 00:14:44,720 Now let's come to the solutions of Einstein's equations. So on the right side, we have a spherical distribution of mass. 149 00:14:44,720 --> 00:14:49,910 Then the solution for the metric can be found to be found by Schwandt Grid in 1916. 150 00:14:49,910 --> 00:14:58,400 And this solution is written here. So you can see that it describes two spacetime outside of a spherical asymmetric distribution of mass. 151 00:14:58,400 --> 00:15:06,530 So if you put em to zero here, you see that you'll go back to Makowski technical skills, spacetime now. 152 00:15:06,530 --> 00:15:13,370 So this metric describes, for example, the good approximation spacetime around spherical, symmetric objects such as Earth. 153 00:15:13,370 --> 00:15:18,890 If you if you model Earth by way, circle by circle, symmetric body. 154 00:15:18,890 --> 00:15:27,500 Now what happens? So you may notice in this metric that you have this dangerous value of R of radios. 155 00:15:27,500 --> 00:15:33,330 Then this term here vanishes. And here you have a singularity because you have zero in the denominator. 156 00:15:33,330 --> 00:15:35,760 So this is known as the short shoot, Reynolds. 157 00:15:35,760 --> 00:15:42,370 Now, in most cases for use is completely harmless because, for example, for URF torture, Regulus is about one centimetre. 158 00:15:42,370 --> 00:15:47,640 Right. So this expression doesn't apply inside the bodies, only applies outside the body. 159 00:15:47,640 --> 00:15:56,790 So it's completely harmless. But if you have some powerful forces which take our earth and squeeze it into the little bowl of rate of Regulus, 160 00:15:56,790 --> 00:16:02,400 which is less than one centimetre, then it mentals. Of course, in this case you will get a black hole. 161 00:16:02,400 --> 00:16:08,730 So look, also very interesting objects. You can have, of course, neutral black holes like Schwarzschild one. 162 00:16:08,730 --> 00:16:13,800 You can add charge. So then you can have Reistad Nordstrom black hole. You see the method generalises. 163 00:16:13,800 --> 00:16:18,330 You have a charge here and you can have taken black holes that these black 164 00:16:18,330 --> 00:16:23,370 holes are rotated charge black holes which are known as Catton Human Bacall's. 165 00:16:23,370 --> 00:16:30,330 So that calls have a number of very interesting properties, mostly related to behaviour of their horizons. 166 00:16:30,330 --> 00:16:35,550 So that particular entropy in temperature can guess the shape of the black holes. 167 00:16:35,550 --> 00:16:39,540 That was done in 1970s by Bic and Stein, Corkin and others. 168 00:16:39,540 --> 00:16:46,500 And I'd refer you to a wonderful dog by a John Chocho in one of the Saturday mornings devoted to entropy, 169 00:16:46,500 --> 00:16:55,200 where he explains in full detail why it is reasonable to assign it to assign entropy to do it to a black hole. 170 00:16:55,200 --> 00:17:02,490 So Hawking showed that the black holes in mitigation at the quantum level and therefore one can associate temperature with them. 171 00:17:02,490 --> 00:17:11,130 And moreover, so you can look at Expression's first watch and look how black holes, for example, Templeton Temperature will contain H Bar here. 172 00:17:11,130 --> 00:17:15,650 Right, for example, for a solar mass black hole. This temperature is fifty nine Kelvin. 173 00:17:15,650 --> 00:17:22,290 So it's very, very small. Now the entropy on the other hand is gigantic because it has a bar denominator. 174 00:17:22,290 --> 00:17:26,320 And you can, you can do a little exercise and compute. What's the answer. 175 00:17:26,320 --> 00:17:35,610 It, for example of a sort of mass black hole is gigantic. Moreover, these people like Hawking, but Carter and others, 176 00:17:35,610 --> 00:17:40,530 they established that the loss of black hole mechanics are actually similar or 177 00:17:40,530 --> 00:17:44,520 in fact identical up to the definition of letters to the loss of black hole, 178 00:17:44,520 --> 00:17:51,870 of the loss of ordinary thermodynamics. So, for example, there's a field which says up the horizon area is not decreasing function of time, 179 00:17:51,870 --> 00:17:56,790 but we have second law of thermodynamics, which says that to antibusing not decreasing the function of time. 180 00:17:56,790 --> 00:18:04,710 And as in science adjusted entropy and horizon, are related by this Formula One water horizon area. 181 00:18:04,710 --> 00:18:12,310 And therefore, this resembles. So these laws of liquid mechanics, the they actually are the laws of black hole. 182 00:18:12,310 --> 00:18:16,360 But I'm a mixed equilibrium. So this is all equilibrium. 183 00:18:16,360 --> 00:18:25,670 That's fine, but now we would like to see what happens beyond beyond black hole from the 90s, beyond equilibrium state. 184 00:18:25,670 --> 00:18:30,000 Now, we can consider an analogy. 185 00:18:30,000 --> 00:18:35,740 Right, so so suppose we have a normal system conducting sphere placed in an external electromagnetic field, 186 00:18:35,740 --> 00:18:40,370 so external electro magnetic field will disturb this sphere from equilibrium. 187 00:18:40,370 --> 00:18:46,100 It will use surface currents on riskier items and these surface currents can be computed. 188 00:18:46,100 --> 00:18:49,910 This is a rather simple undergraduate problem, a problem in electromagnetism. 189 00:18:49,910 --> 00:18:56,210 You can computer surface currents given the external fuel, and you will see that they obey the law. 190 00:18:56,210 --> 00:19:03,050 The current proportional to the external field with conductivity, which is a which is the coefficient of proportionality. 191 00:19:03,050 --> 00:19:08,460 Now it's important to understand, but we only used to solve this problem. We don't care about microscopic carrier. 192 00:19:08,460 --> 00:19:15,470 So this charged atmosphere sphere, we only care about Maxwell's equations and also bounded conditions on fields. 193 00:19:15,470 --> 00:19:20,990 So let's now do the same with black holes. Take a black hole and place it in an external electromagnetic field. 194 00:19:20,990 --> 00:19:28,610 That was done in the 70s by these people. And then you can it's convenient, introduced the concept of so-called stretch horizon, 195 00:19:28,610 --> 00:19:34,130 which is a time like surface just outside the usual truth event horizon. 196 00:19:34,130 --> 00:19:38,060 So what was discovered was that if you do this, 197 00:19:38,060 --> 00:19:46,010 then a black hole or of a stretch horizon also has induced currents and they behave according to Ohm's Law. 198 00:19:46,010 --> 00:19:50,390 And moreover, you can computer conductivity sigma or resistance or the black hole. 199 00:19:50,390 --> 00:19:58,100 And it turns out that the resistance of black hole. So you combine so basically yourself, Maxwell's equations in Kirks Spacetime close to the horizon. 200 00:19:58,100 --> 00:20:02,960 And what comes out is that the black hole can be viewed as an omic resistor Islamic 201 00:20:02,960 --> 00:20:08,300 conductor with a surface resistance of three hundred and seventy seven ohm or square. 202 00:20:08,300 --> 00:20:13,310 So this unit is typical Forfend Foyles in the thin films. 203 00:20:13,310 --> 00:20:19,850 You can compare with different systems like metal foils or silicon, which have similar numbers. 204 00:20:19,850 --> 00:20:27,080 So this is rather exotic. You can do more. You can take a black hole and place it in an external gravitational wave. 205 00:20:27,080 --> 00:20:31,280 Gravitational waves does too. Typical medium, right? So it passes through this medium. 206 00:20:31,280 --> 00:20:34,340 It distorts. It's a medium. It creates strain and stresses. Right. 207 00:20:34,340 --> 00:20:39,860 And therefore it is a good laboratory to measure response of your body door to its external influence. 208 00:20:39,860 --> 00:20:46,100 And the response typically in terms of fluid dynamics quantities is given by viscosity. 209 00:20:46,100 --> 00:20:50,180 So people computed shear in bulk viscosity or fortunate black holes. 210 00:20:50,180 --> 00:20:57,860 And it is proportional to each bar. Both of them. And if people bought it at time to divide shear viscosity by the entropy density, 211 00:20:57,860 --> 00:21:04,010 they would discover that this ratio is equal to a one of a four by in Planck units. 212 00:21:04,010 --> 00:21:10,220 So we learnt that black holes have properties of the physical medium such as conductivity and viscosity. 213 00:21:10,220 --> 00:21:14,540 Well, this can be embedded in the holographic principle, the holographic principle. 214 00:21:14,540 --> 00:21:20,810 So again, I emphasise that in gravitational systems we have entropy vicious proportional to the area. 215 00:21:20,810 --> 00:21:27,300 Let's say of a black hole horizon, not the volume of a black hole as it would be in the normal, for example, ideal gas. 216 00:21:27,300 --> 00:21:35,840 So it is proportional to volume. So this is manifestation of the holographic principle which says that the gravitational degrees of freedom. 217 00:21:35,840 --> 00:21:41,210 Indeed, dimensions are effectively described by a non gravitational theory. 218 00:21:41,210 --> 00:21:51,640 Indeed, minus one dimension. So now I will give you a very brief introduction to string theory engaged in duality and holography in one's life. 219 00:21:51,640 --> 00:21:57,760 So this slide is a picture which was used by Ludvik Einstein in 1953. 220 00:21:57,760 --> 00:22:03,070 In his philosophical discussions. But we use it for gauging biology. 221 00:22:03,070 --> 00:22:07,540 So you have an object which can be described in different languages. 222 00:22:07,540 --> 00:22:11,260 If you look at the vertical. Right. So this looks this resembles a duck. Right. 223 00:22:11,260 --> 00:22:18,100 So you describe this object as a duck. If you tilt your head and look at it from the left, you will see a rabbit. 224 00:22:18,100 --> 00:22:22,060 So you describe this object in terms of a rabbit, but it is the same object. 225 00:22:22,060 --> 00:22:26,620 You can't say it is rabbit or duck apriority. It depends on on. On this point of view. 226 00:22:26,620 --> 00:22:34,380 So there must be a dictionary between language of rabbit and language of duck, which describes the same object because the object is the same. 227 00:22:34,380 --> 00:22:40,030 Right. So this dictionary between the two languages is called duality in general and 228 00:22:40,030 --> 00:22:44,890 misapplied also to calligraphic duality in holographic duality and string theory. 229 00:22:44,890 --> 00:22:51,940 You have an object, a collection unperturbed, a collection of like brains, and it can be described in two languages, rabbit or duck. 230 00:22:51,940 --> 00:22:55,870 It can be described as open string picture and closed in picture. Right. 231 00:22:55,870 --> 00:23:02,140 And then in language of open think bisher or language or a floating picture. 232 00:23:02,140 --> 00:23:06,040 And that is a quantitate. So. This is not philosophy anymore. 233 00:23:06,040 --> 00:23:11,380 That is a quantitative dictionary between these two languages which allow you to calculate 234 00:23:11,380 --> 00:23:16,330 quantitatively properties of this object in one language or the other language, 235 00:23:16,330 --> 00:23:26,800 depending on your convenience. Now, what is fundamentally important is that when one language, when one theory, one description is strongly coupled. 236 00:23:26,800 --> 00:23:30,240 So you don't know how to calculate. You cannot apply perturbation fuelled enough. 237 00:23:30,240 --> 00:23:36,190 Everything fails. Then the other language is weakly coupled where you can happily calculate everything. 238 00:23:36,190 --> 00:23:42,760 So if you know the dictionary, you can any you're interested in, for example, formalisation of the system on the left. 239 00:23:42,760 --> 00:23:47,900 You can happily methods into biblically coupled system and calculate every quantity you need. 240 00:23:47,900 --> 00:23:51,880 Right. So that's that's a wonderful think correspondence which we will apply. 241 00:23:51,880 --> 00:23:56,770 So in particular. So you have black holes which are doable to not gravitation and degrees of freedom. 242 00:23:56,770 --> 00:24:03,310 Now black holes. So every system in equilibrium, a typical system is characterised by a number of concert charges. 243 00:24:03,310 --> 00:24:10,820 And we also know that if we perturb a not long gravitational system, such as a spinning pendulum here from equilibrium, 244 00:24:10,820 --> 00:24:16,340 it will typically oscillate with some eigen frequency, its normal balls. That will kind of a collection of normal modes in this case as normal. 245 00:24:16,340 --> 00:24:20,770 What is very simple here. So what happens with the hole if you perturb the call out of equilibrium? 246 00:24:20,770 --> 00:24:24,520 Well, we have what's happened. So the black hole will oscillate. 247 00:24:24,520 --> 00:24:26,170 It will emit gravitational weights. 248 00:24:26,170 --> 00:24:33,460 So these are normal modes of black holes known as the quite normal modes because they have non-zero imaginary parts. 249 00:24:33,460 --> 00:24:38,470 And then zero imaginary part emerges because of the presence of the black hole horizon. 250 00:24:38,470 --> 00:24:42,940 So. Well, we know. Suppose we can compute go to eat well relatively easily. 251 00:24:42,940 --> 00:24:46,450 We can compute the spectrum in quite normal spectrum of these black holes. 252 00:24:46,450 --> 00:24:51,520 But the holographic principle tells us that this is mapped one to one in two 253 00:24:51,520 --> 00:24:57,190 non equilibrium properties of a dual non gravitational quantum field theory. 254 00:24:57,190 --> 00:25:02,920 So in particular, that is the regime in this theory, which is described by hydrodynamics. 255 00:25:02,920 --> 00:25:05,980 So I mentioned this diffusion equations and so on, so forth. 256 00:25:05,980 --> 00:25:12,980 And this is quantitatively mapped into the spectra, into the quite normal spectra of a dual lieke hopes. 257 00:25:12,980 --> 00:25:16,080 Right. So therefore, you can compute. 258 00:25:16,080 --> 00:25:22,690 So, for example, in the language of hydrodynamics you have in your system, you have excitations such as sound waves. 259 00:25:22,690 --> 00:25:26,560 So these are quite the particles in every hydrodynamics system. You have sound. 260 00:25:26,560 --> 00:25:32,230 And you have dispersion. The relation for the sound which is given by this equation here, you have speed of sound. 261 00:25:32,230 --> 00:25:35,950 And then you help Duncan off sound waves characterised by viscosity. 262 00:25:35,950 --> 00:25:43,270 So this is all mapped in holography into the Igen spectrum of black holes of dual black holes. 263 00:25:43,270 --> 00:25:45,390 And here is a genuine calculation, right. 264 00:25:45,390 --> 00:25:53,170 So this expression is one of these Igen frequencies off if high dimensional Doyel black hole Deuel to this wonderful FURI system. 265 00:25:53,170 --> 00:26:00,190 So you can just compare a term by term and read off from comparison of these two two expressions. 266 00:26:00,190 --> 00:26:06,220 For example, that the speed of sound, speed of sound v is speed of light divided by Squirtle the free. 267 00:26:06,220 --> 00:26:10,270 And then you can also read of the ratio of share is context to entropy density. 268 00:26:10,270 --> 00:26:18,880 By comparing these two terms and the ratio of eight to all the rest happens to be exactly as expected from these old considerations of 1970s. 269 00:26:18,880 --> 00:26:23,540 You can go beyond that and directly relate them, get Stokes equations and Einstein's equations. 270 00:26:23,540 --> 00:26:28,940 So this is known as a fluid gravity co-respondents. Now, more and more. 271 00:26:28,940 --> 00:26:35,550 So a development of last years is concentrated on understanding the so-called unreasonable 272 00:26:35,550 --> 00:26:40,290 effectiveness of hydrodynamics because it turned out by studying the systems. 273 00:26:40,290 --> 00:26:46,380 So it's a very effective tool to study systems which are strongly coupled and can not be studied by normal means, 274 00:26:46,380 --> 00:26:56,490 such as kinetic theory and similar protractive technique. So what it revealed is a very surprising fact that quite often you can have 275 00:26:56,490 --> 00:27:02,550 hydrodynamics working perfectly well before local thermal equilibrium is established. 276 00:27:02,550 --> 00:27:07,430 So a new term was coined, which is hydra minimisation, not formalisation. 277 00:27:07,430 --> 00:27:11,130 So you don't wait until you have local thermal equilibrium. You'll have your stocks. 278 00:27:11,130 --> 00:27:14,970 Equations are perfectly fine. So it's an open area of research. 279 00:27:14,970 --> 00:27:21,300 So one of them is also shown here. So, for example, you want so you have a dispersion relations for the sound mode. 280 00:27:21,300 --> 00:27:29,190 As I mentioned on the previous slide. And suppose you want to understand the limits of limits of hydrodynamic description, namely, 281 00:27:29,190 --> 00:27:34,050 when does the serious convergence and divergence rates of the series anything serious? 282 00:27:34,050 --> 00:27:39,390 Right. So you want to find the triggers of convergence. So you by making this do a dual black hole spectra. 283 00:27:39,390 --> 00:27:47,820 You can do it rather easily. To do this, you have to consider the expectations of black holes at complex values or spatial momentum. 284 00:27:47,820 --> 00:27:54,840 And then you see, this is an interesting connexion to the algebraic curves because you see the breakdown of perturbation theory happens. 285 00:27:54,840 --> 00:27:59,670 Then here in this region, you encounter a non hydrodynamic degree of freedom. 286 00:27:59,670 --> 00:28:03,810 And this, in algebraic kolff sense means that we start to break curves, opens up. 287 00:28:03,810 --> 00:28:08,070 You see this red star here and you have opening up of this curve. 288 00:28:08,070 --> 00:28:12,270 And this limits the limits, the applicability of hydrodynamics. 289 00:28:12,270 --> 00:28:15,120 So the radius of convergence actually is finance. 290 00:28:15,120 --> 00:28:23,190 And you can actually computed in a particular theory which has its gravity Duell description, which is quite, quite a remarkable thing, I believe. 291 00:28:23,190 --> 00:28:32,100 All right. You can also you can also think of how the domain of applicability of hydrodynamic description depends on coupling, 292 00:28:32,100 --> 00:28:37,170 because you can have systems which are strongly interacting. You can have systems that should be clean. 293 00:28:37,170 --> 00:28:41,760 So there are not hydrodynamic supplies uniformly for all to Coplin value. 294 00:28:41,760 --> 00:28:47,280 That's that's that's a question that I saw in in this holographic the fiscal aglukkaq tools. 295 00:28:47,280 --> 00:28:51,900 You can find the answer to this question. The answer is no. No, that's not uniform. 296 00:28:51,900 --> 00:28:57,030 You can have dependents. You'll have dependence on the applicability of hydro, which varies. 297 00:28:57,030 --> 00:29:02,700 And if coupledom. So it's actually so hydro is more actually applicable according to this graph, you see. 298 00:29:02,700 --> 00:29:12,330 So hydro is more applicable in green domain. When you have a strongly interacting system, when then then the ability at Origin to be couplet. 299 00:29:12,330 --> 00:29:20,610 So this is one of the examples of how it's a little bit if you helped generically to understand the behaviour of fluid dynamical systems. 300 00:29:20,610 --> 00:29:29,310 So let me come to let me come to conclusions. So we have seen that black holes have entropy and temperature. 301 00:29:29,310 --> 00:29:36,270 And in equilibrium, they behave like thermodynamic systems. And we think we understand why, because of this holographic principle, 302 00:29:36,270 --> 00:29:41,060 it simply means that we know what the microscopic degrees of freedom are, which equilibrate. 303 00:29:41,060 --> 00:29:48,870 Right. These are microscopic degrees of freedom expressed in this language of non gravitational theory duel to a particular black hole. 304 00:29:48,870 --> 00:29:57,690 Now out of equilibrium horizon. So black holes exhibit fluid like properties which were described by membrane paradigm in 1970s sunlight in ages. 305 00:29:57,690 --> 00:30:02,660 But now the work of black hole physics has led to his discovery of gauging duality. 306 00:30:02,660 --> 00:30:08,010 A little bit of few. Yes. If you correspondence or a dark duality. Because it's like that. 307 00:30:08,010 --> 00:30:15,780 So let's call for an anaemic said membrane paradigm for a now fully embedded into this modern Lenn virtual holographic. 308 00:30:15,780 --> 00:30:22,500 Now we also talked about Igen, multiple black holes. And we know that they used very extensively. 309 00:30:22,500 --> 00:30:28,230 So this is very active area of research to study formalisation and discovered a new 310 00:30:28,230 --> 00:30:33,540 phenomena such as Heidrun accusation and hydrodynamic actors and all this stuff. 311 00:30:33,540 --> 00:30:37,800 It's it's really it's really quite fascinating because holography. 312 00:30:37,800 --> 00:30:46,140 So sometimes you may think of these I theory holography. Calculations that completely obstruct them kind of out of touch with real life goes on. 313 00:30:46,140 --> 00:30:57,180 But at least one good use of this is that what this is, is that it inspired new research into fundamentals of fluid dynamics. 314 00:30:57,180 --> 00:30:59,620 So you might have thought that all fluid dynamics is oil. 315 00:30:59,620 --> 00:31:04,620 Its its 18th century, 19th century, your stocks and everything is known that it's not the case. 316 00:31:04,620 --> 00:31:10,980 So fundamental. So people who were doing this. These these this research and in the photography and so on, 317 00:31:10,980 --> 00:31:18,420 they're actually looking at fundamentals of the very basics, of a formulation of kind of mix of applicability, 318 00:31:18,420 --> 00:31:24,360 range of how to theoretically establish was so inspired by hello, 319 00:31:24,360 --> 00:31:30,450 what if you choose to create an image has been recently rewritten to deal with problem of causality. 320 00:31:30,450 --> 00:31:35,730 This is one one one one simple example with possible applications in astrophysics. 321 00:31:35,730 --> 00:31:41,010 So this was this was done really in essentially last year to fall the full extent. 322 00:31:41,010 --> 00:31:52,200 So let me finish with one. One of the marks or in in the in the Soviet Union and in Russia amongst physicists, there was this brutal criterium. 323 00:31:52,200 --> 00:32:04,260 It's a bit of a joke, of course, but but still a brutal criterium of when the work of a physicist is it is actually is actually meaningful. 324 00:32:04,260 --> 00:32:08,310 And the criterium is the following. If in your life's work, 325 00:32:08,310 --> 00:32:14,460 you managed to add at least one line to the Orlando edition stand watch from terms of the 326 00:32:14,460 --> 00:32:20,160 ten volumes of the course of theoretical physics or maybe change one equation there, 327 00:32:20,160 --> 00:32:24,960 then then then it is it is it is something meaningful. You have done something right. 328 00:32:24,960 --> 00:32:35,460 So let me just finish by saying that what is happening now in foundational foundations of new dynamics is very much of this Colaba, 329 00:32:35,460 --> 00:32:42,660 because certain things in London Revolutions Vol. six will have to be amended because of this work. 330 00:32:42,660 --> 00:32:46,980 And I'm quite happy to report this, at least in philosophical terms. 331 00:32:46,980 --> 00:32:56,110 Thank you very much. I will also Prussia's. And Sondre, can you on share your screen? 332 00:32:56,110 --> 00:33:01,050 Yes. Hi. Thank you. Great. 333 00:33:01,050 --> 00:33:02,760 So we got some questions for you. 334 00:33:02,760 --> 00:33:10,920 First of all, in terms of recommending a book, Neil Smith asks, can you recommend a book primer so people can learn more about this? 335 00:33:10,920 --> 00:33:14,730 Yes, I just so did the book. 336 00:33:14,730 --> 00:33:19,840 The book on holography or the book on. So, yes, there are, actually. 337 00:33:19,840 --> 00:33:30,210 And so if they're talking about this specific applications of holography to hydrodynamics, that is a book which actually one of the offers. 338 00:33:30,210 --> 00:33:37,720 So it's a it's a it's a collection of offers. And one of them was actually a Royal Society fellow here in Oxford. 339 00:33:37,720 --> 00:33:41,700 Haha carful that is Olenna. Now he is a faculty in Barcelona. 340 00:33:41,700 --> 00:33:50,910 So I believe it's probably easier for me to write and chat, to be exact to the exact title and everything as a reference helps. 341 00:33:50,910 --> 00:33:55,560 But yes, I can, I can recommend some. Yes. Right. 342 00:33:55,560 --> 00:34:03,890 So Professor Taylor has recognised the and seventy seven items as the impedance of free space. 343 00:34:03,890 --> 00:34:11,250 So why did we end up with that number and what does the black hole contribute? 344 00:34:11,250 --> 00:34:16,160 I don't know if so, it's I mean, 345 00:34:16,160 --> 00:34:27,690 the free 77 is the outcome of the of the equations that the meaning of this is not entirely clear because I didn't mention this, 346 00:34:27,690 --> 00:34:31,800 but so I said that it is embedded in two. Hello, kind. 347 00:34:31,800 --> 00:34:34,290 It's understood why we have these properties. 348 00:34:34,290 --> 00:34:45,100 But there is one sticky here that 377 comes for water shoots, black holes which are simple, logical, deflect and flush. 349 00:34:45,100 --> 00:34:50,820 What should black holes in this in life? Flat space. We don't have a graphic description. 350 00:34:50,820 --> 00:34:56,370 You might have noticed that bulk viscosity of black hole is negative. 351 00:34:56,370 --> 00:35:02,490 So difficult business is this is a sign that your system is unstable and indeed ordinary. 352 00:35:02,490 --> 00:35:07,110 Swash a black hole in some particular flat space is unstable. Get the [INAUDIBLE] irrigation. 353 00:35:07,110 --> 00:35:11,340 So it has negative specific heat also. Right. So this is for this system. 354 00:35:11,340 --> 00:35:15,570 We don't have a full and graphic description in terms of a stable quantum field theory. 355 00:35:15,570 --> 00:35:26,880 And so this free 77. At least at the moment, it's not entirely clear what what meaning you could you could you could assign to this. 356 00:35:26,880 --> 00:35:33,070 However, the ratio of shear viscosity to entropy density happens to be universal for all horizons, so-called black holes. 357 00:35:33,070 --> 00:35:36,230 So this is a universal statement, which is extremely powerful. 358 00:35:36,230 --> 00:35:42,750 So in particular, regardless of whether or not you have some particular flatback black hole or some politically ADF black hole, doesn't matter. 359 00:35:42,750 --> 00:35:52,690 So this ratio stands stays to be it wonderful by. So Stephen Burke asks, does the black hole duality have any consequences? 360 00:35:52,690 --> 00:36:02,680 Two things we can observe about actual black holes. Probably not, except that. 361 00:36:02,680 --> 00:36:07,120 So because so these are not astrophysical astrophysical objects. 362 00:36:07,120 --> 00:36:12,070 So like a mentioned eye clock and temperature, for example, is in typical these Allama to kill them. 363 00:36:12,070 --> 00:36:18,940 So it's not something that you could easily, easily observe. Now, what may happen is that form. 364 00:36:18,940 --> 00:36:27,550 So this duality of these holographic considerations, apart from clarifying the fundamental so hydrodynamics percent, 365 00:36:27,550 --> 00:36:38,200 they can also help for understanding primordial black holes and behaviour of of of a universe right after the big bang. 366 00:36:38,200 --> 00:36:46,180 Because there it's quite likely that gravity it is actually contains a number of terms beyond eyesight. 367 00:36:46,180 --> 00:36:47,200 But it's gravity. 368 00:36:47,200 --> 00:36:54,490 And by using this technique, you can actually maybe predict something about the spectrum of gravitational primordial gravitational waves. 369 00:36:54,490 --> 00:37:00,900 But this is for the future, because, of course, at the moment we cannot we cannot detect primordial gravitational waves. 370 00:37:00,900 --> 00:37:12,300 And I would take the second question from John Kettler next, so so can you explain what exactly you mean by the spectrum of a black coal? 371 00:37:12,300 --> 00:37:22,500 Yes. So the spectrum of black hole is philosophical, is no different from Igen mould to normal moles of any, let's say, mechanical system. 372 00:37:22,500 --> 00:37:24,960 Right. So I have I have a system here. Right. 373 00:37:24,960 --> 00:37:32,960 So this system has this system has a number of Igen modes, which in principle you can you can calculate like classical mechanics. 374 00:37:32,960 --> 00:37:37,170 Right. So. So black holes are classical objects, a particle, whole congregation. 375 00:37:37,170 --> 00:37:40,890 So they are solutions of classical theory of gravity or Einstein's theory of gravity. 376 00:37:40,890 --> 00:37:46,070 And what you can do, like with any other object, you take equilibrium values, for example, 377 00:37:46,070 --> 00:37:50,190 Solutia equilibrium solution, Stine's equations, and you perturb it a little bit. 378 00:37:50,190 --> 00:37:55,440 So you have Method Jimeno. And then you have a small filtration plus Delta germanium. 379 00:37:55,440 --> 00:38:02,460 And you solve Einstein's equations. You'll lead linear ice them and you find the spectrum of linear ice, Einstein's equations. 380 00:38:02,460 --> 00:38:08,610 All right. So this becomes a boundary problem similar to classical mathematical physics of 19th century, 381 00:38:08,610 --> 00:38:11,840 except that it is known for emission because of the presence of a phrasal. Right. 382 00:38:11,840 --> 00:38:16,500 So this is a classical Igen Moltz pretty much like this in the Sphinx. 383 00:38:16,500 --> 00:38:26,760 Right. So then Jonathan Digest's, is there an intuitive picture for how a hydrogen nemi description can work without local civilisation? 384 00:38:26,760 --> 00:38:35,010 Is it just because the system is so strongly coupled that you can still get collective behaviour without the centralisation? 385 00:38:35,010 --> 00:38:41,330 Yeah, this is a very good question. The honest answer to this is we don't know at the moment. 386 00:38:41,330 --> 00:38:45,800 In fact, as I mentioned, this is a pretty, pretty active area of research. 387 00:38:45,800 --> 00:38:49,670 What people discovered is so you see a lot in normal systems. 388 00:38:49,670 --> 00:39:00,630 Usually it's very hard to detect how the system actually formalises if you don't have paternity of access to the degrees of freedom which caused this. 389 00:39:00,630 --> 00:39:09,890 This formalisation right now in holographic systems, we are blessed with this dictionary so we can actually access this and see how the system. 390 00:39:09,890 --> 00:39:17,390 So what happened? So. So basically, you take you take a local, local, local density of so take this energy momentum. 391 00:39:17,390 --> 00:39:22,190 Tons of components. Right. Which in equilibrium, for example, components not long. 392 00:39:22,190 --> 00:39:26,360 Zero zero becomes equilibrium. Energy density. 393 00:39:26,360 --> 00:39:31,640 But long before equilibrium happens. And I'm not talking global equilibrium, but local equilibrium. 394 00:39:31,640 --> 00:39:37,160 Long before that. This same quantity. You can write down equations of motion for this, right. 395 00:39:37,160 --> 00:39:42,020 In kinetic theory. If you were able to solve the loop of chain completely, you y chain. 396 00:39:42,020 --> 00:39:46,790 Then it would be the analogue right in holography, helpful gravity. You can do it rather easily. 397 00:39:46,790 --> 00:39:50,510 Or you can put it on a computer. It's probably usually just easier to assimilate. 398 00:39:50,510 --> 00:39:54,080 So what people discovered it and that that was discovered in the last five years. 399 00:39:54,080 --> 00:40:01,190 So they discovered that that in these divinities degrees of freedom, you have so-called hydatid than mean contracts. 400 00:40:01,190 --> 00:40:06,440 So all behaviour, regardless of initial conditions and you start off to start with, 401 00:40:06,440 --> 00:40:12,200 you have trajectories attracted to one curve in dynamical space and the face space. 402 00:40:12,200 --> 00:40:19,580 And this curve is stable and attractive by definition is something where, you know, which is which is which is extremely robust. 403 00:40:19,580 --> 00:40:23,870 So this attractor is the answer. It's not maybe intuitive answer. 404 00:40:23,870 --> 00:40:27,250 But it is the best answer we have at the moment of why hydrogen, 405 00:40:27,250 --> 00:40:33,740 any kind of demonstration or hydrodynamic behaviour happens even before local equilibrium. 406 00:40:33,740 --> 00:40:39,020 It definitely happens at the local equilibrium, that's for sure. But the surprise was that it actually happens before. 407 00:40:39,020 --> 00:40:44,960 And this is an active, active area of research. And so one last question. 408 00:40:44,960 --> 00:40:50,060 Andre Alexis Hughes IV. Could this work on black holes? 409 00:40:50,060 --> 00:40:59,120 Give us could the work on black holes. Give us any hints on what settings to put into the particle accelerator that we heard about earlier? 410 00:40:59,120 --> 00:41:07,340 Yes, definitely. In fact, one of them is is used very extensively for the last 10 to 15 years. 411 00:41:07,340 --> 00:41:17,120 And this is the ratio of share viscosity to an entity. So for Khushi game, we don't have a holographic duel, 412 00:41:17,120 --> 00:41:23,570 but we do have holographic doors for systems which are quite similar to CCD in terms of hydrodynamic behaviour. 413 00:41:23,570 --> 00:41:27,970 And about 20 years ago, by a holography, 414 00:41:27,970 --> 00:41:36,620 the ratio of sheer viscosity to entropy density was computed and it was established that it was universal for all systems which have is gravity duels. 415 00:41:36,620 --> 00:41:41,180 So what community, the Asian community to work in working on these matters? 416 00:41:41,180 --> 00:41:46,850 What they're using now is a benchmark for all of these simulations of your stocks and KBI collisions. 417 00:41:46,850 --> 00:41:51,380 Is the value given by holography each bar? Over for you, Kate Bolduan. 418 00:41:51,380 --> 00:41:55,310 This is a standard entry, which is which is which is already used. 419 00:41:55,310 --> 00:42:01,220 And there are other examples, but this is probably the most prominent one. Thank you. 420 00:42:01,220 --> 00:42:10,160 If people have further questions, they can ask them to the speakers in the breakout rooms because we hope you will now join us in the breakout rooms. 421 00:42:10,160 --> 00:42:18,290 The way this works is that there's a new You Are Out, which is in the email Michelle sent you on, which I've also put into the chat. 422 00:42:18,290 --> 00:42:28,190 So you need to log on to that newsroom place and then you can hopefully move yourself into the right room when you arrive. 423 00:42:28,190 --> 00:42:33,050 You should see a breakout room icon on the list of icons at the bottom. 424 00:42:33,050 --> 00:42:41,850 And this is the thing with Foursquare's. If you click on that, you'll get a list of rooms on who is in them and you can join the one you want. 425 00:42:41,850 --> 00:42:47,430 And Michelle and I will be around to try and rescue anybody who's lost in cyberspace. 426 00:42:47,430 --> 00:42:55,910 It would be great if you could stick to about six people in each room so we don't get overcrowding anywhere. 427 00:42:55,910 --> 00:43:03,380 So what remains to me is to say thank you very much to the speakers this morning, to Steve and Bruno and Andre, 428 00:43:03,380 --> 00:43:09,740 who've taken a great deal of time, first of all, to find jackets and ties for the first time for about six months. 429 00:43:09,740 --> 00:43:16,880 And, of course, to prepare these these talks, it's hard giving talks on Zoome. 430 00:43:16,880 --> 00:43:21,630 And it was great and interesting. And thank you very much. Deeper. And Andre. 431 00:43:21,630 --> 00:43:24,610 I also want to say thank you very much to Michelle Bosher to Michelle, 432 00:43:24,610 --> 00:43:32,380 who's put all this together and has done all the e-mailing and has worked out how this thing works and things like that got copses all organised. 433 00:43:32,380 --> 00:43:39,430 Thank you, Michelle. So I'll sign off now. Thank you very much for joining us and hope to see you in a minute. 434 00:43:39,430 --> 00:43:44,766 In these breakout rooms. Goodbye.