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Welcome back to The Talk of the Morning, which is from Professor Andre Star, next.
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Andre got his undergraduate degree at Moscow State University and then pitched it New York
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University and then had postdocs and fellowships in the states at CERN in Canada and Southampton.
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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.
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Andre is from the particle physics group and he's interested in the application
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of string theory to quantum field theories and in particular in philosophy.
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And he's going to explain to us what to Locher fears. So thanks, Andre.
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Over to you. Thank you very much.
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So look me for a screen. And hopefully.
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If you could just confirm it when you don't get on Lowden's. Good.
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Thank you, everybody, for joining. So we'll talk a little bit about a slightly more exotic complications for hybrid of Lennix,
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which is fluid gravity, duality and hydatid mimics mix of black holes.
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So here is the outline of a book. We'll discuss a little bit relativistic, kind of mimics the foundations.
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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.
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And I will also remind you about black hole thermodynamics. Then we'll discuss what happens if you perturb black holes, all equilibrium.
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So out of equilibrium are described by a so-called black hole membrane paradigm.
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And I will discuss this in some detail.
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And then we will embed all of all this picture into the modern sort of modern theoretical framework, which is known as holographic duality.
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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,
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as I Stine's equations of general relativity close to the horizon. So black holes.
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And we will finish by discussing some recent gravity inspired new advances in the relativistic hydroponics.
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So relativity credit remix is necessary when fluids and gases move of speeds,
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which are comparable to the speed of light in such situations, are not so uncommon.
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As Steve already mentioned in his stock. So first of all, of course, we have multiple applications in atavistic astrophysics,
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in particular, if accretion disks, black holes and stars and so on.
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But also here in URF, if you have high energy cosmic rays which are coming to Earth and striking the ordinary mantra,
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we produce zillions of particles and particles behave that in anemically.
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And they are described. His behaviour is described by relativistic hydrodynamics, as was shown by Fantome and Landow in 1950s.
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You can also do artificial experiments here on Earth in accelerators such as Rukun.
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LHC is also Steve mentioned in his first stock. Then you create the so-called coagulant plasma.
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And choirgirl plasma is a quantum strongly interacting fluid.
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So it is described by relativistic hydrodynamics, but not by kinetic fury.
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So this is sort of a rather interesting object to study. So in relativistic domain, we have new features.
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Again, Steve already mentioned this. But let me mention this again. So energy, momentum and mass are no longer separate quantities.
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They are tied together by formulas like this, one of which, of course, is equal terms.
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Two squared is the simple limit. But we also have momentum in the game.
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In more general. Second, and therefore it makes sense to go to different variables.
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So do not consider density of mass alone because mass can be converted to energy and vice versa.
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But to consider instead energy density as a basic variable and momentum density and as often happens in special relativity,
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you have to recast all these objects into four dimensional language,
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into the language of Mankowski spacetime, where every object will have four components.
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So here you have the object, which is known as the energy momentum denser in which the package is energy density and momentum density.
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And you have these indices, A and B running from zero to three as appropriate and special relativity.
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Another point in the relativistic systems is that the number of particles is no longer conserved.
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Right. For the same reason as this formula shows that you can if you have enough energy,
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you can create zillions of particles out of vacuum, particle antiparticle pairs.
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And so it doesn't make sense to talk about conserved quantity, which is a number of particles.
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But we can have other conserved quantities in the game, such as the only charge left on charge.
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And they are really concerned, but they have to be written in four dimensional language of special relativity.
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And so the main hero here, it would be the density of some sort of charge, for example.
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But you take charge and then the other components, the components of the current X, G,
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Y and Jay Z are tied together to this density of conserved charge in the conservation equation, which again,
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in four dimensional language, can you simply read them as a forward divergence of this for current J and conservation of origin,
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momentum is presented by the conservation of TAAB in the following equation here.
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So these are the conservation laws in the relativistic domain and these are the main building blocks of hatred of Lennix relativistic domain.
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So let me remind you again about foundations of hydrodynamics. Right?
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So if you wait, so suppose you have a system of two Mystikal, not many, many, many, many constituents.
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If you wait long enough, the system equilibrate, hopefully.
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Again, this is not guaranteed. But in most systems, we observe the equilibration.
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If you wait long, long for a long, long time, just before this equilibration on very large scales of space,
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the system will be characterised by time and space dependent densities of conserved charges.
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Because in thermal equilibrium, when you wait for infinity right for eternity,
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it is characterised by globally conserved charge of just a handful of globally conserved churches in thermal equilibrium.
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So if you just make one step back in time before everything has the calibrated,
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you will see that these conserved churches acquire dependence on space and time.
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But still, there are just handful of disconcert churches. Right.
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But these densities of conserved churches are the main fundamental degrees of freedom of hydrodynamic description.
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So this is this is the the key the key assumption, if you want,
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because it's sometimes very hard to derive either description from from fundamental principles such as Latron Children Donnell's.
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You can do it with kinetic beauty, but not a every fluid has a kinetic description.
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Of course, this is so. So let me add a little bit more to that.
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So we have fundamental degrees of freedom, which are densities of contempt charges.
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Now, what about the equations of motion? For me is density is often surcharges.
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So equations of motion come from conservation laws and the so-called constitutive relations.
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So let me explain. This is very simple example of the consideration of a charge.
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So suppose because you want to charge rent, but when a charge in four dimensions,
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the conservation law, as I mentioned earlier, is just a forward divergence equal to zero.
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So this is a microscopic law which holds all this. Now, but in the hydrodynamic regime.
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So this Jay here. Right, it has four components. Do not the density of charge and then J x j jay wages.
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These are components of the cut. But in the hydrodynamic regime, the only degree of freedom allowed is the density of conserved charge.
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J Not so. We have to have another equation which would express components of the current through these fundamental degree of freedom,
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which is the density of conserve charge. How can we do this?
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This is done in effective fury as the infinite series which is compatible before symmetries of the system.
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So what happens? So here we have a simple first term which says that if you have a gradient of the density of charge.
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Suppose the density of charge here is higher than here, then the current will flow.
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It will flow proportionally to the gradient. Right. So there's some coefficient of proportionality which happens to be diffusion constant.
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All right. And then you can have more and more terms added to the fired higher gradients.
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So this is known as the gradient expansion. If you combine these two equations, you will get the equations of motion in hydrodynamic reaching,
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which in this case is nothing but a diffusion equation with energy momentum.
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Denzel, it's a similar story. You have microscopic conservation law and then you have constitutive relation,
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which is an infinite serious in terms of gringo's more and more derivatives.
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So if you take term devout from K to serious with terms only containing loaded widgets at all.
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And combined with conservation law, you will get what is known as relativistic euler's equation.
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If you allow invis truncation, the first derivatives use only, but no second, which is the higher.
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And combined with this equation, you get them just getting to know your stocks equations.
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If you allow second order in derivatives, you get generalisation, often get stocks equations known as Biomet equations and so on.
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So in principle, this is the way to build the build hydrodynamics. So this is a scary formula.
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But let me just just freude for a second. It shows this first term, which contains only first derivatives and loving and nothing else.
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And what I would like to emphasise that for derivative structures of this complicated crocodile here is completely universal for any liquid to gas.
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It is absolutely universal. What is not universal is the set of these coefficients which multiply.
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It stands out to structures. These coefficients eight are cut, I love and so on.
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And no one is Transperth coefficients. And they corrected eiseley method of the fluid, the fury at hand.
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So for each fluid, they are different. They have to be computed from the microscopic underlying microscopic view.
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And this is what difference what what makes, for example, hydrodynamics of water.
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Different from the dynamics of formula plus. All right, so one important coefficient that is shared is Capozzi.
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So share viscosity can be understood as a measure of internal friction in the fluid on gas.
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So suppose you have two layers of fluid or gas moving to slightly different velocities.
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For example, top layer is a little bit faster than the lower level. Now, particles of both layers can penetrate these layers.
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From from from top to bottom and vice versa. They carry momentum.
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So this particle, for example, from its slow layer, can penetrate this one.
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Right. And it will carry a horizontal momentum of this, which will slow down the upper layer.
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And likewise, the particle from the upper layer can penetrate the lower layer.
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And it will speed it up because it will carry some momentum a bit.
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So if viscosity is a measure of how much this transfer of momentum is actually transferred by this bogus motion of particles.
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So this is internal friction. It's no different from when you when you have your poems.
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Right. And doing this right, you feel heat. So this is internal friction. No different from what is happening in here.
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And viscosity is a measure, quantitative measure of its internal friction.
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So now let us abandon abandon the reduced equity dynamics for a while.
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For a while, we come back to it and go to gravity and black holes.
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So we'll generate a little activity is a fury of classical gravity, classical meaning,
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not quite Einsteins equation determine the metric of space and time.
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And these equations philosophically so very often here and philosophically,
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they encode the following situation that if you have on the right hand side distribution of mass and energy encoded in energy momentum,
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Tenzer, then you can determine the geometry of spacetime.
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By solving this equation, because on the left hand side,
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you have objects such as symmetric cream on Tenzer and so on, which encode geometry of spacetime.
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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.
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All right. So this is this is what Ben Stein's equations are doing now.
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This is similar to Maxwell's equations, where you have also left one side and Right-Hand side.
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On the right hand side, you have distributional charges and currents in space and time.
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And on the left hand side, you have electric and magnetic field encoded in this for potential, Amy.
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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.
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So this is sort of kailasam. Now the main hero in science equations is of course symmetric Denzel.
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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,
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then if I got a theorem tells us how to compute infinitesimal distance between points, let's say B and C, just use.
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This can be written more generally because this is the quadratic form which which has the X squared UI squared.
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But no crust term gets the way more generally.
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You can write down the distance between two points and one general space, for example, curved space or a sphere.
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And see where you do have of the organon terms. And these old diagonal terms.
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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.
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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.
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In this simple example. Right. We have a diagonal metric. Very, very simple.
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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.
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So an example of a flat Mankowski space, of course, is a metric line element of which is given by this expression.
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And we have time here entering the game because this is special relativity, the minus sign list if you want.
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This is the contents of special relativity. In one line. Right. And we have time joining in the spatial directions.
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And this is just a metric of ordinary Euclidean three space. Written in circle words.
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Now let's come to the solutions of Einstein's equations. So on the right side, we have a spherical distribution of mass.
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Then the solution for the metric can be found to be found by Schwandt Grid in 1916.
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And this solution is written here. So you can see that it describes two spacetime outside of a spherical asymmetric distribution of mass.
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So if you put em to zero here, you see that you'll go back to Makowski technical skills, spacetime now.
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So this metric describes, for example, the good approximation spacetime around spherical, symmetric objects such as Earth.
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If you if you model Earth by way, circle by circle, symmetric body.
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Now what happens? So you may notice in this metric that you have this dangerous value of R of radios.
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Then this term here vanishes. And here you have a singularity because you have zero in the denominator.
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So this is known as the short shoot, Reynolds.
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Now, in most cases for use is completely harmless because, for example, for URF torture, Regulus is about one centimetre.
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Right. So this expression doesn't apply inside the bodies, only applies outside the body.
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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,
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which is less than one centimetre, then it mentals. Of course, in this case you will get a black hole.
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So look, also very interesting objects. You can have, of course, neutral black holes like Schwarzschild one.
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You can add charge. So then you can have Reistad Nordstrom black hole. You see the method generalises.
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You have a charge here and you can have taken black holes that these black
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holes are rotated charge black holes which are known as Catton Human Bacall's.
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So that calls have a number of very interesting properties, mostly related to behaviour of their horizons.
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So that particular entropy in temperature can guess the shape of the black holes.
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That was done in 1970s by Bic and Stein, Corkin and others.
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And I'd refer you to a wonderful dog by a John Chocho in one of the Saturday mornings devoted to entropy,
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where he explains in full detail why it is reasonable to assign it to assign entropy to do it to a black hole.
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So Hawking showed that the black holes in mitigation at the quantum level and therefore one can associate temperature with them.
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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.
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Right, for example, for a solar mass black hole. This temperature is fifty nine Kelvin.
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So it's very, very small. Now the entropy on the other hand is gigantic because it has a bar denominator.
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And you can, you can do a little exercise and compute. What's the answer.
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It, for example of a sort of mass black hole is gigantic. Moreover, these people like Hawking, but Carter and others,
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they established that the loss of black hole mechanics are actually similar or
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in fact identical up to the definition of letters to the loss of black hole,
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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,
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but we have second law of thermodynamics, which says that to antibusing not decreasing the function of time.
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And as in science adjusted entropy and horizon, are related by this Formula One water horizon area.
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And therefore, this resembles. So these laws of liquid mechanics, the they actually are the laws of black hole.
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But I'm a mixed equilibrium. So this is all equilibrium.
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That's fine, but now we would like to see what happens beyond beyond black hole from the 90s, beyond equilibrium state.
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Now, we can consider an analogy.
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Right, so so suppose we have a normal system conducting sphere placed in an external electromagnetic field,
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so external electro magnetic field will disturb this sphere from equilibrium.
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It will use surface currents on riskier items and these surface currents can be computed.
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This is a rather simple undergraduate problem, a problem in electromagnetism.
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You can computer surface currents given the external fuel, and you will see that they obey the law.
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The current proportional to the external field with conductivity, which is a which is the coefficient of proportionality.
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Now it's important to understand, but we only used to solve this problem. We don't care about microscopic carrier.
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So this charged atmosphere sphere, we only care about Maxwell's equations and also bounded conditions on fields.
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So let's now do the same with black holes. Take a black hole and place it in an external electromagnetic field.
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That was done in the 70s by these people. And then you can it's convenient, introduced the concept of so-called stretch horizon,
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which is a time like surface just outside the usual truth event horizon.
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So what was discovered was that if you do this,
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then a black hole or of a stretch horizon also has induced currents and they behave according to Ohm's Law.
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And moreover, you can computer conductivity sigma or resistance or the black hole.
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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.
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And what comes out is that the black hole can be viewed as an omic resistor Islamic
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conductor with a surface resistance of three hundred and seventy seven ohm or square.
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So this unit is typical Forfend Foyles in the thin films.
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You can compare with different systems like metal foils or silicon, which have similar numbers.
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So this is rather exotic. You can do more. You can take a black hole and place it in an external gravitational wave.
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Gravitational waves does too. Typical medium, right? So it passes through this medium.
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It distorts. It's a medium. It creates strain and stresses. Right.
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And therefore it is a good laboratory to measure response of your body door to its external influence.
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And the response typically in terms of fluid dynamics quantities is given by viscosity.
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So people computed shear in bulk viscosity or fortunate black holes.
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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,
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they would discover that this ratio is equal to a one of a four by in Planck units.
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So we learnt that black holes have properties of the physical medium such as conductivity and viscosity.
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Well, this can be embedded in the holographic principle, the holographic principle.
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So again, I emphasise that in gravitational systems we have entropy vicious proportional to the area.
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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.
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So it is proportional to volume. So this is manifestation of the holographic principle which says that the gravitational degrees of freedom.
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Indeed, dimensions are effectively described by a non gravitational theory.
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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.
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So this slide is a picture which was used by Ludvik Einstein in 1953.
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In his philosophical discussions. But we use it for gauging biology.
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So you have an object which can be described in different languages.
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If you look at the vertical. Right. So this looks this resembles a duck. Right.
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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.
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So you describe this object in terms of a rabbit, but it is the same object.
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You can't say it is rabbit or duck apriority. It depends on on. On this point of view.
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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.
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Right. So this dictionary between the two languages is called duality in general and
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misapplied also to calligraphic duality in holographic duality and string theory.
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You have an object, a collection unperturbed, a collection of like brains, and it can be described in two languages, rabbit or duck.
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It can be described as open string picture and closed in picture. Right.
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And then in language of open think bisher or language or a floating picture.
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And that is a quantitate. So. This is not philosophy anymore.
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That is a quantitative dictionary between these two languages which allow you to calculate
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quantitatively properties of this object in one language or the other language,
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depending on your convenience. Now, what is fundamentally important is that when one language, when one theory, one description is strongly coupled.
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So you don't know how to calculate. You cannot apply perturbation fuelled enough.
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Everything fails. Then the other language is weakly coupled where you can happily calculate everything.
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So if you know the dictionary, you can any you're interested in, for example, formalisation of the system on the left.
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You can happily methods into biblically coupled system and calculate every quantity you need.
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Right. So that's that's a wonderful think correspondence which we will apply.
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So in particular. So you have black holes which are doable to not gravitation and degrees of freedom.
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Now black holes. So every system in equilibrium, a typical system is characterised by a number of concert charges.
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And we also know that if we perturb a not long gravitational system, such as a spinning pendulum here from equilibrium,
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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.
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What is very simple here. So what happens with the hole if you perturb the call out of equilibrium?
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Well, we have what's happened. So the black hole will oscillate.
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It will emit gravitational weights.
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So these are normal modes of black holes known as the quite normal modes because they have non-zero imaginary parts.
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And then zero imaginary part emerges because of the presence of the black hole horizon.
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So. Well, we know. Suppose we can compute go to eat well relatively easily.
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We can compute the spectrum in quite normal spectrum of these black holes.
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But the holographic principle tells us that this is mapped one to one in two
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non equilibrium properties of a dual non gravitational quantum field theory.
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So in particular, that is the regime in this theory, which is described by hydrodynamics.
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So I mentioned this diffusion equations and so on, so forth.
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And this is quantitatively mapped into the spectra, into the quite normal spectra of a dual lieke hopes.
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Right. So therefore, you can compute.
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So, for example, in the language of hydrodynamics you have in your system, you have excitations such as sound waves.
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So these are quite the particles in every hydrodynamics system. You have sound.
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And you have dispersion. The relation for the sound which is given by this equation here, you have speed of sound.
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And then you help Duncan off sound waves characterised by viscosity.
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So this is all mapped in holography into the Igen spectrum of black holes of dual black holes.
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And here is a genuine calculation, right.
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So this expression is one of these Igen frequencies off if high dimensional Doyel black hole Deuel to this wonderful FURI system.
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So you can just compare a term by term and read off from comparison of these two two expressions.
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For example, that the speed of sound, speed of sound v is speed of light divided by Squirtle the free.
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And then you can also read of the ratio of share is context to entropy density.
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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.
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You can go beyond that and directly relate them, get Stokes equations and Einstein's equations.
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So this is known as a fluid gravity co-respondents. Now, more and more.
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So a development of last years is concentrated on understanding the so-called unreasonable
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effectiveness of hydrodynamics because it turned out by studying the systems.
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So it's a very effective tool to study systems which are strongly coupled and can not be studied by normal means,
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such as kinetic theory and similar protractive technique. So what it revealed is a very surprising fact that quite often you can have
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hydrodynamics working perfectly well before local thermal equilibrium is established.
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So a new term was coined, which is hydra minimisation, not formalisation.
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So you don't wait until you have local thermal equilibrium. You'll have your stocks.
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Equations are perfectly fine. So it's an open area of research.
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So one of them is also shown here. So, for example, you want so you have a dispersion relations for the sound mode.
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As I mentioned on the previous slide. And suppose you want to understand the limits of limits of hydrodynamic description, namely,
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when does the serious convergence and divergence rates of the series anything serious?
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Right. So you want to find the triggers of convergence. So you by making this do a dual black hole spectra.
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You can do it rather easily. To do this, you have to consider the expectations of black holes at complex values or spatial momentum.
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And then you see, this is an interesting connexion to the algebraic curves because you see the breakdown of perturbation theory happens.
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Then here in this region, you encounter a non hydrodynamic degree of freedom.
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And this, in algebraic kolff sense means that we start to break curves, opens up.
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You see this red star here and you have opening up of this curve.
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And this limits the limits, the applicability of hydrodynamics.
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So the radius of convergence actually is finance.
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And you can actually computed in a particular theory which has its gravity Duell description, which is quite, quite a remarkable thing, I believe.
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All right. You can also you can also think of how the domain of applicability of hydrodynamic description depends on coupling,
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because you can have systems which are strongly interacting. You can have systems that should be clean.
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So there are not hydrodynamic supplies uniformly for all to Coplin value.
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That's that's that's a question that I saw in in this holographic the fiscal aglukkaq tools.
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You can find the answer to this question. The answer is no. No, that's not uniform.
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You can have dependents. You'll have dependence on the applicability of hydro, which varies.
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And if coupledom. So it's actually so hydro is more actually applicable according to this graph, you see.
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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.
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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.
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So let me come to let me come to conclusions. So we have seen that black holes have entropy and temperature.
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And in equilibrium, they behave like thermodynamic systems. And we think we understand why, because of this holographic principle,
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it simply means that we know what the microscopic degrees of freedom are, which equilibrate.
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Right. These are microscopic degrees of freedom expressed in this language of non gravitational theory duel to a particular black hole.
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Now out of equilibrium horizon. So black holes exhibit fluid like properties which were described by membrane paradigm in 1970s sunlight in ages.
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But now the work of black hole physics has led to his discovery of gauging duality.
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A little bit of few. Yes. If you correspondence or a dark duality. Because it's like that.
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So let's call for an anaemic said membrane paradigm for a now fully embedded into this modern Lenn virtual holographic.
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Now we also talked about Igen, multiple black holes. And we know that they used very extensively.
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So this is very active area of research to study formalisation and discovered a new
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phenomena such as Heidrun accusation and hydrodynamic actors and all this stuff.
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It's it's really it's really quite fascinating because holography.
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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.
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But at least one good use of this is that what this is, is that it inspired new research into fundamentals of fluid dynamics.
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So you might have thought that all fluid dynamics is oil.
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Its its 18th century, 19th century, your stocks and everything is known that it's not the case.
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So fundamental. So people who were doing this. These these this research and in the photography and so on,
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they're actually looking at fundamentals of the very basics, of a formulation of kind of mix of applicability,
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range of how to theoretically establish was so inspired by hello,
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what if you choose to create an image has been recently rewritten to deal with problem of causality.
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This is one one one one simple example with possible applications in astrophysics.
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So this was this was done really in essentially last year to fall the full extent.
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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.
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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.
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And the criterium is the following. If in your life's work,
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you managed to add at least one line to the Orlando edition stand watch from terms of the
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ten volumes of the course of theoretical physics or maybe change one equation there,
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then then then it is it is it is something meaningful. You have done something right.
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So let me just finish by saying that what is happening now in foundational foundations of new dynamics is very much of this Colaba,
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because certain things in London Revolutions Vol. six will have to be amended because of this work.
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And I'm quite happy to report this, at least in philosophical terms.
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Thank you very much. I will also Prussia's. And Sondre, can you on share your screen?
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Yes. Hi. Thank you. Great.
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So we got some questions for you.
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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?
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Yes, I just so did the book.
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The book on holography or the book on. So, yes, there are, actually.
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And so if they're talking about this specific applications of holography to hydrodynamics, that is a book which actually one of the offers.
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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.
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Haha carful that is Olenna. Now he is a faculty in Barcelona.
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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.
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But yes, I can, I can recommend some. Yes. Right.
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So Professor Taylor has recognised the and seventy seven items as the impedance of free space.
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So why did we end up with that number and what does the black hole contribute?
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I don't know if so, it's I mean,
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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,
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but so I said that it is embedded in two. Hello, kind.
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It's understood why we have these properties.
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But there is one sticky here that 377 comes for water shoots, black holes which are simple, logical, deflect and flush.
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What should black holes in this in life? Flat space. We don't have a graphic description.
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You might have noticed that bulk viscosity of black hole is negative.
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So difficult business is this is a sign that your system is unstable and indeed ordinary.
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Swash a black hole in some particular flat space is unstable. Get the [INAUDIBLE] irrigation.
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So it has negative specific heat also. Right. So this is for this system.
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We don't have a full and graphic description in terms of a stable quantum field theory.
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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.
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However, the ratio of shear viscosity to entropy density happens to be universal for all horizons, so-called black holes.
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So this is a universal statement, which is extremely powerful.
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So in particular, regardless of whether or not you have some particular flatback black hole or some politically ADF black hole, doesn't matter.
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So this ratio stands stays to be it wonderful by. So Stephen Burke asks, does the black hole duality have any consequences?
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Two things we can observe about actual black holes. Probably not, except that.
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So because so these are not astrophysical astrophysical objects.
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So like a mentioned eye clock and temperature, for example, is in typical these Allama to kill them.
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So it's not something that you could easily, easily observe. Now, what may happen is that form.
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So this duality of these holographic considerations, apart from clarifying the fundamental so hydrodynamics percent,
365
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they can also help for understanding primordial black holes and behaviour of of of a universe right after the big bang.
366
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Because there it's quite likely that gravity it is actually contains a number of terms beyond eyesight.
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But it's gravity.
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And by using this technique, you can actually maybe predict something about the spectrum of gravitational primordial gravitational waves.
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But this is for the future, because, of course, at the moment we cannot we cannot detect primordial gravitational waves.
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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?
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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.
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Right. So I have I have a system here. Right.
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So this system has this system has a number of Igen modes, which in principle you can you can calculate like classical mechanics.
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Right. So. So black holes are classical objects, a particle, whole congregation.
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So they are solutions of classical theory of gravity or Einstein's theory of gravity.
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And what you can do, like with any other object, you take equilibrium values, for example,
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Solutia equilibrium solution, Stine's equations, and you perturb it a little bit.
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So you have Method Jimeno. And then you have a small filtration plus Delta germanium.
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And you solve Einstein's equations. You'll lead linear ice them and you find the spectrum of linear ice, Einstein's equations.
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All right. So this becomes a boundary problem similar to classical mathematical physics of 19th century,
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except that it is known for emission because of the presence of a phrasal. Right.
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So this is a classical Igen Moltz pretty much like this in the Sphinx.
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Right. So then Jonathan Digest's, is there an intuitive picture for how a hydrogen nemi description can work without local civilisation?
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Is it just because the system is so strongly coupled that you can still get collective behaviour without the centralisation?
385
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Yeah, this is a very good question. The honest answer to this is we don't know at the moment.
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In fact, as I mentioned, this is a pretty, pretty active area of research.
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What people discovered is so you see a lot in normal systems.
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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.
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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
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So what happened? So. So basically, you take you take a local, local, local density of so take this energy momentum.
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Tons of components. Right. Which in equilibrium, for example, components not long.
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Zero zero becomes equilibrium. Energy density.
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But long before equilibrium happens. And I'm not talking global equilibrium, but local equilibrium.
394
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Long before that. This same quantity. You can write down equations of motion for this, right.
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In kinetic theory. If you were able to solve the loop of chain completely, you y chain.
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Then it would be the analogue right in holography, helpful gravity. You can do it rather easily.
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Or you can put it on a computer. It's probably usually just easier to assimilate.
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So what people discovered it and that that was discovered in the last five years.
399
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So they discovered that that in these divinities degrees of freedom, you have so-called hydatid than mean contracts.
400
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So all behaviour, regardless of initial conditions and you start off to start with,
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you have trajectories attracted to one curve in dynamical space and the face space.
402
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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,
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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
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And this is an active, active area of research. And so one last question.
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Andre Alexis Hughes IV. Could this work on black holes?
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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?
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Yes, definitely. In fact, one of them is is used very extensively for the last 10 to 15 years.
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And this is the ratio of share viscosity to an entity. So for Khushi game, we don't have a holographic duel,
412
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but we do have holographic doors for systems which are quite similar to CCD in terms of hydrodynamic behaviour.
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00:41:23,570 --> 00:41:27,970
And about 20 years ago, by a holography,
414
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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
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So what community, the Asian community to work in working on these matters?
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What they're using now is a benchmark for all of these simulations of your stocks and KBI collisions.
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Is the value given by holography each bar? Over for you, Kate Bolduan.
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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.
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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.
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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.
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So you need to log on to that newsroom place and then you can hopefully move yourself into the right room when you arrive.
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You should see a breakout room icon on the list of icons at the bottom.
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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.
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And Michelle and I will be around to try and rescue anybody who's lost in cyberspace.
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It would be great if you could stick to about six people in each room so we don't get overcrowding anywhere.
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So what remains to me is to say thank you very much to the speakers this morning, to Steve and Bruno and Andre,
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who've taken a great deal of time, first of all, to find jackets and ties for the first time for about six months.
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And, of course, to prepare these these talks, it's hard giving talks on Zoome.
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And it was great and interesting. And thank you very much. Deeper. And Andre.
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I also want to say thank you very much to Michelle Bosher to Michelle,
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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.
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Thank you, Michelle. So I'll sign off now. Thank you very much for joining us and hope to see you in a minute.
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In these breakout rooms. Goodbye.