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