Fine, so let's continue our discussion. Let me start with a two or three minute review of what we talked about last, in the last lecture yesterday. You'll remember that yesterday, motivated by two or three strands of motivation, the first being an attempt to try to find an analytic approximation, or, you know, to find some useful analytic approximation to highly nonlinear behavior of black holes. The second being to make sense of this, to make precise this feeling that has been expressed over the last 50 years or so, that there is a sense in which the physics of black holes reduces to the physics of a membrane that lives at or near the event horizon of the black hole. And the third being to see to what extent one can, in any context, do something like ADS-CFT for Schwarzschild black holes. Okay, the second and third are more or less the same motivation, okay? We decided to study the dynamics of black holes in a large number of dimensions, okay? We followed Emperor Suzuki and Tanabe to explore the metric of a black hole in a large number of dimensions and realized that this metric was characterized by two lens scales. There was R naught, the size of the black hole, and R naught by D, the thickness of the black hole. And the important thing was that in the large D limit, these two lens scales were very, there's a hierarchy of scales between these two lens scales. The thickness is much smaller than the size. We then reviewed the computation of Emperor Suzuki and Tanabe of the quasi-normal modes of these black holes. And we saw intuitively how you might expect that while most modes, most quasi-normal modes for this black hole should have frequencies of order one over the thickness, which is D by R naught, it was possible, depending on the details of the problem, that some modes would have lower frequencies of order one over R naught. We saw from our intuitive motivation that at any given angular momentum, you should expect only a finite number of modes to be light, whereas you should expect an infinite number of modes, perhaps zero to be light, whereas you should expect an infinite number of modes to be heavy. The question, the interesting question was, did these light modes exist? Emperor Suzuki and Tanabe did explicit computations, found the spectrum of these light modes, and you'll remember we quoted their frequencies for scalar spherical harmonics, the frequencies where R naught times omega was plus minus square root of L minus one plus I times L minus one. And for the vector spherical harmonics, R naught times omega was I times L minus one. The sign of our frequency, we were looking at modes that went like e to the power i omega t, so positive imaginary parts corresponded to decay. We may contact with these formulas, perhaps in this lecture, once again. So we, given the fact that there were these light modes separated by a huge mass gap from an infinite number of very heavy modes, we decided to try to see if we could find an effective non-linear theory of the light modes. As we emphasized in the last lecture, this happens very commonly in physics. For instance, in string theory. In string theory, we have a few massless particles separated by a gap from very many massive particles. If you were just looking at the spectrum of the theory, you would see linearized massless particles, linearized massive particles. Now, because of the gap, you could ask the question, what is the effective non-linear theory of the light modes? That question, of course, has been asked in many ways in string theory and has a beautiful answer, Einstein's equations. So the effective theory of the non-linear theory of the light modes, Einstein's equations, perhaps in type two super-gravity, type two string theory, souped up to give you the equation of super-gravity. But because of the gap, it was consistent to talk of a non-linear theory of these light modes, ignoring the heavy modes. If you ask, what is the effective non-linear theory of the light, the massless modes of string theory, and in the first excited state, there would be no answer to that question. Because non-linear effects would bang to the first excited states to produce the second excited state, okay? So that's not a consistent question in itself. But there is a consistent question about, what is the effective non-linear theory of the light modes of string theory, the massless modes of string theory, because of the mass gap? In a very similar way, we're asking the question, what is the effective non-linear theory of the light modes of the light quasi-normal modes of the large D black hole, okay? That's the question I'm going to try to address, at least in part of this lecture. Now, at the end of the last lecture, I told you that it will be useful in addressing this question to keep in mind an analogy, namely, a similar question that has been asked and successfully answered in the past. And this question, the answer to this question goes by the name of the fluid gravity map of ADSEFT. At the end of the last lecture, I reviewed that, but I think I went too fast for you to really understand. So I'll spend another 10 minutes this lecture, just going through that review more slowly, just so that you keep the analogy carefully in your mind, who are for it. You remember that when we would discuss the analogy, we switched gears to considering Einstein's equations with a negative cosmological constant rather than the vacuum Einstein equations. This is just for the analogy. Nowhere else in the talk will there be a negative cosmological constant. I don't want you to be confused about that. Just for the analogy we did there. And we switched gears looking at four-dimensional gravity. We can do it in arbitrary dimensions, actually, but I'm emphasizing we're doing four-dimensional, five-dimensional gravity, five-dimensional gravity, just so that you see that for what I'm saying here, large D is not important, okay? And we discussed that while ADS space was one of the solutions to the equations, we discussed that there was also another interesting solution, which was this black braid, which had the dual field theory interpretation of the thermal equilibrium, okay? Now, something I didn't tell you about in the last class because we were so rushed is this, that before you start doing anything fancy, the first thing that you might do is to try to linearize Einstein's equations around the black braid. Okay? You linearize Einstein's equations around the black braid more precisely find the quasi-normal mode spectrum around the black braid. This historically was what was first done, it was done in the early 2000s. Okay? The quasi-normal mode problem in ADS is the problem of linearizing Einstein's equations subject to the following boundary conditions. Ingoing of the horizon, that's always what you do for quasi-normal modes for the horizon, but normalizable at infinity. And you remember we discussed why? The boundary conditions always should be that you're not smashing the black hole, you know? Doing something to it. In flat space, doing something to it is sending something in. In ADS also, doing something to it is sending something in. But the way you send something in in ADS is by turning on non-normalizable modes of the boundary.  Okay? This, the computation of the quasi-normal modes was what started this whole thing off by Soroka, Sohn, Coptun collaborators.  The first class of modes, and there are infinitely many of these. Okay, so, sorry, I should back up. In our black hole problem, we first used symmetry to say all modes transform in spherical harmonics on the sphere. In the black brain, there's an easier symmetry than spherical symmetry. It's just translational invariance. Okay? So all your modes will be taken to be e to the power i omega t plus e to the power i kx. And then everything non-trivial is functions of the radial direction, this radial direction in ADS. It's all modes that assume to have this, this time and space dependence. Okay, this is k dot x. Is that clear? The problem of quasi-normal modes goes as follows. A, around the black hole, the problem was for every angular momentum, what is the set of integers? What is the set of discrete set of omegas you get for quasi-normal modes? Here the problem becomes very similar for every k, for every momentum in the spatial direction. What's the discrete set of quasi-normal modes that you get when you solve the problem? Okay? Once again here, there are two kinds of modes. There's an infinite number of heavy modes and a finite number at each k of light modes. The heavy modes had the property that omega sum function of k, but when you take k to zero, so you go to the long wavelength limit, okay? That function of k goes to some pure number times the temperature. That's the only thing it could go to in this problem because there's only one mass scale in the problem, namely the temperature, okay? And the important thing is that for the heavy modes, this number is non-zero. In fact, as you go to heavier and heavier modes, it grows. But all that we care about is that for the heavy modes, it's non-zero. However, there was some special modes which had the properties that the quasi-normal mode frequencies went to zero as k went to zero. You went to the long wavelength limit, these quasi-normal modes frequencies went to zero. Okay? And in fact, when you worked out the quasi-normal mode problem carefully, you found analogs to those formulas. You found omega was plus minus k by square root three plus i times a number times k squared by t. So two modes like this. And also omega, some other numbers, a number prime times i k squared by t. Actually, it's a degeneracy, but there are two modes like this. Okay? So you found four, you found four light modes. What do I mean by light? By light, all I mean is that as k went to zero, omega went to zero. These are zero modes. These have been normal modes rather than quasi-normal modes. Had there been no imaginary part? These would have been genuine light excitations which you might have tried to find an effective action for. Okay? But in this problem, things are dissipative. That's what makes these problems. And also that problem, the one we will come back to most of this lecture, different from integrating out the massive mode and finding an action, more difficult as well as more interesting. Okay? Now, so what we see here is that we have these black brains and we have a set of light modes. These modes are much lighter than the heavy modes if we go to the long wavelength limit because then k is much, much smaller than t. So in that limit, in the long wavelength limit, you might ask, reasonably ask the question, what is the effective nonlinear theory of these light modes? The light modes exist. So they should exist some effective nonlinear. Okay, that was the question. That was the analogy. Now, the four modes are omega is plus minus k by square root two, that's two. And these modes, but the same frequency come with a degeneracy of two. These turn out include dynamics to be the sound modes and the shear modes. And the degeneracy is just that there are two directions in which to shear. The two transverse directions to the wave. This is in four dimensions. If we were doing fluid dynamics in D dimension, that would be a D minus two degeneracy of that. Exactly, it's just the collective coordinates, the goldstone modes. Exactly. So in order to try to understand that, as I reviewed in the last class, what we did was to first take this black brain and rewrite it in a different set of coordinates, these Eddington-Finklstein-Ingoing coordinates and also looked at the exact solution of the black brains with a boost. So this metric here with U constant and T constant was an exact solution of Einstein's equations with a negative cosmological constant. In fact, large diffume-orphism equivalent to the original brain, done nothing. But then we looked at metrics in which we took the same form of the metric, but allowed U and T to vary slowly. The idea being that surely since the solution is, this thing is a solution when U and T are constant, if it varies very slowly, it should be near to a solution. Now, I wanna emphasize one thing. It was very important we did this in the right coordinates. And that's gonna have an analog in the problem that we'll solve in five minutes, or we'll start looking at in five minutes. And the reason it was very important that we worked in the right coordinates, one of the reasons is as follows, goes as follows. You see, black holes are regular solutions at the event horizon. But you wouldn't know if you looked at that. If you looked at a black hole, it looks irregular at the event horizon. Einstein thought Schwarzschild's solutions had a singularity of the event horizon.  It looks like it has a singularity, but it doesn't, you have to work to see that it doesn't. But it's a slightly dangerous game, because something that looks like it has a singularity, but doesn't, might turn out to have a true singularity if you change something a little bit. And what we're interested in is changing the solution a little bit. Go on, wanna work in coordinates where a small change may turn a coordinate singularity into a genuine singularity. On the other hand, these Eddington-Winkelstein type coordinates, okay? A manifestly non-singular at the horizon. And therefore, remain non-singular if you make some small change. There are more and more motivations, but since this is not an electric and fluid gravity, I won't discuss those motivations in great detail. But what was very important was that we did this in the right coordinates, okay? Trying to implement the slowly varying thing in different coordinates that are related by singular coordinate transform can give you different starting points, okay? And then, as I reviewed in the last lecture, what we did was that then we could show that this was the first term in a systematic expansion of solutions of Einstein's equations. You have to correct this. But it was possible to correct it to solve Einstein's equations, not just a leading order in wavelength in units of temperature, sorry, of derivatives in units of temperature. But first, for some leading order, provided the starting point was not completely, was not completely arbitrary, but obeyed some equations of motion. Equations of motion were the equations of conservation of a stress tensor. And the stress tensor was made up of this velocity and temperature field in the following fashion. Leading order was t to the four, four u mu u nu plus eta mu nu. Plus the first sub leading order, there was a t-cube term plus a shear tensor term. I won't even define what shear is because fluid gravity is not the main point of this lecture. But okay, and blah, blah, blah, blah, blah. And this whole procedure's consistent only if this equation of motion is obeyed. What was important as we emphasized in the last class was that there were as many equations of motions as variables, okay? And so this procedure established a one-to-one map between two apparently different dynamically problems. First problem, solving Einstein's equations in ADS space in spaces with event horizons in the wrong wavelength limit. Second problem, solving the equations of hydrodynamics. These, the conservation of stress tensor by the stress tensor's function of velocities and temperatures. It's a fancy way of saying the equations of hydrodynamics, Navier-Stokes equations, relativistic generalization of Navier-Stokes equations. Okay, and if you could solve one problem, you could solve the other. And you might think that this problem is a bit simpler than the other problem because it has no gravity, it works in a fixed background. It's one lower dimension than the other problem. Now, you might ask, did this hydrodynamic problem that we looked at, did it, you know, what is the connection between that and the light quasi-normal modes that we started this discussion with? So the connection is simply this. You take these equations of hydrodynamics and it's one obvious solution. The solution is u is equal to 1, 0, 0, 0, fluid's addressed, and t is equal to constant, equilibrium. That's the solution that corresponds to the black ray. When you take these equations, just hydrodynamic equations, and linearize around the solution to find the spectrum of small fluctuations. And what do you get when you do that? You get this, which is the same as this. So there's non-linear theory. Is the non-linear theory of the light modes? And we see that from the fact that when we take this non-linear theory, put it around the solution of interest and linearize, we recover the lightness, okay? So we, by this means, we have checked that we found the right non-linear theory. It's hydrodynamics, which reproduces these linearized fluctuations as sound and sheer oscillations. But it's much more than the linearized theory. It describes all kinds of things. People have now, by now, this is an old story, and people have looked at it in great detail. For instance, people have shown that you recover turbulent solutions in this limit. This is a huge story with fluid gravity. It's not our concern at the moment, except it's an analogy. This ends my review of the fluid gravity correspondence as an analogy to what we're gonna be doing. Any questions or comments before we proceed to the actual problem at it. They're linear, yes. So the quasi-normal modes, it's exactly, the analogy is exactly like what we said about your string theory. Suppose you're doing vertex operator calculations. You have vertex operators for massless gravitons, and the vertex operator tells you that the gravitons obey the equation del squared h mu nu is equal to zero plus some gauge conditions. Those are the equations of linearized gravity. All they do is give you small fluctuations. Little boring gravity waves. But the full theory is Einstein's equations of general relativity, which has much more. So that's an indication that there exists a nonlinear theory. But it doesn't determine the nonlinear. Is this clear? Are there questions or comments? Excellent. So now we're gonna go to the problem at hand. We're looking at black holes in large D, and we wanna find an effective nonlinear theory of the light modes. The more the effective theory that will allow you to understand what happens after something's thumped. The theory settles down, but in a full nonlinear fashion. That's the question. That's the problem. We've said this. Okay, now let's recall the steps here. The first step was to move to the right coordinates just to study the equilibrium solution. So we're gonna imitate that. The first step is to view the basic Schwarzschild black hole solution in the right coordinates. Now what are the right coordinates? Well the right coordinates are coordinates that will turn out to be convenient for what you wanna do. So what will these right coordinates be? Almost the same as the coordinates we use for fluid gravity, but with a little twist in the tail. So let me show you these coordinates. Let's start with the Schwarzschild metric in Eddington Finkelstein coordinates. I'll write it down, and then I will ask you if you, let me write it down first.  Now this is not the same as the metric I wrote down at the beginning of the last class, but exactly the same manipulation that went, that took us from this metric to this metric with u being one zero zero zero. We'll give us that. It's exactly the same manipulation. Namely, the r here is the same as the Schwarzschild r, but the v here is T Schwarzschild was equal to v minus integral one by f of this one minus r naught. It's exactly the same manipulation, so I won't go through it again. Is this okay? Anyone confused about this? In fact, this is where Eddington and Finkelstein invented their coordinates.  Okay, great. So you might think, and this is what we thought for a while, that we should look at the problem in Eddington-Finkelstein coordinates, but it's somehow very inconvenient. And the inconvenient thing is that it's tied to a particular frame. What proves more useful for us is to do a second coordinate change, starting from Eddington-Finkelstein coordinates to what I call Kerr-Schild coordinates, okay? And the thing about Eddington-Finkelstein that proves inconvenient is the following. When you set r naught to zero, this space reduces to flat space. Visually obvious that the space is flat space. To get the space back into form, a form of flat space that is completely manifest, namely dx mu dx mu, you have to do a further coordinate transformation. The idea of Kerr and Schild was, well, you see, these coordinates are nice because they're good at the horizon, but they're not so natural for infinity, okay? Kerr and Schild, okay, on the other hand, the Schwarzschild coordinates were nice at infinity because they were manifestly flat-spaced there, but not so good at the horizon. So Kerr and Schild thought, you know, had the idea of inventing a coordinate system that was good both at infinity and at the horizon. Let's see how you do that. We did, to go from the Schwarzschild coordinate to the Eddington-Finkelstein coordinate, we did the coordinate change, ts is equal to, I wrote that somewhere. I erased it, I made it, okay? ts is equal to v minus dr by one minus r naught by r to the power d minus three. Now, what does this become at infinity? At infinity, this is ts is equal to v minus r. To get infinity back to what it was in Schwarzschild coordinates, now let's make the coordinate change. v is equal to t plus r. So that, if you plug that into here, you'll find that at infinity, t is the same as ts. But because all of the singularity business comes from this guy going to zero, and since this is a non-singular coordinate change at r equals r s, this coordinate will remain non-singular at the event horizon. So now you've got a coordinate, by doing this, you have a coordinate that is manifestly flat at infinity, but continues to be non-singular at the event horizon. Okay? It's a convenient coordinate system and one that I will employ extensively through these lectures. You will see why it's so convenient in two minutes. Let's just implement it first. So all I have to do is to take this and plug it in here. Okay? So let's do that. We've got two in a dt plus dr dr minus dv squared in a one minus r naught by r, sorry, minus dt plus dr, the whole thing squared, to one minus r naught by r to the power d minus three. Okay? So let's write this as two dt plus dr into dr minus dt plus dr, the whole thing squared, that's the one part, plus dt plus dr, the whole thing squared, into r naught by r to the power d minus three. Now, here we just simplify the dr squared term which was minus, sorry, this is dr. This was minus dr squared, but there's a two dr squared here so that just becomes dr squared. We get dr squared. The dt dr term, that's two dt dr, minus two dt dr, goes away. And we're left with minus dt squared, plus of course, the part I've not written which is r squared, omega d minus two squared. This part is simply the metric of flat space. This, you could rewrite as dx mu, dx mu, okay? But there's an addition, and the addition, can people see down here? Probably not, right, let me ask. And the addition, so the final metric is d r squared is equal to, oh, maybe I should, it's better to write in the following way.   So this is, to be totally clear, d mu rho by square root of d mu rho, d nu rho eta mu nu, okay? And oh is equal to n mu minus u mu, okay? Why is this the same as this? Sorry, why is this the same as in explicit coordinates, this is, you know, it's, this is the same as the statement of the metric d r squared is equal to dx mu, dx nu eta mu nu, plus plus dt plus dr, the whole thing squared over r by r naught to the power d minus three, okay? And u mu, in this particular case, was simply minus one, zero, zero, sorry, I wrote that, I was a bit disorganized while writing that, maybe you can take a look at what I've written for a half a minute, and tell me if it's clear, okay? Now the final form of the metric is flat space plus something, this something manifestly decays at infinity, and is naturally written in terms of a function defined in flat space and a one-form field defined in flat space. The one-form field is u mu, the function is rho, rho of course gives rise to another one-form field, namely it's normal vector, n mu, okay?  Questions or comments about this, is this clear? How is it related to curtshield time, yes? So what we had was that T s was equal to V minus integral d r by r, what was it? Yeah, just substitute back, yes? So it's like a tortoise coordinate with r removed, yes? So the tortoise coordinate reduces to T minus r at infinity, remove that part, but you let the stuff happen at the horizon that desingularizes the horizon, okay? Great, so it's a very clever coordinate, but for us, firstly it's non-singular at the horizon. Secondly, what's really important for us is that it's naturally written in terms of mathematical structures that are naturally defined in flat space. Now you remember what we were after. What we were after was to demonstrate that solutions of black hole dynamics are one-to-one correspondence with the motion of a membrane that lives in flat space, okay? For this purpose, it's very nice to deal with metrics defined in terms of auxiliary quantities that naturally live in flat space, not in the metric itself, because in the dual theory, we're interested in quantities that live in flat space, not in this preformed metric itself. The dual description, namely membrane, has no metric. Just lives in flat space. This is a complication we didn't have to deal with in fluid gravity, because in fluid gravity, all the structures lived at the boundary and the boundary had a natural metric. Here, even though the metric in the bulk has changed, we're looking at dynamics in the bulk, we want to deal with effective dynamics of something living in the undeformed flat space. And the Kerr-Schild form of the metric very naturally regards metrics as constructed out of one forms and functions living in flat space. So that's very convenient for us. Excellent. Now, the next thing we did for fluid gravity was to take our solution and boost. So we'll do the same thing here. We take the solution and boost it. But having written it in this form, the boosting is simply totally trivial.  Okay, so boosting just replaces this line by the equation U squared is equal to minus one, U is equal to constant. This is an as good solution of Einstein's equation, the exact solution. What does it represent? It represents a black hole, it's not sitting there, but it's hurtling somewhere at velocity U mu. Clear, trivial, nothing interesting. What's the next thing we did here? After boosting, we decided to make the boost parameters functions of space and time. And the temperature functions of space and time. Let's imitate the procedure. Okay, so suppose we take this metric here and in that metric, just take U mu to be U mu of X. We demanded here that the functions of space and time were functions that were varying on very long length scales compared to the temperature. In this problem, we do not have the luxury to vary on very long scales compared to the analog of the temperature, namely R naught, because we live on a sphere and there are no length scales larger than R naught. However, we do have the ability to vary on very long length scales compared to the membrane thickness, R naught by D. This is the key point. The fact that there were two length scales in this problem allows us to be on long length scales with respect to the smaller length scale while still fitting inside the sphere. We will demand that this variation, the length scale of variation, let's call the length scale of variation, is much, much greater than one by D. One by D, let's say. In particular, when we actually implement our analysis, we will assume that there's no D in this problem. This varies on length scale one, not as some inverse power of D. We also here in this problem allow the temperature to vary as a function of where we were. What's the analog of that? Roughly what we wanna do is to allow R naught to vary as a function of where we are, but there's something else that had no analog in the black-brained problem. And that's this.  There's no particular reason why our back hole should stay situated at the same point. Move around. So the analog of allowing the temperature to vary, the right analog for that just turns out to be very simple. It turns out to be the following. Take rho, this function rho, to be an arbitrary function of x. Take the function rho as I've written it, to be an arbitrary function of x. By x I mean x and t, all coordinates of Minkowski's space. Okay.  Now, as you will see in two minutes, there will be restriction on u and rho to get the program started on. But for now, we just let u and rho to be arbitrary functions of x. The justification is that it works. Hang on for five minutes, ask that question. A, yeah, hang on for five minutes. In this problem, what got us started was the almost obvious statement that this quantity, while not an exact solution of Einstein's equations, solved Einstein's equations to lowest order in the derivative expansion. Because at lowest order in the derivative expansion, you take no derivatives of t and no derivatives of u. If you don't take derivatives of t and u, you don't know the difference between whether this configuration is varying or not. And the non-varying solution solved Einstein's equations. Once you had that, you could roll the machine. Maybe just a brief interlude here about something genuine. You know, what we are doing both in fluid gravity and in this problem that I'm looking at now is perturbation theory. What we've done is identify a small parameter to try to systematically construct a class of solutions in perturbation theory in this parameter. And though you might not understand this when you do your undergraduate courses, perturbation theory is an art rather than a science. And the art goes as follows. You wanna find some exact solution that lies somewhere here. You've got a parameter in which to perturb. The art is in choosing the starting point of your solution to be nearby to you. If you start here and try to perturb there, won't work. What you have to do is to find the starting point of perturbation theory. And for that there are no rules. You have to use intuition, you have to guess. You have to keep trying till it works. What do I mean by starting point works? What I mean is that the starting point is near the solution that you want and solves the equation that leading order in your parameter. In non-trivial uses of perturbation theory, this is the interesting step. The rest in the end is mechanical. You know what to do. Solving some equations. Where physics, the interesting physics intuition comes in is in choosing your starting point. Okay? Here we had a nice choice of starting point and we wanna check whether this is an analogously good choice of starting point for our perturbation theory. Yeah, that's the question we're asking. So the way that question becomes precise is following. What we want to ask is does this configuration solve Einstein's equations at leading order in large d? Forget about some leading orders for now. We can use perturbation to correct the theory, to correct it up if it solves a leading order. We can correct it up to some leading order, but does it solve a leading order in large d? This is an acceptable solution at leading order in large d. Yeah, that's the question we're asking. So let's look at this solution for a minute. This configuration for a minute. Let's look at it. This, to answer this question, will take us a little time. To answer it properly, we'll take us a little time. But let's first look at the question, look at this metric and say what we can say about it on general rules.  Okay, note that that was the case here. For instance, for the static black hole, U was in the 1-0-0's at chip yaw in the time direction, whereas N was in the radial r-adaptation, okay, okay. Oh, and there was one thing here, I'm sorry. When I boosted, I needed to tell you what r was.  You understand, r is the spatial, is the magnitude of the spatial direction orthogonal to velocity. That's what it was before boosting. The boosting just, this is a boost, a boosted version of that statement, sorry. So the boosting involves replacing r by this along with replacing U. I'm sorry, I should have mentioned that before, sorry for that. Is this clear? Sorry, so to come back. So to come back, what we're doing now is to look, so this velocity vector was normal to N. We're gonna interpret the statement as follows. We will be particularly interested in the surface, rho is equal to one. For instance, in the case of the Schwarzschild black hole, rho equals one was the event horizon, because r is equal to r naught, okay. We'll be particularly interested in that surface and the surface rho is equal to one, we will define as the membrane world volume. This velocity field here is normal to the normal vector to rho. So in particular, normal to the membrane world volume. Now, this statement is simply the fact that the velocity field is a field that lives on the membrane, okay. It's an intrinsic vector field on the submanifold, namely the membrane world volume, okay. So, now let's go back to the analysis that we wanted to do. The analysis we wanted to do was the following. First thing I want you to note is that O mu is a null one form field. O dot O is equal to zero. Why is that? It's because N dot N is equal to one, U dot U is equal to minus one, and O dot U is equal to zero, pretty clear. Now, simply from the fact that O is another one form field, okay. This form of the metric, and now my analysis is for general U mu and rho. Not just the lack of a metric. If we wanted to invert the metric, we want a G mu nu, it's extremely easy to do, okay. I'm gonna give you the answer and then you'll see if you believe me. Where all raising is done by the metric, eta. Why is this the case? In order to check that this is the inverse of that, what we have to do is to take the inverse metric and dot it with an index of the metric and see if we get delta or not, okay. So eta dotted with eta, upper dot of the eta, lower gives delta, no problem, okay. But there are three other terms. One of the terms, the most difficult term is has an O dotted with an O, but O dotted with O is zero because O is another vector field, okay. So that leaves you with two remaining terms. One of these terms has an eta dotted with an O and the other term has an eta dotted with an O, but with a minus sign. So these just cancel each other. Because O mu is this null vector field, inverting the metric was very easy. It wouldn't have worked if this was an arbitrary vector field because you would have got contamination from the O square term, is this clear? Okay, so now the thing I'm gonna do is to determine what is the norm of the normal vector. What is the norm of the normal vector in the spacetime metric rather than in flat space? Remember that the normal vector was defined to have unit norm in flat space in the eta mu new metric. What is the norm of the normal vector in our actual metric, okay. That's very easy because when we dot through eta we get one because n was defined such that n dot n through eta is one. And when we dot n with O, we get one because O is n minus u and n dot n is one, u dot n is zero. So we get one minus one by rho to the power d minus three. Is this clear? N dot n in the metric that we're looking at is one minus one by rho to the power d minus three. The really nice thing about this formula is that this is equal to zero at rho equals one. Now what does that tell you? Rho equals one is a co-dimension one sub-manifold of the whole space. N is the normal vector to that that co-dimension one sub-manifold. What we've just seen is that the norm of the normal vector of that sub-manifold is zero. Okay, now manifolds, sub-manifolds, such that the norm of their normal vector is everywhere zero have an n. They're called null manifolds, okay? And they're sort of interesting things, normal vectors. For instance, the manifolds that include the normal vector in their tangent space because the manifold is defined, the tangent space is defined as all the vectors that are normal to the normal vector, but n dot n is zero. So the normal vector lies in the tangent space. Okay, these are interesting manifolds and would be interesting just for mathematics, but we're not mathematicians since I'm not a mathematician, and I'm interested in them for physics. Where have we seen null manifolds before?  Black hole event horizons are null manifolds.  That the event horizon is the unique null manifold which agrees with the non-event horizon of the static equilibrium, the stationary equilibrium black hole at late times. What have we seen here? We've seen two things. We've seen that rho equals one was the event horizon of the Schwarzschild black hole. Because that was simply r equals r naught. Second, we've seen that in great generality rho equals one is a null manifold. So if this metric that I looked at has the property that it settles down at late times to a Schwarzschild black hole or as I will show you later to occur a black hole or anything stationary, okay? Then this null manifold has particular physical meaning. It's not any old null manifold. It is in fact the event horizon of a spacetime because then it would be the unique null manifold that agrees with the non-event horizon at late times. Is this clear? Now, as you know, just as in fluid gravity, this u and rho will not turn out to be arbitrary functions. They will have some equations of motion and the equations of motion will be dissipated. And so we'll plausibly guarantee that at late times everything settles down into a stationary configuration. In fact, probably you can show this, okay? So we will assume that at late times, that while at finite time, u and t are whatever they are, at late times it just settles down to equilibrium. And therefore the configuration rho equals one, the sub-manifold rho equals one has a beautiful physical interpretation. It's the event horizon of a spacetime, okay? So first thing we've learned about this metric. Metric has an event horizon. We can write down what the event horizon is. It's the manifold rho equals one. Beautiful statement. Usually very hard to find event horizons of spacetimes. Okay, here it's very easy. Okay, please. What do you mean? Yes, but then I changed it, right? I made this an arbitrary function of, for instance, had I extended it such that u dot n was not necessarily equals zero, then it wouldn't have been the event horizon. It wouldn't have been a null manifold. Certainly it was the event horizon of the Schwarzschild black hole, but now we're looking at a class of solutions that's more general than the Schwarzschild black hole, but for this full class it remains the event horizon. Okay, good. Other questions, comments? Okay, now, why is it important that this is the event horizon? This is important for us for the following reason. That rho greater than one is outside the event horizon. As you can see from the fact that when rho goes larger than one, you reduce to flat space. Rho less than one is inside, okay? We want to solve, but we want to solve Einstein's equations. Okay, we want to solve Einstein's equations, but we're not interested in solving Einstein's equations everywhere. We only want to solve Einstein's equations in order to predict the evolution of the outside, okay? What happens inside for rho less than one is not our concern, okay?  We only want to see what a large deligo observer will observe when he's sitting outside the black hole.   But the great thing about event horizons is that they cause the boundaries. So what happens inside the event horizon just doesn't affect what happens outside at all.  Okay, certainly that's what I thought when somebody told me the statement first. But it's true, and in fact it's a crucial element, ingredient in the numerical relativity program. People who do numerical relativity stop their codes once they show they're inside the event horizon because they don't care, and it's very unfortunate that they didn't care because otherwise they would have to run their codes up to the singularity which would have trouble. Okay? So it's a remarkable thing about general relativity that there are these causal boundaries. So you don't have to, if you're interested in the outside, you don't have the, you can forget about the inside. So we're gonna forget about the inside. In fact, we can do better. We'll do a bit better. We'll solve a bit into the inside, but we don't care. What happens, happens for rho less than one. That's between God and the suicidal people, okay? Not our concern. Okay. So we're interested in rho greater than one. Rho equals one rho greater than one. No, this is genuine event horizon. Genuine event horizon, yes. That's what we're heading towards.  Okay? Which perhaps goes along the lines of what you're, if you're asking for more than that, I don't know what to say. But this, these are near the event horizons, as we will see, these are little patches of schwarzschild black holes. Hang on. Actually, you know this well, but, okay. Please. Yes. Yes, exactly.  That was a crucial element, okay? Now, Atisha asks a good question. Normally, an event horizon is a very etiological thing. We could be sitting inside an event horizon, depending on a shell that will collapse in the future, we would not know it. How come in this situation, we know so well where the event horizon was? She's very similar question in fluid gravity, so let me take a minute to answer that question. Okay. In fluid gravity, the answer to that question is that, that event horizons are much less etiologically in the ADS space than in flat space. Why is that? The definition of an event horizon is this. It's a causal boundary that separates points from, separates those points that can reach the boundary of ADS from those that cannot. Okay. Now, unlike in flat space, you can reach the boundary of ADS in finite time. So suppose you know that a point from here can go whoosh and reach the boundary of ADS. Then you know you're outside the event horizon, no matter what is done here. You can send 20,000 shells in the future, won't affect that. You were outside the event horizon. Okay. And this happens over a time that's set by the radial position of where you are. And in fluid gravity, that's basically over a time set by the temperature. So fluid gravity, positions of event horizons are a causal, but only to the extent one over T, okay? One over T is a short lens scale in the problem. Everything's varying on lens scale, large compared. So essentially fluid gravity, the fluid variables locally determine the event horizon. That was crucial for the consistency of the whole fluid gravity picture because event horizons define entropy currents and the entropy current and fluid dynamics is a local function of the fluid variables. What's the situation here? Actually it's very similar. It's very similar because we are looking at solutions, because we're restricting attention to class of solutions. The class of solutions are such that outside a little region of around here, you reduce the flat space. That little region is only of thickness R naught by D. So normally in flat space, you have to get all the way to the boundary and that takes an infinite amount of times, okay? But in our class of solutions, in our class of solutions, once you get out of this little shell, it's flat. So you know you're gonna make it to the boundary, okay? The class of solutions we're looking at will not allow some strong gravity waves in addition. If you were doing that, you would have to do a different analysis, okay? But in this class of solutions, as you see, outside this little shell layer, space is just flat. So once you get out, you're home, okay? So this distance being one over D tells you that the location of the event horizon is essentially local in time over time scales one over D. Very similar to the graph. So now we know where the event horizon of our space sits. That's solved half of our problem because we don't have to worry about solving Einstein's equation for Rho less than one. We still have to worry about it for Rho greater than one. But what can we say about Rho order one greater than one? Okay. Suppose we look at Rho minus one equals order one, okay? Then this metric is exponentially close to flat space. I'm broken the wrong metric. This metric is exponentially close to flat space because we've got some unit norm one form divided by a function that's larger than one to the power D. That's extremely small. So distances such that Rho minus one is order one is flat space and flat space happens to be an excellent solution of Einstein's equation. Up to exponentially accuracy for Rho minus one of order one, our metric automatically solves Einstein's equations, okay? Where is it not automatic? So let's do a more serious estimate of that. Where it is not automatic is as follows. Let's write Rho as equal to one plus Rho minus one, okay? And then Rho minus one will be small. I'll just multiply and divide this by D for fun. Actually, I should really be doing this by D minus three but since D is large, D and D minus three are the same thing. Now we're interested in one over Rho to the power D minus three but I'll just write it as D because it's irritating to carry the minus three alone. Which is one over one plus D Rho minus one by D to the power D, which is approximately if this thing is not too large, E to the power minus D into Rho minus one. Imagine for instance that this has had fixed as D is taken to infinity, okay? So what this is telling us is that we have to, this stuff is non-zero provided Rho minus one is of order one by D. If Rho minus one is of order one by D, Rho minus one is alpha times one by D. Alpha is any number no matter how large that held fixed as D goes to infinity, the equation is not automatically solved. But for larger values of Rho minus one, the equation is just solved to very good accuracy in the largely extension. So what's the situation? The situation is that we've got this membrane surface. Rho equals one, okay? That's the membrane surface, Rho equals one. There is a little thickness around this membrane of order one by D where we have to worry about whether this metrics all Einstein's equations or not. Outside this region exponentially approaches flat space. Wonderful, solve Einstein's equation.   Unicorns could be created there for all we care. It's causally separated from what we do. So in order to ensure that Einstein's equations are solved for the purposes of predicting the outside, all we need to do is to check whether they're solved in this little region. Is this clear? How much time do I have left? Minus one. Okay, okay, so then we'll wait till the next lecture, which is just in the afternoon, so that I can further analyze the question in this little next lecture. Thank you.


going to kick it off. Good evening. How are we doing?  Good. Good. Well, welcome to the 12th annual celebration. This would not happen if it were not for you. So thank you, thank you, thank you very much. It is because of you that ILAP is engaged in some noble causes. So we will celebrate that tonight. Before we do, I have to thank CTN, Community Television Network. I've been informed that I'm on a five-second delay because sometimes I just get very excited and say crazy stuff. But we will be able to watch this on Time Warner Cable Channel 5 in the Greater Portland Area and also on demand on their website, which is CTN5.org. I want to thank them personally for taping this event. The other thing they have done is they are actually live feeding this to one of the Trump rallies as a politics on my sleeve. Yes, sir. But they're live feeding it to show how saying some people can be in the sea of insanity. So here, here. So allow me to introduce myself. My name is Kerem Durda, born in Pakistan of Turkish parents, came to the United States when I was 17 and a half, went to an all Benedictine Catholic College, which I did not know at the time. It is very funny. Over beer one day I will tell you the story. Came over to UNH, met my wife in 1993. So it's a good day. And settled in Maine. Because I was born in Pakistan of Turkish parents, came to the United States and have been fortunate enough to work and run a couple of global companies. I am the poster child for Homeland Security, what not to do. I can give you secrets about Homeland Security that you may not know of.  I know because I've been in the time out section many a time. Many a time. So I'm blessed with three kids, a sophomore and a boy and two girls in the seventh and fifth grade. I am under strict orders by them and my dear wife not to embarrass them. I can embarrass myself but I cannot embarrass them. So that is my story and I'm sticking to it. If you do Google me, you'll find out some interesting stories about me but one interesting thing is there have been 68 different versions of my last name. Inclusive of the all famous, can I please speak to Mr. Dirtbag? Which creates an interesting dynamic because it's mostly telemarketers and then I get to say to them what is your name and that's really that that's when the wall breaks down and they start talking to you which is interesting. So I want to take the opportunity to introduce a dear friend of mine, the executive director of ILAP. She has been working since 2000 to better lives. She's passionate, articulate, has concern and care, is a decent human being. And I'd like her to come up here and say a couple of words. Thank you, Sue. Thank you for having me. Good evening and welcome to ILAP's 12th annual SELA Soiree. Thank you all so much for coming this evening. Thank you for supporting ILAP, for supporting our immigrant community and for helping to make this another sold out event again this year. Thanks so much. First I'd like to thank our event sponsors and our raffle donors. You can find them listed in our program. If you see them tonight, please thank them. Many have been donating year after year and without them we would not have a SELA Soiree. So we really appreciate that support. I'd also like to recognize our incredible planning committee and especially Sally Newhall from Sea Glass Events who's our event coordinator, our development director Loretta Prescott, Olivia Orr on staff and all the incredible volunteers who helped put this event together tonight. Thank you so much. And a special thank you to Karim Durdog for being our emcee tonight. We really appreciate that. Thanks so much. So every year ILAP serves over 2,000 people helping them gain legal status. Another thousand people come to our education and outreach events. So how many people can you imagine it takes to get this work done? Well, at ILAP we have just nine staff and over 200 volunteers who help support them to get all this work done.  People and without ILAP, there would be no place for low income immigrants to go in Maine for help getting through that complex immigration process so that they can get the legal status they need so they can stay in the country and build their new lives here in Maine. ILAP staff and board are really the heart of the organization. It's their dedication and their commitment to ILAP's mission to really make ILAP such an amazing organization and we really appreciate everything they do. I'd also like to recognize somebody else who's really was the heartbeat that started ILAP. Beth Stickney was ILAP's founding executive director. I know she's in the room here tonight. She can see it over here. Beth is recently back from Italy and we're so glad to have her back in Maine. Beth had the foresight in the vision 23 years ago to start a pro bono project with a few volunteer attorneys. I think a few of them are in the room this evening representing asylum seekers. And as the immigrant community grew over the years ILAP has grown as well. In 2000 we became a staffed organization and we now as I said have nine staff and 200 volunteers serving 2,000 people a year. So it's really incredible and ILAP was really the foundation of what has now become a network of organizations, advocacy groups, service providers, leaders in the business and government who are all supporting and welcoming our immigrant community. So we really, if it weren't for Beth, we wouldn't have ILAP and this would be a very different place. We really appreciate and gratitude for everything that she's done and for her continued support and advocacy for the immigrant community. Thank you. Have better time for us to gather together and celebrate our immigrant community. When you can't open a newspaper, you can't churn on the TV or the radio without hearing ugly words of anger and fear and hatred and racism. These are poisonous words that encourage dangerous action and response. But we can counter that intolerance with positive words of celebration, support and inclusion and action that promotes a community where we celebrate and we appreciate our diversity and we accept and understand our differences. And by being here tonight, you're part of that message because you understand the important role that immigrants play in our community. You understand the diversity and culture they bring, the new ideas, the skills and the talents that they bring to our workforce. They bring diversity and vibrancy to our community. And that diversity is what is and what always will be part of our society, a real critical part. So thank you all. And take this energy with you. Take it back with you to talk with your family, your friends and your community, people in your community because celebrating our immigrant community here tonight and then outside the doors after we've left is the way that we will be able to overcome that fear and hatred and racism that we see out there. We really appreciate you being part of the celebration tonight to help celebrate and support I LAP to support our immigrant community. We have a really exciting program ahead of us this evening. We have a quaba ensemble, which is a West African dance and drum group. We're really thrilled to have them here. We also have many others have helped to make this a beautiful and delicious evening. We have Empire, Taco Trio and Jewel of India and Coffee by Design. We also have Dogfish at the bars, Adam Burke who helped with coaching, A.V. Technic with the light and sound and Del Nagoy who had the beautiful outfits you've seen on our raffle volunteers. And of course, Pandora who's brought us once again these beautiful lights. We really appreciate that. So I hope you all had a chance to buy some raffle tickets. I do want to let you know that we will be picking the winners at the end of the program this evening. And you do need to be present in order to win. So make sure you hold on to those tickets and listen in at the end. We also have some dessert and coffee that will be following the performance. So I hope you enjoy the evening. Thank you again so much for coming. And I will turn things back to Karim. Thank you. Sue in confidence told me that she's thinking of running for the governorship. I say yes. It's about time actually, a woman who believes in immigration rights. I don't know. I think it's time. I think it's time. I am thankful for iLab to select me for this for this honor. Loretta told me that she saw me on hosting Turkish Idol, the pop show. I don't know. I think she watches way too much TV, especially international TV. I don't recommend it. The soap operas are really droll and boring.  So I would recommend watching Turkish TV, Pakistani TV, whole different story, whole different story. So hey, look, it's time. So I want to welcome the Akamwa ensemble out here. You know that music is a part of life. It's the rhythm that keeps us going. It gets us through some tough times. It helps us celebrate some good times. I hope that you enjoy them. I hope you clap with them and you dance with them. Because if you don't, I'm coming around you and we're going to do it together. So let's give a warm hand out. I said, move away. The new boogeyman is in town. You see that dancing? I'm a firm believer. We listen to that music. We at least live two years longer with the energy. And I've been told I can't move my feet because I'm supposed to present, but I can't help it. Come on. Boogey is about telling stories, stories. And I am one of those many millions of people that have stories came to make a life in the United States, thanks to the nobility and grace of many, many people. And I think there's nobility and grace in what iLab does. There's nobility and grace in the life we try to create. Whether it's trying to survive the visa immigration, the visa process or the word permit process, or having somebody advocate for us. I strongly believe to the bottom of my core and my dancing feet. That what iLab does is noble and graceful. It helps us create stories. Yes. It helps us create stories. It helps us tell our stories. And we have a special, special speaker who was going to tell us her very, very valuable story. So I welcome Carmen Sanchez. Please. Thank you. I'm going to tell you my story, how iLab helped me to United States for love. I have to live Peru, all my own business. I decide to take a raise and live everything behind. When I got here, unfortunately, the thing changed. I found myself in abuse marriage. In that time, I feel alone, trapped. I lost a sense of what I was. One day, a nurse was able to see my eyes, the pain I was feeling. So she was able to help me to go to the family crisis. Thus, family crisis referred me to set up an appointment with iLab. When I walked to iLab, at that time, I didn't have any proof. Nothing to prove the pain was my heart. The lawyer, iLab could open my heart. She listened to me carefully. The most important thing, she believed me. Eventually, I trust her, was able to tell her my story. It was really, really hard to tell her all the detail. Also, the process with immigration was long, but Jennifer was there with me throughout. Finally, was we able to get my legal status? Since to iLab, I smile and cry. Island means to me, protection, support, home. In other words, island means to me, one community, one family. Finally, I was able to obtain my legal status. Guess what? Today in the morning, I became America's citizens. This is the proof. Citizenship means to me a lot. Because it gives you equal rights. I feel that I am part of this land. I have a role to play. I have a big commitment. And also, I feel this is home now. The most important, I think, even more precious, I am here as my own person. Thank you, iLab. Thank you, Susie Rocher. Thank you, Jennifer Bailey. I am very grateful for your wonderful work that you have done. I will be eternally grateful to you. I said in Spanish because I speak Spanish. Actually, I speak Spanish. But I said, thank you very much, Mrs. Jennifer Bailey, for your amazing and extraordinary work.  Thank you, all of you, for letting me to share in my, sharing with you my story. I appreciate it a lot. Thank you. Thank her for her story. I want to thank her because it's not easy sometimes to tell our stories. It takes courage on your part to listen to us and give us a little space in your lives. It takes courage from our side to articulate things that sometimes are sometimes very, very tough to articulate. And so we are gathered in this space to share each other. And I'm incredibly proud that you are now an American citizen. Incredible. When I became an American citizen shortly after 2001, prior to that, my wife and I went for an interview, which I think lots of us go to interviews. And I remembered the interview saying to my wife, so who is this alien relative? Because on the forums it says alien relative. And my wife, dear wife from South Portland, Wellesley graduate, you know, tough. He says he is not my alien relative. He's my lover. I was like, yeah, the interviewer pretty much said, we're done. Goodbye. You're approved. So the other curious thing is that, you know, I'm a soccer fanatic, soccer fanatic. And so I'm blessed with a couple of occasions seeing the United States and the Turkish national team play together. And I must say that I stand up for the anthem of both countries. I wear the jersey of the US team in the first half and then the Turkish team in the second half. It's not divided loyalty. It's just you have more fun by having two sets of jerseys. And so in that way, in that way, I want to thank my on the behalf of all of us for making us part of your fabric because it is our fabric. And I don't think we should let anyone tell us any differently. Now we're going to do some fun stuff, because iLab does a lot of work and we have to help them. Stuff they do isn't for free. It costs money. I don't know if you realize this, but they actually cannot apply for federal grants, because what they do, the work they do is with undocumented human beings. Isn't that interesting? They cannot apply for federal grants to help other human beings. But we can get federal grants to do research on mice. I find that curiously strange. But we are going to do a reverse auction. And we are going to raise, I kid you not, $25,000. We're going to raise $20,000. And then a dear friend of ours, Imad Khalidi, who is the CEO and president of Auto Europe here in Maine, has placed another $5,000 as a match. I have been asked not to leave the stage till that happens at great personal risk. I'm also a great poker player. I can take my clothes off for money. I urge you not to try me, because for a good cause, I will do so. So the way it's going to work is we're going to start with some large amounts, and then we're going to work ourselves down. And in the course of that, other than public shaming, the only leverage I really have on you is on your good conscience. And have some giggles and laughs at the same time. So just as a point of fact, and I wanted to read this out. Asylum seekers taking the case of the government without an attorney see an 88% denial rate, 88%. When I laps get involved, it's 97% success rate. So think about that.  So in that vein, we're going to start out for 1000 bucks. I am seeking a whole bunch of people to donate 1000 bucks each. Now I know some of you. I will not call upon you yet. So there are some dear friends. So who do I have leading the charge? Thank you. I didn't even have to undo a button. Thank you. Thank you. Did you see that move the guy I'm taking? Did you see that movie had? I mean, I got jeans on, but I mean, that was amazing. I got it. I got it. Oh, yeah, it takes here. Conditioning workout. I think there's a DVD right there. African rhythm music. I mean, I don't know. Here's here's here's a here's another interesting fun fact. This is really interesting. So when the unaccompanied child crisis happened in 2014, I let was the one who helped the kids. Just just think of it. I left helped the kids during that 2014 crisis to have them safe harbor here. So now we have a potential second, third generation. Thanks to I laps work. Just think about the impact that that's a multiplier impact. You know, there's an ancient Talmudic saying you help one life, you help a universe. It's amazing. I haven't told that due to some system failure, not to be blamed on Microsoft. We need everybody who plays $1,000 again. And we're not going to blame Bill Gates for this. Yeah, did we get it 242 235 328 117 314 234. Thank you. Thank you. You just introduced me to your wife this evening. So yes, yes. We need one more. One more. Okay, you know, I'm going with the I start small. I'm serious. One more. I'll think I'll think yeah. Oh, 198. Yes, I will save that for next time. I do sing very, you know, thanks to YouTube, I can catch up on all my old Urdu and Turkish songs. Oh no, I do sing some journey songs. Remember journey? All right. I'm having a good time. I hope you guys are too. So next, we're at the level, another level. And I may join you guys. But before I do that, we're going to the next level of $500. And I want to give you a sense of what $500 does in Pakistan. Actually, when I was growing up, 500 bucks actually got us a whole month's worth of water via tanker. We didn't have water while going around it. You get it maybe once a week. So 500 bucks paid to bribe the water tanker guy to come to our neighborhood and give us water. So just, you know, 500 bucks. But what 500 bucks more importantly, or as importantly does is gives I lap the opportunity to have an attorney to represent a human being who's fled violence, persecution, intolerable pain that we sometimes cannot relate to, and at least gives them a leg up in the immigration process. That's what 500 bucks does. So I want some $500. Give us 500 bucks. Yes. Thank you. So I'm going to read out the numbers that they were going to thank them. 322 137 336 187 342 346 301 171 207. This is this is just a lot of fun. I must thank you guys. I'm just so sweet. So sweet. So not a fun fact. Not a fun fact. And this is this is that this is actually a true story. When I was applying when I was applying for my green car, actually, you know, in the old days, you had to go through multiple, multiple processes.  So I was called for an interview in at the JFK building in Boston. Because I wanted to now apply for my green card. So I went there, you know, Yes, I've been here for the interview. So say, Well, we have a problem. What's the problem? Well, we've lost your file. You lost your file. And you're calling me over here interviewing me. Why? Well, we have to tell you that now is going to be another year in a half. Well, obviously, I lost my, you know, and but but I had, I had a colleague who knew a lawyer in these in these matters, made a bunch of phone calls. I had somebody talk on behalf of me to go in and say, We don't care if you lost the file. This man is not going to wait another year and a half in limbo. But that's what I lap does. That's what people like I lap do. They give us a voice in this Kafka esk maze maze that don't don't be fooled. It's all online by now is an online maze of trying to make sense of things. So that's where I lap I lap comes comes in handy. Potentially the other place I lap also comes in handy is for people like me when we're going to Homeland Security and the guy runs my US passport. And as this look and the reason is the reason is my name is misspelled on so many different places that some time ago, actually, I was on the no fly list, which makes for very fun entertainment. When your flight gets diverted to Rome, and you're singled out to come and have an interview, talk about 474 people really mad at you. Because they make somebody made a mistake somewhere and diverted the flight. So but here's where I lap I lap comes in handy because when something like that happens, we need support. We need somebody to listen to and say to us, I got your back, because now you are part of us. And the US makes us a whole. So in that vein, in that vein, we're not going to go to $300. And to kick it off. I pledge $300. I have a number somewhere 178178. That's actually I was bribed to do that. And I'm just kidding. Being Turkish and Pakistani bribery. Ooh, yeah, we know about bribery. So $300. Let's go. Otherwise, I'm going to crack down. Okay. 240 145 155 273 305 123. Oh, they're pointing at each other. 167. You know, don't do that in Turkey or in Pakistan. No, sir, do in Pakistan. Do not do this. That is that is bad. So don't. Oh, now you're really doing it. Oh, Bob Barker got nothing on me. Nothing. So you need more 313. Connor in Turkish beer, okay. So we're in which means three is in Turkish is so we need three more. We need to get to which is two. We go count down. Come on, guys. 312. That's our independence. 312. Yes. Oh, come on, guys. One more. You know, if I could tap dance, I'll do tap dance. I was gonna. Well, I'm not gonna say it. I was gonna say something political, but I'm not gonna. No. No, I'm not. I'm not. I'm not gonna say it. Claude, where are all these guys? All right, we have we have one more tranche to go. This is at 50. And we need to $50 200 a hundred.  That's what it is. I'm sorry. It's ridiculous. I mean, no, seriously, look, she gave me these things. All the color coded and all this stuff. And you know, I mean, really, I'm a guy. I'm a guy. Seriously. And I'm a hybrid mutt on a Pakistani Turkish American. I'm already confused. And you gave me these three colors.  Seriously. All right.  We got 275 307 326 258 244 236 162. Okay, hot dang it. I'm gonna do 40 push ups to you guys or I'll keep on doing push ups. I saw I how many more do we need? Five more. You did that again. Okay, we're doing I'm doing push ups till we get five more. Seriously. Let's go. Come on guys. He's 200 dollars in my pocket. We're 17 and a half. I didn't quit. I'm not gonna quit right now. Let's go. Let's go one more. This is a hundred bucks. And for that, many, many, many. So let's do 100. You know it. Come on. You guys got great food. I keep those hands up because I want to thank each and every one of you personally. Do we have that? Yes. 293 346 347 188 161 290 184. Keep them up. 345 249. Thank you. 333. Oh, yes. We got to go and play the lottery tonight.  Do we get them? You guys haven't seen some some funky dance moves. The thing is you do the crossover and go around. Remember the old James Brown days? They used to go on his knees. Okay. Do we want to go more? Absolutely. 50 is the last level. 50 is the last level. And I'll tell you what 50 does. I believe the on one of the one of the things that, you know, we say when we swear in, I feel like one of those Android, I tell you what 50 bucks does is it gives our fellow human beings a chance to hold the job to be able to vote to have a voice and to get preference when family members want to visit because as United States American citizens, they get that preference. So before I ask you for your 50 bucks, I want to tell your story. My dear mother has been coming from Turkey to visit us for the last 15 years. She's a sweet woman. But just like most immigrants and their families, they love to bring food like fresh food. She's nuts dates, you know, and for the last 14 years, she's been very fortunate that when she goes through immigration, they don't question her.  She's perfectly fluent in English, by the way, perfectly fluent. She said, I don't know English. I don't speak English. Oh, keep on going. Anyway, but last year, they said, No, you have to open it up. So she got interviewed for three and a half hours, three and a half hours. And you know, she loves to smoke is a long flight from Turkey. And so she said, I have to smoke. They're like, you can't smoke here. And she said, I'm a 78 year old woman. I've been smoking three packs a day for 45 years. I need to smoke. So they get agitated at her and says, you cannot be agitated at me. You're the same age as my son. And who's your son? Get him to like, Oh, I think we know him. You know, because I've been I've been nailed so many times at Boston, I've been actually, I kid you not true story. I'm gonna keep it really short. But they ran my password again. Before I knew it, two people came up to me, escorted me.  It's not. It's the underground HQ of Homeland Security. They open up just like a Star Trek. So they took me in actually, and they interviewed me for an hour and a half. Yeah. So it's really freaky. Anyway, coming back to my mother.  She said, Well, it's jam, fresh mulberry jam. What do you got over there? Fresh Turkish cheese. What do you got over there? Sausage. That's when the guy you actually brought sausage to the United States.  And I don't know how she said that, but they took everything else but left the sausage for her. And so when she came out, she's really, really mad. So that's what 50 bucks gets us. Okay. Sausages. So we need 50 bucks from a lot of people right now so that I can get sausage. If you want Turkish sausage, by the way, I'm saying tulumba.com. So 50 bucks. Let's go. Let's go. Let's go. All right. I don't think I need to unbutton anymore, but I may have to. Are you getting up? What do you want me to say? 371, 174, 108, 114, 367, 113, 151, 255, 168, 179, 185, 209. The reason I can go because I'm a huge Pearl Jam fan and Pearl Jam fans are trained, trained to do so. Are you a Pearl Jam fan? Yes. Yes. Anybody more? What? My friend, where you going? We're gonna dance. We're gonna dance. We're not done. Did I say, did I say thank you to you guys? So special. Thank you. No, the kids want to come up. These darn kids come on stage, guys. You guys look good. You guys look good. So they have something special for all of you. And I almost took a Madonna like fall, whichever in pretty cool. But what are we going to say? Thank you. I'm Turkish. We dance like this in Turkey. We do. We do. I'm not lying. I'm not lying. Great. So are we going to do the raffle stuff? Yes. So the raffle. I don't know if you guys have taken out. Thank you guys. Thank you so much volunteering. Thank you guys for volunteering. So the raffle. All right, guys. So have your tickets ready. If you have cloned yourself. What? You coming to? Did you get a ticket? No, of course you do. Come on over. I'm just pulling your leg. Okay. All right. So our friend is going to help us pull some tickets. In the event you have cloned yourself and your true self is not here. You cannot win. So you have to be here to win or all the way down.  Boxes from each bucket. Okay, each bucket. Okay. Now, just like the Oscars. This has been approved by Price Waterhouse Cooper and Libran for following certain procedures and avoiding conflicts of interest. That's not necessarily true. But I thought that these handsome people should deserve deserve a hand of applause for not rigging the election on this one. So you start. So this is this is for the humanities package. Pick the right number. All right. Everybody get him out. Two, four, one, zero, seven, seven, eight. Yes. Is it real? We need to do a quality check. Thank you so much. So she gets them from back there, right? Oh, I got it now. Now we have the cuddle up package. Oh, cuddle up. Number is two, four, one, zero, four, two, eight. Hey, stop clapping before it's announced. Cuddle up package. Okay, next one. Oh, this this is a good one. Okay, this is the big beer package. All right, why don't you come up, come up over here. Mix it up. New series, two, four, zero, nine, seven, one, two. First ever mustache man to win a raffle price. Thank you so much. So you get to keep and she will she will guide you to your to. Okay, fine wine package. I believe that's what my wife used to call me, like fine wine package. Definitely brand new series on this one. Brand new. I know, I know, I know. Well, that's why we're an immigration kind of crowd, you know, we like to mix it up. Mix it up. four, two, seven, one, one, eight. I'm gonna take care of you. I'm gonna take care of you. What is your number? You know, both in Turkey and Pakistan, you know, national elections have been rigged just on the basis of pieces of paper. We did. So I'm gonna take care of you. I'm gonna take care of you. All right. So this is the main sports package. May you fare well in this endeavor. Okay. New series. Two four zero. Is it is a close to four zero? Two four zero nine eight three one. I got a pen. Do you need a pen? People have done worse with a pen. Yeah, I'm gonna read it again. And then I will say the same number in Urdu and Turkish for you know, multicultural effect two four zero nine eight three one. Also known as Do, char, suffer, no, art, teen, egg. Yes, you got it. All right. One more time. Oh, for verification. Are we? Let me say it with a clipped British accent for clear Lawrence Olivia articulation. Two four zero nine eight three one. All the way from downtown Abbey. Conflict of interesting that we talked about. Okay, last one wellness. Just like tonight, which has contributed to our overall wellness. This ticket gives you the key to wellness. It's huge responsibility. Huge. You got to win. I'm selling time. You got to win. Okay. I don't know. I'm two. I will say fun. Yeah, thanks for everything. No, we really enjoyed it. Oh, thank you. Thank you so much. Everybody gets to enjoy those great raffle raffle raffle tickets. And I want to thank the volunteers to they did a great job. But more importantly, I like to thank everybody who screamed. I just love it. All right. So I got I got two announcements, two announcements to make really, really quick. There's actually a conference coming up on May 21. That's really important is it's called empower the immigrant woman. It's in Hannaford Hall. And it's for and about immigrant women with a jobs form in the morning and a gala in the evening. So try to get information from the desks over here to get some information because it's a really important event. I don't know if you guys know this, but women make the world go around. So they do, they do. And on a serious, serious note, serious note, there's actually a study that was released by the Gates Foundation talking about the importance of women economic development in third world countries. I urge you to take a look at that. We know, we know the importance. We just need to do a better job. Second, second, second announcement.  So important, important things. We know Peter, Paul and Mary. We know them, right? Okay. So they have been kind enough, kind enough that in June, they're going to perform a concert, a benefit concert, where the proceeds will go to I lap. That's in June. And it's called one like many candles is at the congregation betham in South Portland. So it's a free event. It's a free event. There will be reception at the end of it. All to benefit I lap all the information is on their website, which is i lap main dot org. If you type in some other crazy website, you know, go for it, but it's i lap main dot org. And they asked me to thank everybody again in terms of Empire, Jewel of India, Taco trio, the guys, the guys from Whole Foods for all this, all the good work that they did and fed us. So I want to thank all of you. I want to thank the volunteers. I want to thank i lap for making me make some push ups. But from the bottom of my heart, I thank you for making a difference in everybody's lives. Have a good night. Thank you.