Thibault Damour - Gravitational scattering at null infinity: asymptotics, BMS symmetries, (...)

So I wanted to complete what has been said before. Lego VGO Kagra has now detected 390 events about and one of the most beautiful is this one from 14 of January 20125 where the real data after whitening is this gray thing you see here these are templates okay uh and this is the highest signal to noise ratio and this allows really to check the quiz normal modes to a few percent and prove the cur nature of the merging black holes. Now just to establish the notation uh I will talk in the first part about waveforms from coalesing binaries and uh the difference with uh from hyperbolic encounters. So the notation uh h munu is defined this way without the infamous factor two of a shocken uh it's a joke uh from the the waveform you project it on a null frame at infinity and you what I will call the complex waveform is the coefficient of 1 / r which is essentially the combination of the two polarization with a minus i in this convention and I will discuss the issue of what happens beyond the one / r. Now when you have coalesing in spiraling and coalesing binary black hole this is a space-time diagram where time goes up. Okay, just and we have seen this is the type of waveform for coallesing binaries but I will be here interested in waveforms emitted by scattering trajectory. So just to have in mind that they are very different from this because you have a splash of radiation when the two thing get close and the type of waveform you get is this. There are the two polarizations and on these waveforms when the velocities are relativistic you see clearly that there is a memory uh which means that the value of h at the end of the scattering event is different from the value at the beginning and what will be important in what I will tell about is the way you go towards uh actually towards minus infinity you you go towards this limit uh with some slope also now so I will be in four dimensions there will be no cosmological constant uh we will solve Einstein's equations in the case of two black holes this is rich equal zero and I wrote down in harmonic coordinates the explicit form of Einstein's equations which are nonlinear but not extremely complicated finally okay you can write them easily So uh historically I'm going to talk about subtleties about what happens in the infrared that infinity at the various type of very far from the systems. This issue has been greatly clarified by the after many previous works but let's say the work of man Bondi and his colleagues and uh of reach in around 1960 has been important for clarifying things uh although the work of Vladimir Faulk before contain actually a lot of very clear results. Now one of the basic uh idea is to set up a coordinate system where instead of having the usual coordinate which is time in flat space time time would be t minus r here you say I want an exact solution of the econal equation for null waves. uh that is to say a family of null hypersurfaces outgoing null hyper surfaces uh each null hyper surface is characterized by one value of u and u is a solution of this okay then you use coordinate system where u is used as time and then some radial distance and some angles you try to fix the metric in a rigid way by imposing as many coordinate condition you want this is the bondi gauge and then I want to insist here the then they made the assumption that all metric function entering this gauge fig coordinate system admit expansions to all orders in one / r. This was the main uh assumption. Now uh this assumption um has been uh reformulated in a sense in a very elegant geometric manner by Roger Penrose who introduced the idea of let us focus on the structure at infinity of this type of spacetime radiative spacetime asytoically [clears throat] flat by distinguishing various ways of going to infinity. So the usual way to get massless waves at infinity is called scri plus. Okay, this is a future null infinity. It is this type of structure here. If you go to infinity in space, then this is called space-like infinity I can go to infinity in the past at the velocity of light or you can go to infinity slower than the velocity of light. Okay, just for you to know there are those five type of infinities and the idea of Roger was mainly around these things to assume that the u there is a conformal transformation of the physical metric gimmu by a certain factor which essentially is 1 / r which brings infinity at finite distance so that the conformly related metric jihad munu now was assumed to be smooth uh in a sense of admitting even extensions beyond sky where the spacetime does not exist. So uh so this is the analog of saying the previous bondi things admitted expansion to all powers in one over r here you assume it is smooth and actually it's very important to be at least c4 for some uh things to be true now what were the main results uh of the bondi sax penrose approach the main uh one of the result was the so-called peeling peeling behavior okay So in the formulation of Roger Penrose the conformal compactification this peeling behavior means after you do uh the conformal transformation the vile tensor of the conformal matrix chat hat which is numerically equal to the all by definition of the vile tensor if we indices this way uh vanishes on sky plus and vanishes smoothly like the first power of omega. which means that if you divide by omega, you have an object which is a finite measure of curvature at infinity. Okay. And this is more or less equivalent if you assume uh C4 here to the other formulation of peeling which is that if you decompose the V curvature the val curvature has 10 real components in all which can be packaged in five complex quantities and in the notation of Newman and Pedro these quantities are called S0 1 S 2 3 SI 4 and the peeling theorem says that maybe I will need some thing here. Yes. And the peeling theorem says that the usual uh radiation uh oh I forgot uh 012 34. Okay. Sorry. >> It's there. >> It's there. It's there. I should have Yes. The usual radiation cipher the one over R part of the waveform appears in the curvature. The curvature is made of two derivative of the waveform. That's why what appears here is actually the second u derivative of what was the complex waveform and this is pi4. Okay. Then the pi 3 goes like 1 / r² 1 / r cube 1 / r4. But the crucial thing is the uh fastest decaying component size zero which is this combination of things should decay like 1 / r5 and this is equivalent to this. So this is called a theorem but this theorem depends on the assumptions and uh okay so this was one of the big results of the bond sax penrose approach another thing was the discovery by bondi met and then generalized by sachs of asytoic an asytoic symmetry group of equations near future inf null infinity and uh I have given The result here uh this group the BMS bondi met sax group um is obtained by combining conformal transformation of the sphere at infinity. So at infinity the two angles theta phi make a two sphere s2 a conformal transformation of a two sphere in in this complex coordinates sterographic coordinate is an SL2 C uh transformation so it's an omographic transformation with arbitrary complex number A B CD modulo the determinant it needs you have six real parameters and these six real parameters this group is omorphic to uh the group of Florence rotation of uh rotations in space and boost. Okay. And then the surprise was in addition you have something which are called super translations where the time u so remember u is essentially t minus r plus logarithmic corrections that these things uh could be shifted by arbitrarily angular dependent shift. So you change the proper time the time at infinity in an angular dependent way. If you restrict if you decompose this so the so-called super translation in multiple moments the multiples L equals Z and L equal one they contain four independent parameters and this is equivalent to the prankar translation acting in in spacetime in the bulk of spacetime but you have this thing which are huge generalization of the prankar translations and the problem was from the group theory point of The translation subgroup of this group is uniquely defined as a normal fourdimensional subgroup. Okay, it's the only one physically it means from the bondi sax penos construction at infinity you can define p mu the radiated angular linear momentum at infinity in a totally an ambiguous everybody agrees what is a good definition of losses of energy and linear momentum but there is no way to define a preferred normal subgroup which would be the lawren group the lawens group appears but there are many lur groups. Okay. And if you make a super translation, they are not equivalent to each other. So it means you cannot define a priori uniquely angular momentum and this will play a role and is still playing a role. Now uh yes so so the peeling theorem was uh so actually it was an assumption. It was saying if we assume everything is nice and decays like power laws there is this peeling. Okay. And early on people starting with couch torance Novak Goldberg and Winnie Kur said but maybe u there could be also solution of Einstein's equation which do not have those nice expansion in one of R there could be logs appearing uh are we sure that this is the the best thing okay and in particular wikur in 1985 said the a kind minimal violation of the idea that the conformal curvature tensor vanishes linearly in the distance to the future null infinity omega could be that it vanishes but like omega log of omega so it means there is something singular because if you divide by omega there is no limit but it's rather mild okay but this was just said maybe this could exist and then push and others have studied general spacetime solution of formal solution of Einstein equation because now if you ask the question is it compatible with solving Einstein equations to write formal expansion at infinity that contain power in 1 / r and log of r. The answer is yes. When you start putting a log at some order it will proliferate but you can put logs there are solution formal solution of this type. Okay. Now if we turn to more uh rigorous or all order result uh yes so maybe I should site that Elmut Fredish in 1981 proved that the peeling is satisfied if you give initial data uh for hyperbolid thing that is to say if you look at spacetime and then you have square plus here and you give data which decays sufficiently fast on not on a slice at t equals zero but on a slice like this then he showed that if the thing is smooth enough here it stays smooth in the future so there exist solution of Einstein equation of this type rigorous that are peeling and this is linked to a result of luke blanche working within the multipolar post minkoskan formalism I will mention in a moment which is perturbation theory but to all orders he could show that if the spacetime in this framework was stationary before some time in the past then peeling is okay. Okay. But at the same time, I mean a little bit later, Christo Kleinman in their uh very monumental work on proving stability of Minkovski space actually uh they have estimates on how the curvature decay at infinity and these estimates say that the simplest consequences of peeling which is that P4 goes like 1 / R and P3 goes like 1 / R square are valid for very general solution given from t equals0 thing but after that the estimates leave open the fact that maybe they don't peel although my understanding is they cannot prove that they do not really peel although I I expect that for generic solution they looked at uh yes they would not peel now I want to mention something that I learned recently when Samuel Gala visited here it's the a Nice work by compare Gala and V of 2024 of putting together all five infinities uh and modular assumptions that is to say you you describe formal solution of Einstein's equation which admit asotic expansion here here here and at this corner here you use a type of expansion valid near space-like infinity that were introduced by Bobby Vag, Bobby B and B Schmidt long ago. You do a similar thing with anatic continuation toward this thing and then it gives a way of putting together and what was slightly surprising to me is I mean because you impose matching condition at all corners you have only one BMS group for everything. So if you do a BMS super translation here you have to do the same essentially of the analog everywhere and then from this point of view BMS would be a symmetry of all infinities >> but here the matching is not this antipal matching >> it's more subtle it is it contains this with subtleties and I will come to this because apparently there are more subtleties even than uh that will part of the later story which got changed two day ago when I got an email of compare. Uh so these are fresh news. uh [clears throat] now ah yes so what I was saying before is people said you can have peeling if you assume good one over expansion or maybe you don't have peeling but this was purely from looking at possible solution of unshine equation at infinity it was not rooted in the source I mean what you want to know for instance for scattering if you have two masses that come then they collide or I mean they they scatter at impact parameter then they go away. what is the structure at infinity and uh concerning uh peeling at square minus yeah I should have said that I mentioned the peeling theorem on square plus there is an analog thing if you assume alapenos that everything is smooth conformally here you have the same peeling theorem except that it's reverse that pi zero goes like one / r because it is the analog of radiation and s four behaves like 1 / R5 but what they showed >> can you explain perhaps why so much focus on this feeling why should we care you said you said the first two they go as >> because let's say yes from the physics point of view u the wave is at 1 / r okay angular momentum depends on data at 1 / r and 1 / r² and r cube okay if you have logs appearing already at one / a a cube there is a problem of defining angular momentum some integrals become divergent or become conditionally convergent. So it is true that there is like a folklore people especially in England started saying this is the penrose thing and therefore everything will be defined this way uh but um one can re-examine everything I'm not okay I will talk about peeling violation this peeling violation do not mean that everything disappears okay if the peeling was very strongly violated then you would have nearly no good integral at infinity. There are even solution of Einstein's equation constructed by Lydia Berry for instance rigorous solution where you cannot define total energy uh of the spaceime. Okay, there is infinite energy in some sense. So we want still to do some physics. Anyway, the question I want to ask here in the case of scatter, what can we say about peeling the structure at infinity? And a first answer was given by Walker and Will and then confirmed by me little bit later saying that even in linearized gravity the peeling would be theorem on square minus is violated in the sense that the component that should decay like 1 / r5 decays like 1 / r4. Okay. But uh then I did another computation back in 1986. Um and then I found that for a more subtle thing which are now tail effects so it's not linearized gravity we have heard today about tail effects it means the gravitational waves uh are back scattered uh by the the cool type curvature of spaceime and u and they propagate inside the light cone and not just on the light cone and this delays the propagation of the waves and gives the uh infrared effects and um and they are proportional to G * the total energy of the spacetime G * the total mass and then I found that the tail effect acting on quadrupar waves violated peeling like one over R4 now this issue uh yes that indeed you could say who cares but u it has attracted recently a lot of attention first he uh I remember I told that to Christo Dulu who amplified this and said there is probably another source of peeling violation then Kberger studied this for years Radu Royan and others I don't remember all the authors have done a calculation which suggests that indeed in scattering you have peeling results peeling violation although it's not clear exactly what they have proven uh recently in 2026 six two different groups including copera got also um said that there is indeed a violation of this type but they said we disagree by your factor two of the result of tibo this is where we come to the recent thing especially because I was signing I I was the referee for this but I was signing the referee report so it's public I said okay uh it is interesting should be published though I think there the problem with this thing but two days ago for told me oh yes there was an error in the fundamental equation we were using and then there is an extra term to be added and now maybe we are compatible so it's still not totally clear what is the final result now I want just to give an idea of the multipolar post minkoskan formalism so this is a formalism that we started with look uh in back in 1986 Then it was developed in collaboration with Bala for years. Luke pushed the formalism to very high accuracy. So this formalism is solving Einstein equations by combining several approaches. Uh it's called multipolar post minkoskan. Its full name is PN matched multiple prominos because in an region outside the source let's say the source are two objects moving around outside the source you expand Einstein's equations you expand the metric in a post minkoskian expansion just powers of g then for instance h1 satisfy this h2 satisfies nonlinear terms in the right hand side we all know this but now you need to compute these integrals and the way to be computer is to Ah but the general restarted solution of waves is can be decomposed in multiples. He gives something explicit on the right hand side and then we developed explicit methods to compute those integrals. One loop, two loop, three loop. Okay. To very high order uh and then you can get explicit solution. Okay. uh uh and then you match to the source so that the multiple moments that appear in the external scheme are connect are really linked to explicit expression on the source and I've given here explicit formula just to show for the quadripole for instance the quadripole at what you measure the coefficient of the decomposition of the wave h at infinity in in the quadripole uh is measured by this as function of the time U and it is expressed by a certain quantity M which is itself expressed in another quantity I which is the source quadupole moment. The source quadruple moment is obtained by explicit integral over an effective source which combines uh which is essentially the land sheet sum of the timu of the matter and the tow gravitational of the gravitational field including all nonlinear terms in the near zone here and then you have nonlinear effects in the wave zone like tail effects memory effects instantaneous tail of tail etc. Can you remember in this calculation what is given and what is computed? >> What is given? >> What is given? Yeah. What is given as input? >> Nothing is given. Einstein's equations. Then you need to say >> what do you say about the source >> here? Nothing. The formalism is very general. Then you say my source will be a neutron star which oscillates will be two neutron stars moving on. Then you need to solve the equations of motion of the source. solve timu new equals zero and then insert this explicitly. Okay. Now yes so now I I'm coming back because uh in view of these discussions so there was my old result about peeling violation which stayed dormant for a long time then people got interested in this and as they were dis uh let's say there were some results in tension with each other as people say I said okay let me reexamine uh in a new way what I had proven using the work of Luke Blanche, Cha Compair, Oliveri and Ali Sange which did uh good work to connect the metric as given in the multipolar post Minkovkin formalism to the first interesting nonlinear order including tail uh in a bond like gauge okay which allows to connect the bondi type expansion to the MPM formalism in a clear way. Okay. Uh but what I want to explain is the following. The essence of this idea that there is peeling violation come from interesting thing in the infide. Okay. So it's not just a calculation peeling not peeling it is connected to infight structures in gravity. And this infight structure are the following. If I consider that the quadrupole moment is in MPM formalism is when I look at its behavior in the infinite path. So for instance if I have a scattering situation I expect the quadruple moment to describe two bodies coming with some velocities at lowest order but also uh their trajectories in spaceime are curved because they interact gravitationally. When you compute this, you find that the qual moment has a part which goes like t square straight line trajectories and then a t log of minus t. Okay, which means that when you compute now the waveform at infinity using tail corrections, nonlinear corrections, you find that these coefficients actually they correspond to for the moment you measure at infinity for the waveform decomposed in its quadruple part that this waveform goes to a constant. So it's the value of the waveform h at minus infinity in time going to constant. This constant measures the pipj measure the two velocities of the bodies. Okay. And and then the next term that is in one / t where t is the time in the past. For some strange reason people call this tail. Although this b has nothing to do with tail. Actually it is the logismic deviation of the word lines due to their gravitational attraction in a postmikoskian way but it is there okay it's it's tail in the sense that the waveform goes through a constant modulo one / t thing which decays okay so anyway this thing are in the waveform and now the point I want to >> this is time like path this is I I >> so here it's to yes sorry this no this is Uh first this is function here it's the variable of t here it is more um u that you say the the the future the time but you take the limit of the time at infinity >> past future null infinity >> it's the past or future null infinity here but but this thing actually is valid everywhere in space time okay including in the other and that will be yes because what will happen essentially it's because at future null infinity In the past you will get this as violation of peeling and you will get this as violation of peeling on sky minus. Okay. So it contains several violations of peeling in a very simple manner. Now um yes so for instance so I I I did recently some new computations to starting from the waveform okay but keeping now the terms beyond the 1 / r okay 1 / r² 1 / r cube and things like that. And what you find is uh when you look um when you look at null infinity here on square plus you find that beyond the term in 1 / r which is the usual waveform which exists there is a term in 1 / r² whose coefficient is min -6 g ² e the a coefficient. So the a coefficient remember was this. So the value of the waveform at minus infinity okay enters in the next term in 1 / r square and although you could say 1 / r² looks as good as 1 / r actually this violates peeling because when you compute the size zero curvature tensor from this you find that this is proportional to this and therefore you get a violation of peeling. Okay, so this is just a red derivation but using your uh recent result just to see within MPM where is this violation to be sure it is there. Okay, with the same coefficient minus 6. But now um I I I push this calculation also of peeling violation on sky minus which are more complicated because there are also tail effects to take into account. And then there are two terms one which is the old result I had got which comes just from linearized gravity which is this B. So B is the one over T coefficient. But there is also a tail term with a numerical coefficient that I want to double check before showing it exactly. Uh okay. Now um I'm saying this because up to two days ago there was this paper of compare and Sebastian Robert saying we get something like that but we have not the same coefficient here. uh and in their paper they use matching to get antipodal relation and the delicate things is that they were missing terms there. So the they they have a good framework for understanding better antipodal but I think there are subtleties that we have started to discuss with Ali to understand better. So it shows that it's still an open problem to understand this thing but an interesting problem to understand infrared thing at infinity as this is it's a conference on string theory. So I want to pay homage to the founder of string theory we is also in a sense the uh initiator of a lot of the effort uh that EFT people now are doing and string theory people. Uh in 1990, Amati, Daniel Amati, Marello Chafaloni, Gabriel Venidiano uh computed uh the higher order gravitational deflection and soft brush the in plank energy super string collisions which means low modes of the string essentially gravitons okay colliding at super plunk energy but computing this two loop H diagram and They could explicitly compute the two loop contribution to the aonal the log of the impact parameter transform S matrix. Okay. U getting this for the two loop contribution and deducing from it the scattering angle. Okay. Actually there is a subtlety here but let's not enter into this. And I remember when I heard in Italy um conferences, lectures by Gabriel on this, I realized that this was a quite interesting thing that might be useful for LIGO type physics and what we were doing. And uh then I I I thought about it and I I showed how to use scattering result from postminkoskian theory and import them to better compute what is the let's say aonian of two black holes going around each other and in this paper uh I mentioned the the work of Amati Chafalo in Veneziano and I urged amplitude experts to use their novel techniques to compute the two loops scattering. Okay. Few months later, Chung Rostin and Solo said something of the same type. Okay. at the time from classical gravity because yeah I should have said that starting in the actually it started in the 50s but let's say in the 80s uh this group of people and among Ital was one of the workers here uh had computed the the one loop uh equations of motion and metric generated by two world lines but then we realized that going to higher order and you see it's the same H diagram as the two loop before was looked difficult and then we said okay we stop and then we use post Newtonian approximation which is simpler to compute the integrals okay but um as we know u the group var succeeded first in getting this and what is very beautiful because it is again string theory flavored is that the first calculation use the double copy which is the idea which comes from KKLT which comes from Fubini Veniano vertex operators which are factorized uh saying that young mil is the square uh sorry the square of Yenstein then they could compute explicitly the two loop amplitude and the surprising thing is when taking this was for two massive particles going to arbitrary velocities not ultra relativistic scattering and you would have expected that when you take the ultra relativistic limit you should forget about the masses and get the result of ACV I'm a teach in Venezuelan the surprise was that there was a divergence and you did not get the same result so this raised an issue how to reconcile this what is what was missing in some sense and uh then what happened is um I realized by using um an old result with Donato Bini here saying that if during a collision you lose angular momentum and energy this changes the scattering angle by a quantity kaira that is easy to compute from this simple formula. Then I computed what is the angular momentum lost during the collision of two uh particles and I got uh this result and when you add this result to the result of zurn you get something which agree with ACV. Okay. So at this stage everything looked perfect. You need radiative effects. The high energy limit is finite. Everybody is happy. Ven was happy again. Uh although okay I will not tell about the bottle of wine [laughter] which I drank with Julio. Uh now subtleties. So um Gabriel Lev and Ediano with uh Gregory Viloviski then um then um who were among the people like me who said we need to solve this thing and they had also separately uh with Rulus who understood radiative effects Carlo were important. Okay. Uh but they insisted on the following point and this is what I want to say. There is a puzzle. The puzzle is the following. I I did not say it but now I say it. The energ the loss of angular momentum when you have the scattering of two bodies goes like the second power of the coupling constant G. But the loss of energy goes like the third power of G. And from a quantum point of view if you say but the energy is carried by gravitons it means you do not lose gravitons uh with finite energy at order G square. How can you lose angular momentum? Because in quantum field theory, angular momentum is carried by gravitons. Each gravitton has a spin plus or minus 2 h bar. So there is a puzzle and um and at this stage if I had given the only computation giving the result people could have said the result is wrong. But there were many different groups including the the work of Julio said no no everything is correct. uh and then I then in the paper this is taken from the paper of Gabriel and Gregory uh the low the angular momentum loss is of lower order in the coupling constant than the energy loss and they said it got to the point where at a recent workshop in GGI no I think uh there appeared a graviton having zero energy and robust angular momentum this state of affairs is one of our concerns in the present paper. Okay. So the point is how come angular momentum has this peculiar property that from the quantum point of view you should not lose angular momentum there are no carriers at infinity. So it's the point of what is at the quantum level a zero energy gravitton. Okay a gravitton should be on shell uh omega square= k². If it has zero energy it does not exist. So okay, this is the conceptual point of view which is still bothering Gabriel. Uh I think and I think it's good to keep in mind things that uh you know should worry no >> that bother Gabrielle. >> Yeah. [laughter] Uh hey let's not you will see my last slide. Okay. uh now uh so and then in their paper apart from just saying this they said but this is linked to the BMS frame this is linked to the super translation ambiguity so this is that's where the you know this is the topic of my talk to say infrared effects symmetries at infinity zero frequency gravitons things they are all related angular momentum ambiguity uh and what they showed explicitly is that if you Start with a waveform of this type with a one / r coefficient you call f and if you do a super translation so this result here the this value of f here by this 4 gm over this this is the value obtained from postmikovskan perturbation theory this is the value also you find in weineberg's 1965 paper in weineberg book on gravitational waves in 72 the collision I mean from perturbation theory you want to today the the waveform at minus infinity as a pp divided by np the quadruple formula says that immediately okay so how can it be wrong but anyway what they say if you f if you add the super translation you modify the one over r coefficient of the waveform and if you choose beta by this value the veniano vil koviki value with a log uh you can gauge away this you can say that the incoming shear is zero. Uh but remember that in my previous slide the incoming shear so the incoming shear was this aig. Yes, let me say this because I said it quickly. Uh this thing uh or in the second derivative plus tail effects of the quadrupole moment. This quantity is precisely the uh the quantity which is responsible for the angular momentum and that Gabriel and Gregory showed you can gauge a wave by a thing if you want to have no angular momentum loss but from this point of view there are other consequences of this say like this thing is gauge invariant you cannot gauge away this so in a sense this thing is there okay I'm not saying it's a proof I'm just saying there are subtleties is here. um and yes and and this played a role recently I will be brief here I don't want to take more of your time it's the last talk you are tired in uh over the recent years um after calculation that existed first in the 70s people could tackle the one loop waveform okay before I was talking about the the exchange of gravitons between two massive word lines uh which defines a force or Hamiltonian a potential between the two word lines. But uh two word lines can not only exchange gravitons but they can emit gravitons uh both from inside and from the from the sides also. And then uh several different groups and they representative of these groups here computed the the one loop waveform. Um recently there have been progress and clarification both by Stephano and by Carlo Heisenberg and Rodulo Russo. Um there are cut terms which are important. So at some stage with Donato and with Andrea Geralico we said okay there are those beautiful results but the multipolar post minkoskan formalism developed by Luke for many years is what is used by LIGO and it is important to compare the predictions of this formalism developed over many years and which is used to the highest level EFT computation. So u with donato we we we computed this for the scattering okay usually the mpm formulism is used mainly for quasi circular orbits okay or small eccentricity orbits here it is a very different situation so we use the same formula but the calculation are slightly different in technically and then we we compare to this and the reason what I'm saying this is in the comparison first in the first stage of the comparison We were surprised that even the Newtonian level was incorrect that you say the the three groups that said the waveform should be this and then it did not work at the Newtonian level but then the cut term was added there. Several other effects were added. So at some stage everything worked fine but I want to insist on uh subtleties. Okay, because subtleties are important and there are two types of subtleties. One subtlety is that in the computation you need to take into account epsilon over epsilon where you are in dimmerg and you are in four minus 2 epsilon dimension. So scheme dependent a prio contribution but from the mpm point of view they are there. Okay. So you need uh a scheme which gives this good epsilon over epsilon and uh in a sense zero energy gravitton that is to say because either you argue you can replace zero energy gravitons by something or you include them as a disconnected diagram. Okay. uh that you in a cut is you couple zero energy gravitons with non-zero energy gravitons and then this is necessary to get something linked to the venetov koviski super translation but there is a factor today I don't want to enter into the details we have a recent paper where we have checked that this is true in detail but it shows how subtle the comparison is and how interesting it is to compare EFT QFT based results and string theory based result to uh other calculations. Okay. And ola that is bad. Yes. No, it's just this and my conclusion is uh simply uh a sentence of pankare because you see in the for many years people thought the asyto structure at infinity has been fully understood by bondi saks penrose there is the BMS group. Then I did not mention this but there is Boskeeti and Compilia are working within the U in the vein of the strummingers group and thing like that. So people understood that infrared effects, zero frequency things are subtle things. And then I agree with Pankare that finally there are no problems the big problems of physics are never definitely solved. When there are important problems they are more or less solved and I think that this infrared structure of gravity uh is still with us. There are things to clarify. Okay. And that's the main takeaway message. Thank you for your attention. >> [applause] >> question [sighs] >> maybe I have a question if if you work in the BMS frame where you remove the initial shear your claim is that you will still get in violation >> uh so I don't know yes okay it's a question while preparing the slide I said but it is there Okay. To be checked. Okay. Uh it's just it's a warning. Okay. >> Yes. So, so I I have a question about this comparison. So, you mentioned that there's subtlety, but on which side of the comparison does the subtle lie? Is it on the side of your way of computing both cos or is it always on the side where you have to be super careful? Where do you have to be careful? question >> here in that case I mean in that case this was on the EFT side we never had any doubt or anything at one loop let's say at one loop the MPM formalism is absolutely clear and has no ambiguity there are by the way they are UV divergences because you put point masses but these are understood they don't reflect in the quadrupole moment and what you comput but uh Luke has pushed now the MPM computation to something which is three loop or beyond and there you have is you is obliged to use demor both in the wave zone and in the near zone and there are subtle terms there we are discussing with Luke where in the final answer there are things that depend on one / epsilon and its finite part in both regions okay uh so this is why it would be important and we are working on these two compared to what exists on the EFT side and when there will be two loop results we will see uh I do not I mean in principle from all the work of of Luke I think the subtleties are under control but it's always good to compare >> maybe I comment that one of the subtleties is not inherent to the QT approach because this disconnected terms if you do the calculation in the Kish basis not in the basis with two copies of the fields then there those terms are not there you just write all the diagrams and >> no but you must include them we have >> they're automatic because they come from the epsilon yes >> of that propagator >> but they are there you mean >> they are there but not as a cut because there are no cuts that computation >> there's no zero frequency graviton that's >> okay but they will contribute the same quantity >> yeah yeah it's absorbing the different epsilon of that propagator yeah we check is or the angular momentum actually if you do it that way you need that but you can do the computation in a different way where there's no zero frequency grab anywhere >> it maybe is already what July was answering but I was still not clear on whether the angular momentum puzzle got resolved the fact that the angular momentum violation shows up lower order in G Newton >> why it is lower order >> no I understood why it is lower order but has a problem with either resolution to the puzzle um there is no solution to the puzzle. If you start saying you do not emit gravitons in the energy wise and you still lose angular momentum. I think from this point I mean technically from the classical point of view the formula giving the angular momentum loss contains this term. So there is no problem. It's a mixing between cool effects and radiative effects. But if you want to say everything should be inert space uh is Gabriel still uh worrying about this. >> Well, I don't know. I mean I guess it's just uh trying to understand what quantity you are calculating, right? So one thing is the angular momentum loss. So the fact that the mechanical angular momentum changes then can that angular momentum can go both to radiated angular momentum but also be absorbed in the field. Yeah. Right. So maybe the radiated angular momentum is carried by non non with non zero energy but there is part of this mechanical angular momentum that stays in the field. So I think it's just as saying it's subtle to define what the angular momentum is. Anyway, it's good to keep subtleties in mind, not to say it's well understood. >> Um, so what's your verdict on BMS charges? Because I remember like there are these celestial amputes which actually got motivated by the existence of BMS charges and my impression uh that I got from discussing with Stephano is that the speeding violation might invalidate the existence. >> Okay. So there are I think two answers. I think people who compute BMS charges with peeling violating space time say you can always define what you want. You define charges. Personally I always felt the only real group of symmetry for the scattering case is the pankar group and I would like to see it coming out uniquely and I never understood uh whether BMS is a group of symmetry of the I it's not a group of symmetry of the full thing. It's a group of symmetry of a partial system. No, when you say radiation is disconnected from the system, there are more symmetries there. What are these symmetries teaching us about the what you want to know about the dynamics was always unclear to me. >> Okay, last question. Not let's thank again [applause] and let us thank the organizers. It goes. [music]