 Hello, everyone. I can see you now all. Okay, so we've just heard Adam telling us about the recent triumphs in cell force. I want to take us back a decade or so to a moment in the development of the field of cell force that I think was pivotal in shaping the program of research in cell force in the past decade. And I'm talking here, I'm referring to the paper by people from 2010 in which he first developed his interest in cell force. And as I was sort of going back to this paper to try to think what I'm going to say, I realized, somewhat to my surprise, that much of what happened later in the field was already there in some shape or form in that paper. So, yes, I'm going to make the point and sort of build the thesis here that there's a clear line leading from that paper to many of the things you've just heard about from Adam. It's all already there in some shape already in that great paper. Okay, so, yes, so here's a plan. I will tell you what the landscape was in cell force as of 2010, turn of the decade. And then I will discuss to you the most paper in 2010 on the cell force and you be in which he describes different ways in which you can use cell force information and to inform and help develop the you be a model. So I'll call them that he or the cell force handles because they were like handles on the geometry of the two body system. Then I'll go one by one and tell you what calculations have been done on those six handles. And what sort of what the profits were from this kind of calculation all the follow follow on the calculation of it. And I'll finish with a little reflection on the role that this work had on the sort of building an agenda or program for for the cell force community thing was extremely successful. Okay, so that was the situation at 2010 we have had already a an equation of motion, a first order equation of motion for the cell force for almost a decade and a half. And progress was quite slow. I think. Yes, it's probably fair to say that a constant source of frustration for table for station was with the slowness and the slowness at which we move in the cell force and community. And much of the work in that in that first decade was about time to convert this equation of motion into practical calculation scheme so we can calculate those every orbits. So there was a lot of progress on that. And I think it's fair to say that the main problem was what we call the gauge problem which is that the question motion was formulated in one gauge, which was not the gauge in which people normally do black hole perturbation theory. And so people try to resolve this two different ways first. First was to reformulate black hole probation theory in the gauge in which we have the cell force, and the opposite way was to reformulate the cell force in the gauges in which people were used to do calculations and in the end, both things work. But until they did work, much of the work was on cell for our self and cell force, and due to a scalar field in so self was on a scalar challenge. And so if you go to literature says that the 95% of the work was done on scale field another toy model like electromagnet magnetism in curve space. The first successes and calculations of gravitational surface came in 2007. And immediately afterwards we were starting to make connection with a real world so up until that point. It was really an effort of a small niche community. And from that point we started to get some physics out of all that. And so, yeah, the first two examples where the calculation of the redshift by Steve that while and the calculation of the East Coast shift due to the cell force by myself read, and Norisago. And, and this kind of early results, I think also attracted tables to to the field, and that was an important result by itself to attract people to the field. And, but it's important for me, for my point to emphasize here that when we did this calculation we didn't quite have a clear sense of why we are doing what we wanted to test our cell force results and it's good to have comparison with post Newtonian results, but we didn't really appreciate that these things can be more important than just that and, and we didn't get that appreciation until tables, people came and really showed us this in this in his paper. So here is the paper, a gravitational cell force in Schwarz's background and the effective one body formalism it was submitted in October 2009 and published in January 2010 so nicely at the beginning of the decade to hold the start of a new decade of cell force results. I will just read to you the first sentence, and because it says it's all we discussed various ways in which the computation of conservative gravitational cell force effects on a point mass moving in a schmarche background can inform us about the basic building blocks of the effective one body. And there were six sets such ways that were described or six handles. The first was the ESCO frequency. The second was the pedestrian advance on slightly eccentric orbits in the limit of circularity. And the third was ADM like energy and angular momentum of the binary of the binary system and, and of course, you know, the non-trivial piece of the, of the energy is quadratic in the, in the small, in the mass of the small objects. So people pointed out you would have to go to second order cell force which seemed like a very, very remote prospect at the time. Indeed, it took another 10 years until Adam was able to calculate it and you saw the result a moment ago. But people suggested that before this is also available, we can have a handle on the energetics using first order perturbation, lack of perturbation theory. So using first order cell force by looking at a special orbit. And this is this orbit here. It's the orbit that is marginally bound. It starts at zero velocity at infinity. And then he falls in and gets trapped at the unstable circular orbit of 4M. So you have to turn off dissipation for this orbit to actually happen. And because you're starting at infinity, you have a well-defined energy and you can relate that to the Hamiltonian of the UB. And you can calculate two things. You can calculate the shift in the critical value of the angular momentum that you need for this trapping to happen or equivalently shift in the value of the impact parameter. And you can calculate the shift in the frequency of the asymptotic circular orbit. And finally, much to my surprise, I found that scatter angle calculations in hyperbolic calculus that was already there in the paper, at least philosophically. It was mentioned there. You can see the budding of the ideas that are already in that paper. So those of us who work in or are excited about these calculations may be surprised to hear that it was already there. Okay, so isco shift. So I'm going to go one by one and tell you about those experiments and where they took us and why they were important. Isco shift. So here's my mass notation. I'm going to follow you here, the mass notation of the paper, the 2010 paper. And this slide shows the perspective of cell force. The next slide will show the perspective of your being done will put them together and right. So at the geodesic level, the motion as we are all familiar can be described in terms of a radial potential effective potential in a precise form. So that if you have a fixed constant motion at angle or momentum constant constant emotion, you have an effective potential. It looks like that that supports a single has a single minimum that it corresponds to a stable circular orbit. As you decrease the angle or momentum and we are in charge of geometry here. The orbit shifts to the left so smaller radii until a point critical value of the angle or momentum where this minimum disappears. You get an inflection point and you don't have any more bound orbits below that value. So this marginal orbit, the innermost stable circle orbit is co happens to be at six and you find it by looking for an inflection point without effective potential. Now, if you add a cell force to the equation of motion, the location of this inflection point moves a little by a small amount proportional to the mass ratio. And you find that the square is shifted a little. Now the shift in the coordinate isn't too meaningful because of gauge dependence. But instead you can look at the shift of the frequency of the isco that you can form this nice dimensionless quantity by multiplying by the total mass. And then you have the structure where you have a geodesic value just six to the minus three halves a plus some cell force correction that it's encapsulated by this coefficient. And since we knew how to calculate cell force, we could calculate this omega and this is the result with ten numerical calculation with an arrow power on it. This is a result and then you can, for example, compare it with post Newtonian calculations. And so this is a result we got a later with the bold and when we have access to the energetics of the orbit once the first law of binary black holes was formulated and talk about this in a moment. And now we can do the same thing from a new B point of view. And so if you look at the EOB Hamiltonian near circularity, it has this kind of structure. There is an a priori and own function of the EOB inverse radius you and of symmetric mass ratio. And this J is a parameter angle of momentum. And you to make connection with cell force, you want to expand that in the small mass ratio. So new is a symmetric mass ratio. And then you're looking for inflection and inflection point of this potential. And so when you identify it, you get a relation between the location of the ESCO and this a priori and own function A that capture the order Q or the mass ratio part of the main EOB potential. And so you get because you need to derivative to get the inflection, you get that radius depends on this A evaluated at the ESCO and the first and second derivative. And at the last stage you want to convert that to frequency so you can extract this C coefficient or the EOB version of that C coefficient and you get something like that. And knowing what the cell force value is knowing this exact benchmark tells you now gives you a constraint on the value of a derivative at the ESCO. Now if you're interested in the in the post Newtonian expansion of this unknown function which is the way it was presented at the beginning of EOB. You also get constraint between the coefficients of that expansion. So two of them were not from this post Newtonian theory. There was a long quest for the next one, the A5 and the A6 and so on. And this kind of comparison with cell force is not allowed us for the first time to put a very tight constraint that related those coefficient. And this really doesn't sound much from our point of view where we now have these coefficients analytically to very high order. But back then it was something completely new, a completely new way of calibrating those EOB coefficients using new information in the strong field. So no longer do you need to extrapolate from infinity using post Newtonian theory. Now we have an anchor point in the strong field. So we're talking about interpolation is much better. Right, but this is just one point. And in the paper, people immediately also suggested all function like that the functional relation that can serve as a dictionary between cell force and EOB calculation. And that function is essentially the periaston advance in the limit of circular orbit. You can calculate as a function of the frequency of the circle of it. So you form this convenient function. This omega R here is the frequency of the radial oscillations about the minimum. So at leading order, this object, if you perturb it a little around the circle of this perform harmonic oscillations with radial frequency omega R. And you divide it by omega to get something dimensional dimensionless that doesn't depend on your time parameterization. And it also has a simple interpretation in terms of the angle of advance per cycle. And so if you expand that in a mass ratio, you get the leading order that is just watch out very simple one minus six X. And here X is a radius inverse radius that's defined from the frequency. Plus some cell force correction dysfunction row. And in this first collaboration with people, we calculated dysfunction row in cell force. These are these blue data points. And we did a comparison with the then available cell force is a post Newtonian approximants to this. And so now you can see nicely how you get a nice agreement at infinity and you can follow on this comparison all the way to the storm field. And it gives you a handle on how the post Newtonian expansion behaves in a very strong field, at least down to the east for you. And that was new, that was entirely new. And again, you can do it, you can do it in the OB. And so from the UBM attorney, you can write a radio equation of motion and you put two of the bar to a circular orbit and that gives you also an expression for the radial frequency in terms of the UB potential. Here you also have a dependence on the secondary potential the deep potential associated with quadratic terms in the ideal momentum. And, and then you can you can write down an expression for the same quantity this omega over angular frequency. This time it involves the two potentials that here expanded in power of the mass ratios. And so again, in the last stage you convert the frequency and you write then the EOB equivalent of this row function has this from here. So now knowing this function in cell force in principle gives you an ODE now and differential equation for the entire potential. Well, it's coupled so you can solve it quite yet, but you have a couple equations for that relates this to potentials everywhere, everywhere from infinity and down to the, down to the ESCO. And so now we have, we have a control over the functional form of the, of the EOB potential. And if you want to walk in a post Newtonian framework, you can then get, get not one just one relation or constraint on the post Newtonian parameters of those things but very many because now you can fit to a function it can extract order by order those post Newtonian coefficients. Now at that point, I think people realize that it doesn't need to wait for us to do self-calculate calculations. Cell force calculation you could do it himself. And, and him being here we can do them analytically. If, if, if, if all you want is to do post Newtonian calculations and you can solve the perturbation equations around the Schwarz's black hole analytically order by order in post Newtonian. So you do a double expansion PN and ESF. And there started a very successful research program in collaboration with Donato Bini and later with there on there at Jeradico, and which quickly attracted many, many other participants and soon everyone was crunching PN parameters. And I think it's fair to say that at some moment around this time, most of the people in the copper community were calculating the post Newtonian parameters are entirely bewitched by this. And it was a really to the to the force. So you can see here results from paper 2016 paper for the function row analytically expanded in a post Newtonian series 6.5 pn 8 pn and 9.5 pn. And, and, and this is gone and, and this was really useful for calibrating you be this immediately improved went for improving the you be more than that immediately went to LIGO, you know, detection pipelines and so on. So this, this work on the, the huge impact on on the field. And then you can draw this nice plots that where you take the cell force data, and you subtract order by order, the analytical terms and you see how you get faster and faster convergence. But now you really have a handle on the convergence of the PN series in the strong field from near the east. Now, if there's something important I learned from table is that is not strong field. After all, one of the six is only halfway between zero and one of the three. So you can't with this bound orbit, it's, it's hard to get below below the school and you do want to go below the school to the really strong field and that you can do with energy. And, as I mentioned before, the paper mentioned that possibility of using second order and binding energy. Again, very more prospect back then so I'm just flashing the plot that Adam showed you before but I want to emphasize one feature of it which is that if you can calculate the binding energy of unstable orbit below the screen all the way down to the light ring. This is this portion here. So it gives you much more handle on the really strong field a part. Fortunately, as soon after people's paper there was this remarkable idea of the first law of binary black holes that allowed us or provided kind of local energy that's accessible from the first order metric perturbation. So it's written here as formulated in this paper from the tech pose and banana. Given the first order perturbation you can construct this quantity that that while a redshift is one of the inverse of the full velocity of the object along along its trajectory. You can expand it in in in small mass ratio and given that redshift function, you can construct the binding energy to order cell force. And as a first test you can also locate these go by minimizing this finding energy and you get and you get the same result. Now you have access to the energetic of the problem from the first order perturbation and you can take it down to the light ring. This is what we did in later collaboration with people here we have a calculation of the binding energy all the way down to the to the light ring now. So that was very helpful. It helps, for example, detect an issue with a cell force. Sorry, with the eob formulation a certain divergence at the light ring that was later resolved by changing the gauge of the eob formulation. And later on, when there was a formulation of the first law for eccentric orbits, it was also it also allowed this kind of game to calibrate the the last potential of the eob formulation, the q potential associated with high eccentricity. Right, but going back to the paper before second order formulation cell force was known is known and before the formulation, the first law was known. People said we could still use a first order information to get a handle of the dynamics and that was that's done by looking at unbounded orbits. And so the first idea was to use use this marginally bound orbit, which I just described before, which is a kind of funny thing where the in state, you start with an in state that is two particles infinitely separated in flat space. And the outside state is a tightly bound orbit strong field that has helical symmetry. And that's very useful because you can relate the notion of energy in helical symmetry to the notion to the usual bonding bonding ocean of energy at infinity. And so, given a cell force we can calculate two things on it we can calculate the shift in the critical value of the angular momentum and the shift in the asymptotic frequency. And that gives you a direct handle on the eob potential eob is a Hamiltonian formulation so if you know the energy you immediately can translate it to information on the potentials. Without the intermediation of the first law and provides a check also on the first law formulation. And that calculation we did much much later it took many more years because almost every all the cell force technology computation technology is is adjusted or adapted to bound orbits it took a lot of time for us to be able to do unbound orbit and and these are the results. And so this is the normalized frequency of the of the last year of the synthetic orbit and this is the shift and this is the angular momentum. So you can see that the cell force shift the angular momentum by something like one point three ratio in words so you need to shoot the particles slightly more in words in order to be going to be captured is without radiation. The angular frequency is a bit larger. Now back to the of finally the the last thing that was mentioned last handle that was mentioned a scatter angle in hyperbolic encounters. So here instead of looking at the particular unbound orbit we have two parameter family of orbit parameterize with say several mass energy and impact parameter. This scatter angle unambiguously from the out and the in state of the system. And that's nice because it allows you to probe all the way into the to the library light ring with sufficiently high energy. And this is this is the usual thing that physicists do when they want to explore new things they throw things at it right that so this is how you explore the atom so this is the classical probe experiment in in relativity how to probe a black hole. Now, by 2016, I think people gave up on us calculating this in cell force. So we went on and show a completely new way of a calibrating you'll be using postman Kovsky and information on crisis. All new dictionary to translate with postman Kovsky and to European deserve it's on its own. It was a lot of interest around the time because it was fast progress in PM theory because new participants came. People from QC the amplitudes and know how to calculate this thing and found a way of converting their calculations to the gravity calculations. And this is this is my yeah I have one more slide after that and I'm done. Thank you. Okay, yes, I'll be I'll be brief. So, in brief, people had a very important point to make which is knowledge of Kai at one GSF so knowledge of the first order cell force correction to cry. In fact, the termines the full PM dynamics the full meaning not and not only leading mass ratio that all mass ratios up to 4pm order that comes simply from dimensional analysis and some observation about symmetry under mass exchange in this in the object. If you have the second order cell force you can get all the way to six pms are very strong motivation out to do this calculation cell force. And plus the fact that of course cell forces also gives you always the full thing at order mass ratio to all postman Kovsky and orders all also the strong field information. We still don't have a calculation cell for calculation of the scatter angle but we are getting there promptly now. Finally, so these are some results from a recent paper. And what I show here is a particle in a scatter orbit to run a short black on calculating a certain complex health potential from which we get the metric perturbation and the cell force by taking derivatives, and you can see the periastron is here time for zero. So this is calculated along the orbit and here on the right, this is the radiation at null infinity. And you can see some interesting strong field features here. These are these are echoes from the passage of the particle around the periastron back reacting with the particle itself. So not clear if we see those kind of features with a lower the PM calculations. We have several codes now like that time to my figures remain. We do comprise something we are just about not to start calculations of this cutter angle. And hopefully this will allow us to go back to the board and try to extract the physics from that. So, just to get to my conclusions here, a quick reflections on this on this on this on the progress that was made. Importance of that paper so I think it's fair to say that the paper started a new program, which involves many, many people and it is still ongoing and going very strong and that led to significant improvement in way for models for radiation with detectors and to put the fingers off on three new completely new ideas that were there and really helped shape the way people think about these things. It was first conservative self force gives you a handle on the strong field potential so it's not only about calculating the acceleration to get an injury orbit, you can get your information about the gravitational potential in a very strong field. The second is a completely new way of calibrating the OB potential beforehand only PN. Now we have handles in the strong fit using self force information. And the third and that takes me out to Adam Adam stock is is the insistence on using the symmetric mass ratio instead of the ordinary mass ratios. It wasn't stated explicitly in the paper but it in a way in a way for if it was for seeing what will happen next which was will realize that when you do that, you can use self force information to, in fact, get very accurate result at all mass ratios as Adam Adam illustrated. So, so that's it. Thank you very much. It's been it's been a real pleasure working with you and I hope that will will have more opportunity to work in the new in the new future. So, thank you and happy birthday. So, since time is going faster. I suggest that unless people as a comment. No, I wanted to thank you all. Thank you. Yes. So we thank you. All the speakers. Yes. I just don't know how to go. In fact, because it's very fast. So thank you to all those who are in the room and those who may listen from somewhere else. And we saw just a small fraction of the kind of 100 or 200 collaborators you had all over your career. Many many I want to see some that young people who started while starting in the various field. So you still have a lot of work to do to teach younger generation. So thank you to all. And thank you.