 the congratulations to Thibault. And I'm very sorry that I can't be there today myself. We had two restrictive travel rules, but next time I hope I can visit Thibault and pass on my congratulations myself and also the congratulations from my people here in Bonn and particularly I know about Vex and others. But the title was actually chosen on purpose because I think it does not only apply to gravity test with Pulsars, but to Thibault himself. And there are so many contributions, seminal papers that we are at the Pulsar community are grateful for and also me personally. And as you will see in this talk, there are lots of contributions that are really important. And then I have treasured them since I started working in Pulsars and I continue to do so. And the purpose of the talk is to give you both an idea about what Thibault has contributed and also how we actually used his insight. And of course I have to start with this paper somehow because this is one that appeared actually before the first binary Pulsar was properly published in the journal. This is the paper by Thibault at Remo on the Geodetic Possession of the House Taylor Pulsar. And I will come back to this later. I will come back to the paper of course later in this talk. But of course, there's also the famous DD timing model that the Moudiral timing model, which was really a very elegant way of not only solving the equation of motions but also to basically describe in a timing formula that we as observers could use and basically use the theory independent parameters that were introduced for testing our theories of gravity. And all modern timing formulas today actually derive basically from this set of timing equations and model. There is this famous, as we call it these days, DD92 paper, the Danmour and Taylor paper, which is really the standard reference ever since because it is a wonderful description about the post-caplarium formalism and the way we basically just try to extract the physics from the timing. And the nice thing about this paper is it's really complete. It has already so many post-caplarium parameters in it that we're not even measurable at the time when T-Border and Joe wrote this paper. And there's also a compendium, how you test not only general relativity but also alternative theories of gravity. So as I said, it has been a standard reference ever since and I think it's probably on everyone's desks who are doing parts of the timing. Speaking about alternative theories, I have to mention the paper that he wrote with Jill Esposito-Farese and they basically discovered this effect of spontaneous scalarization, which really is one argument why we need to do binary parts or tests because even if you do a test in the solar system close to a Newton star, there can be effects that you won't necessarily be able to measure otherwise. And there is a whole series of papers by T-Border and Jill and again, you will see some of these diagrams in later in this talk as well. T-Border and Jill also, I think worked the first to try to compare and see what the complementive power of binary pulse or test and gravitational wave detector results would be in the future. And I think I will show you in the following slide that this is indeed, I think what has happened with now this beautiful gravitational wave results being observed also. And still going strong, I'm very happy and glad that T-Border is a co-author on this paper here, which is the summary of 18 years of Pulsar Observation of the Double Pulsar. And we have benefited a lot from discussions with T-Border and so a lot of the things that we had sort of discussed over the years have now sort of found the way into this publication which is basically accepted. We're just waiting for the journal to approve the revised version. And so I will use this results basically as showing some of the things that were put forward in the last 50 years and show you what the current state of art is. And by doing this, we'll come across a few more papers by T-Border. But let's see just to look at what the experiment does. Of course, you know, we're looking at pulsars. These are rotating cosmic lighthouses. They send us a pulse or whenever the pulse, the radio beam is pointed towards us. We see a pulse once per rotation, typically. And this is a rather precise clock and we attach it here to the Newton star and the compact massive object. And if you put the whole thing in a binary system, all we do is watching to see how this clock falls in the curved space time around the common center of matter, it's companion. And we measure the times of arrival here on earth. They may be affected by the interstellar medium. But if you observe multiple frequencies and you time very precisely, you're basically able to test how the different theories basically predict this fall to happen and that's exactly what we do. Of course, the first time that it was possible was with the House Taylor pulsars I already mentioned discovered in 1974. The paper came out in 1975. And I think he is the beautiful parabola plot in the latest version that is published by Joel Weisberg who of course also contributed enormously to exploitation of the system. And the system already showed that gravitational waves exists. It showed that the energy loss is as predicted as by GR. It shows that the gravity propagates with the speed of light. It's certainly also showed that GR holds was strongly self-carreter in the bodies. And it was of course a forecast of what happened that W-Star mergers would exist and therefore was a good motivation to build gravitational wave detectors. So that's how it all started. And the formalism that was put in place really neatly put forward by the DD timing model and summarized in the DD design in two paper. Basically, the idea is of course that you have observational here with shown on the left hand side of each equations. And they depend basically on the capillary parameters and the two unknown masses of the system. So the idea is of course, if you measure at least two of these equations you can determine the masses. You have two unknowns and two equations. But if you measure more of these words with the effects then you have over determined your system and you can do n minus two independent tests if you have measured n parameters. There's a beautiful way of course to show this in a graphical way. This is in this mass mass plot where each of these observables produces a curve that depends on the masses. And if the system is described properly by the theory that you assume they're all intersect in a single point which is the unique pair of masses that describes the system. If you have a theory where these curves fail to intersect in a single point then obviously the theory is falsified and should be rejected. And this is of course the mass mass diagram for the Haus-Teller-Pulsar. And here's another paper by Thibault and Joe that I would like to mention because in this paper in 91 there were really putting together all the possible effects that could affect the observed orbital period decay and without that correction in particular here for the relative motion of the system to Earth the curves wouldn't actually intersect and you would assume that you have falsified your R but of course with the proper correction the curves all intersect in a single point and that laid the confirmation of the period decay. Of course the idea that external effects also play a role have been put forward in its various effects for other people like Blandford and Wagner in the past but I think this paper here was really a nice compilation of all the different effects that could indeed affect the observed value. By now we have a system that is superior to the Haus-Teller-Pulsar. It's also famous I think that by now with our Pulsar system we discovered that in 2003 we have two active pulses all within each other in just 147 minutes. We have a recycled Pulsar which is spinning fast and a young Pulsar which is spinning slow orbital velocities of about 300 kilometers per second and we see it from edge on as you will see now hopefully in this animation the tilt of the orbit against our line of sight is just 0.65 degrees. So it's really, really close to edge on and that leads to eclipses and it's a beautiful system to test the GR and you see or any other theory of gravity and you see the effects that we have measured in the system that it will briefly mention in passing at all of them on the next slides. We have now as I said put out a publication or it's about to be published of all observations and we discovered the Pulsar. We have precision astrometry including a parallax and hence the distance measurement which is as you've seen for the Hustler Pulsar is very important. And so we determined the distance to 735 plus minus 60 Pulsar which is pretty good and the transfer velocity is also very small. It essentially stands still where it was born. At the moment we have about 1 million T-rays at times of arrival measurements and we measure the Pulsar parameters very precisely. The most precise Pulsar parameter is actually the periastron advance and we have measured as a level which is exceeding the expected 2PN contribution by 35 sigma. So and that will become important as you will see we may try to measure the moment of inertia of the Newton star. Of course we do measure the orbital period K and here you see sort of the parabola for the Pulsar. It's nicely sampled. The Pulsars approach each other by about seven millimeter a day or the orbit shrinks by 107,820 plus minus seven picoseconds and the expectation from GR compared to the observation is in agreement at a level of 1.3 times 10 to the minus four. This is the most precise test of the GR quadruple formula that exists right now. And our position is actually so large that we have to take the mass loss of the rotational spin down into account as the Pulsar spins down by emitting gravitational and sorry, electromagnetic waves. It's the period changes and that loss in energy is to be taken into account and this is about 8.4 million tons per second but on the other hand it's only 3.2 times 10 to the minus 21 of the mass of Pulsar A. This parabola I think is also I think very nice related to Thibault's work because for instance in his 93 paper he showed that the quadruple formula that is here is the one from his paper actually is also valid for strongly self-gravitating bodies. I think that's important and this parabola nicely shows that it is indeed the case. We also measure light propagation something that not many experiments can do in strong field. And here of course we make use of the orbital inclination angle being so close to 90 degrees which means that the light has to pass the other nuclear star in just 10,600 kilometer distance. And that leads to the lay in the rival times because it has to propagate to the curved space time. And here again you see the red curve is prediction by GR, the blue dots are our measurements. And again that allows us to actually determine the inclination angle of the orbit to that precision. And again, if you compare the observed value with the expectation from GR again as an excellent agreement between the prediction and our experiment. If you actually be look a bit closer and sort of if you subtract the curve and I've done it here again so if you subtract the prediction in its simplest form you actually saw a deviation, a clear signature. And that signature comes actually from two effects. It's actually here we have to take the next higher order a Shapiro Delay contribution into account which basically means that our lens Pulsar B is moving by the time the photon has left A and reaches Pulsar B at its part of the orbit. And that leads to a shift in the Shapiro Delay curve but it is only one contribution. The other contribution is actually a light bending because the space time is curved. And so the Pulsar A has to shoot its photon slightly earlier before superior conjunction, sorry slightly later before superior conjunction slightly earlier afterwards. And that leads to this nice signature here. So this curve actually also tells you the direction of spin of Pulsar A relative to the orbital momentum vector. So we can tell you it's prograde. And actually that bending here makes this 600 kilometers of the 10,600 kilometer distance that the signal passes here. And these higher order effects are indeed consistent what we would have expected from the theory which is shown here by the red curve. So if you compare this as I said to other gravitational experiments which test light propagation, cause we have our image of the black hole here is the Shapiro Delay test of the double Pulsar. And in this diagram where we plot the maximum curvature versus the potential, it is actually quite close to what the gravitational wave detectors can probe. And here's of course the nice precise Cassini result of the solar system. We also have measured that the orbit is relativistically deformed. That is because we have actually three eccentricities when we write down the equations of motion and he has been very much exaggerated effect of how that impacts on the orbit. And even though the effect is not measured with high significance, it's actually important to include this in our timing model because otherwise we would have obtained a wrong parameter of the Einstein delay and would have been offset from GR by about two sigma. But by taking the orbital deformation into account as it was first put forward by the Modera in the in the 85 paper, we can actually show that is very much consistent with the prediction of general utility. I should mention the steering effect. I hear Viaghe had, I think there was interesting race going on in 87 to publish the fact that the contribution there's a contribution of the length steering effect spin over coupling to your observed orbital per procession value. And in fact, so that's written here and it's written such to indicate that the contribution of the steering is actually of the same order of magnitude as the 2pn effect. As I mentioned before, we have measured this with the position that exceeds the 2pn effect by 35 sigma. So there's a principle of a chance to isolate that contribution from the steering and hence measure it. And this is the paper. I was very proud that we discovered this paper in original PDF format on the other day preparing this talk. This is in the, I think reports of the Academy of Science. And here's the new experimental paper that came later. So yes, we see this effect actually because here is a zoom into the mass mass diagram that I'll show you in the next slide in full. And this shift here between the two omega dot lines is the shift that if you take the steering account or not. So there's a significant deviation if you don't take it into account by marginalizing over different possible equations of state, we can determine the mass of the two pulsars very precisely. And in fact, we can then also try to put limits on a moment of inertia that we basically obtain. This is a diagram where we basically is a probability density function of our measurements. And at the moment, we can only give you an upper limit on the Newton star radius is 22 kilometers. Of course, it's not competitive in that sense with, for instance, the nicer results. But as you can see, we start just basically from pulsar timing start to constrain the radius of the Newton star, which I think is a very nice result. And if you follow the paper by who it are, we show you how this will improve quite dramatically in the near future. This is the mass mass diagram for the double pulsar after this 18 years of observations. Each line is actually the thickness or supposedly the thickness of the uncertainty. And as you can see, most of them are very precise. Now we have now seven corpus copiarum parameters. We have this next leading order effects in the signal propagation. We have the most precise test of TR using the quadruple formula. And we have started to probe the moment of inertia equation of states. And I think it's very cool. We need to take the mass loss into account as the pulsar spins down. And we already have started to observe this pulsar but we make a tell us for a show some quick results in one of the next slides. And then they had been timing improves already by a factor of two to three or what we have achieved so far. Yeah, but let's talk about spin procession very, very briefly. Of course, it was this insight by rainbow on seaboard that the, if the spin axis of the pulsar is misaligned with the overall momentum vector, this will lead to a procession of the pulsar around that tool and momentum vector. And that changes the line of sight that we see that we cut the radio beam with and that leads to profile changes. And indeed, as we have seen in the past, the host Taylor pulsar is becoming narrower and narrower and in principle should disappear on 2025 but maybe it just doesn't matter and we'll see how the geometry evolves working on an update on this paper. We have seen this effect also in a double pulsar. There's this beautiful work by René Proton where we've used the eclipses of the pulsar that changes with time because this eclipse is not complete. It's actually because this is a donut rather than a sphere. This clips pattern is modulated and this modulation pattern depends very sensitively on the orientation of the spin axis of pulsar beam as pulsar beam processes that pattern changes and by tracking that change, we can measure the procession rate and that's we validated that with the GR prediction with a precision of 13%. Just as I've mentioned, we already have meek at observations. And so this is a beautiful eclipse pattern that we see with meek cut with awesome sensitivity. And we started to continue that eclipse pattern and this is still preliminary work, but we can already expect that the precision of that test will have probably improved by an order of magnitude or so. And this is a work in progress by Markus Lauer is just done finishing this PhD at Swinburne University. Maybe the most beautiful test of geodetic procession is actually that will be published in 2019 using another relativistic binary pulsar which where we actually see the young Newton star with W. Newton star system. Here we see this beautiful two components in the pulsar profile which comes actually from the two opposite poles. And we can measure in particular the polarization of characteristics of this radiation very precisely. And there's the what they call the rotating vector model which associates this position angle swing with basically a projection of this feed line direction onto a line of sight. And hence as the line of sight changes that slope in that position angle curve is a function of time. And we have tracked this pulsar also for more than 12 years. And here we show you the change in the position angle on one of the poles. And as the pulse actually crosses the magnetic pole the sense of the slope changes swaps so negative to positive. And that is exactly what the rotating model had predicted. And at the same time that allows us to measure the procession rate. And again we can measure this here in this case to 2.17 plus 1.11 degrees per year which again is very nicely consistent with the prediction of GR. So I think that is actually the most beautiful test of geodetic procession as was predicted by T-Bot on the rainbow in 1974. Let me say a few words before I finish about alternative fields of gravity or testing principles. As of course, we already mentioned heard about this on Tuesday, the microscope satellite that T-Bot was involved with. And there's a beautiful very tight limit on the violation of the University of Freefall. There is of course, you can do laser ranging or similar experiments with the moon. And the question is of course, what can you do with binary pulsars? And there's one paper that Gerhard and T-Bot wrote together which basically showed the way how to do this. They basically pointed out that a deviation from a zero-accenticity orbit could be a violation of the University of Freefall. If you have a white dwarf and a pulsar falling together and neglect the potential. And indeed we've used that in the past to produce very nice limits. But nature has been even more kind to us than that because they have given us the triple system which is actually a pulsar with in orbit but two white dwarfs as an inner orbit with a pulsar and a white dwarf which is about 1.6 days. And there's an outer white dwarf which always the pulsar white dwarf system with a period of about a year. And together we basically can track how the white dwarf and the Newton stuff the inner orbit fall in the gravitational potential of the outer white dwarf. And by doing this experiment, Archibald and I produced that limit on the violation of the University of Freefall or we use the strong free know what parameter that was introduced by T-Bot and Gerhard in the 91 paper. And in fact, we have improved on this limit in both in quantitatively slightly but in particular in cleanliness of the test in a paper where we use beautiful non-say observatory data by Guillaume Bisson and in collaboration with us. And that is a beautiful clean limit and it's also beautiful work that Guillaume has been doing. We could of course put this then curve this also in the plot that were introduced by T-Bot and Jill to test in the what we nowadays call the demo of the esposite for gravity. So you have this two parameters alpha not and beta not which are the coupling to the scalar field linearly and for radically and everything below a line is still allowed everything above a line is forbidden. And of course the bottom minus infinity here and the triple system in fact gives you the best constraint for most of the parameter space but even the double part here actually has something to say about this in particular about negative beta. In fact, if you take our timing data that I presented you earlier and you look at the sort of the theory realization of this star here, you see that they resulting in mass mass plot in fact, it looks like many lines that do not intersect. And so this is indeed falsified as it is also beyond that curve here. There's so many things I could mention what else you can do with binary pulsars and I just leave that list on here. Let me just point out to that paper by T-Bot and Jill testing the local loans invariance and there's a nice update by Li Jing Xiao and Norbert Wax from 2016. But again, the idea, one of the idea was produced first by T-Bot and his collaborators in this case, Jill. And so yeah, if you're interested in getting an update of what the current numbers are that two reviews one by Norbert and Li Jing, one by Norbert myself so I can recommend this. Let me finish basically by saying that I think it's a pity that Einstein didn't live to see the discovery of pulsars and the usage of how we deal with them to test relativistic gravity because it's nice because they provide very precise sometimes the most precise tests and often unique tests for some self-gravitating bodies because of the nature of the experiment the measurements are usually clean and precise and so far we haven't found the fault in generativity which means we have tight constraints on alternative fields of gravity which need to pass the binary pulsar test. I think I've showed you that we have done some very significant progress in particular the double pulse interpret system basically building this on the work that he both and collaborators have done. It's beautiful to see that we have now I think to send it to the next level of precision we measure effects that were not possible to measure many years before. We find more systems and with the SKA coming online or Meerkat already and fast we actually do find currently some very interesting binary systems which may maybe eventually surpass the double pulse as the double pulse has surpassed the Taylor pulse. And I just want to point out again that Tivot has really had enormously to exploit these binary pulsars with all the various works that he has contributed. And yes, I think we are still going strong and with Tivot's help then there are many more years to come to do more. And my final slide is, and this is my, I mean there are good, very many quotes from Einstein but as a pulsar astronomer, I like this quote very nice very much because he says is just my English translation that comes to pedantic precision of astronomy to the rescue which are ridiculed silently so often in the past. And he wrote this in a letter to Anna Sommerfeld after he was able to explain the Mercury perillion advance with this field equation. And I like this animated image of Einstein I think it's fake. Anyway, I couldn't help to add this nice plot form and picture from Tivot's comic on the quantum world which I also have at home and really much like. So with that, thanks Tivot. And I've heard you, we shouldn't praise it too much but I'll do it anyway. So thank you very much in terms of helping us with our observations and trying to understand them. Thank you very much. Are there other questions, short questions, comments? Hello, please, yeah. So concerning the test of the strong equivalent principle with the triple pulsar, how do you believe the value or the maximal value of this combination delta which involves the gravitational energy divided by the mass but what about in terms of the not that parameter in front and how does it compare with the laser rounding test? Yeah, so it certainly is not as a make-up. It's not as precise as the lunar laser ranging almost getting there. It's certainly not as precise as the microscope experiment but the order of magnitude I think I have to go back to my slide to actually check but I think we're about an order of magnitude worse than the lunar laser ranging. No, it's 10 to the minus 13. They're not quite there yet but yeah, it's a strong field effect and the measurement at least in our case. So that's why it's so. So in measure of eta, epsilon is 10% and the result that I've done is six so it is more precise. Yes, but in terms of data only that's my question. What is the test? I look it up because it is all the effect. So that's why it's... But if we have a violation of the equivalent principle there should be the same eta in principle in different bodies. Yes. So eta is a good measure to compare tests on different regimes for different systems. You want to be few independent, so you cannot be... Okay, this is another question. In terms of eta, I mean, epsilon is a 0.04% and in terms of a triplet system was 0.02%. In this case, it's in the opposite side as T-ball just in absolute terms, of course it's not but thanks T-ball for making that argument. Very nice questions, Michael. You've seen double system, triple systems, what about more complex system? Is this likely to occur or very unlikely? We have planets. I was just about to say we have one planetary system with three planets at least. But yeah, they're not very good for testing gravity because the planets themselves have not very much mass. Anything more massive than that I think wouldn't be stable enough to survive long enough for observations. It also becomes a little bit messy. So even the triple system doing the theoretical analysis properly was a challenge. And I think that is the beauty of what Jorm has shown in his paper, which I think is much more elegant what we have done than what unarchival mothers have done. But I'm biased then. Okay, so let us say Michael again. Thank you very much.