Interview with Jorge Pullin

0:00 It's the 4th of November, it's at quarter past 3 in the afternoon, and I'm talking to Jorge Penrose. So, well, as I said, I'm interested, for instance, in work on this interesting work on using perturbation. What would you like to know, basically? Well, first of all, although I'm interested in it, I don't know that much about it yet. I've only got the details of it. Well, so this, I mean, if you think about this work we're doing, it's fairly obvious that it should be done. But somehow it hadn't been done. And I think in 1994, there was a conference of gravitational waves and numerical relativity here at Penn State organized by Pablo Laguna. It was the first conference we organized in our center here since we came. We came in 93. The center got started in 93. And that conference, there was a lot of people there. Larry Sparrow was there, which is not always at conferences, but let's put it that way. And a discussion ensued, I don't remember the details very well, at the end of one of the talks. And he said, well, you know, the end point of a collision of two black holes, two black holes merge. They merge into a single black hole. So after some time, the thing has to look like a distorted single black hole. So someone of you guys, Richard, he said, pointing out to Richard Price, should be doing this, right? Treating a collision like two black holes that just merged and treating it as a perturbation of a single black hole. So, well, I was there, and Richard and I were collaborating on all sorts of stuff in perturbation theory at that time. And he said, well, let's take a look at this. So what we did is we took the initial data that the numerical people normally use for colliding black holes, except that, you know, that initial data depends on a parameter that is the separation of the two holes. Normally these people would try to put them far apart. In particular, because these families of initial data that people give, they're constructed in a rather ad hoc way, that is, whatever you can find as initial data you use. And when the black holes are far apart, everything is okay, in the sense that whatever interactions there are between them, are not very relevant. When you bring them together, the black holes start to interact. And therefore, whatever the initial data you're giving has to be much better physically motivated, so to speak, what sort of interactions you're putting in. This is not done. So we decided to say, just take that initial data that people use, and consider the case when the two black holes are very close to each other.

2:30 And they're very close to each other. If you put them really close, what happens is, you know, their parent horizon engulfs them both. If you tear them apart a little bit, the apparent horizon may separate, but the event horizon, if you evolve the space-time, still engulfs both. And if you take them apart even further, you start with two separate horizons. So we said, well, let's just put them real close, so there's a single horizon encompassing everything, so this is clearly a single distorted black hole. I mean, yeah, we can call it a collision of two black holes, because we just took the initial data of two colliding black holes and put them close to each other. Any way you look at it, this is a single black hole. So we decided to treat that using perturbation theory. And the interesting thing is you're given the initial data. It's the same initial data as numerical people. So you don't have any parameters at all. It's that initial data, same as they're using. You're just taking it when they're very close and evolving. So if I do it this way and they do it with a supercomputer, we have to get the same result. There's nothing to adjust in between. So we actually did this. And the remarkable thing was that the approximation worked excellent when the two black holes were very close. But even in the region where you start pushing them apart and starting to have the very beginning of separate horizons when the two start, the approximation was decent. I mean, even when the two black holes were separated by distances, let's say in terms of their Schwarzschild radius, like five or six Schwarzschild radius, mission was working to within, you know, 20-30%. And if you think of the amount of effort that takes to do one of these supercomputer simulations, the fact that with, you know, pencil and paper and a little workstation, you could get results to within 20-30%. And better than that, you're getting waveforms out of this that are accurate to that accuracy. It's rather remarkable. Given the fact that the numerical people were finding that maybe it was going to be a little do a collision of two black holes at what one initially thought, we decided that why not turn this thing into a program and try to analyze as much as we can the last moments of the collision, so to speak, or collisions of black holes that are very close, because it certainly can't hurt, and it can actually help a lot when people are trying to do numerical codes to have a certain regime of the code where they know the answer already.

5:00 So after doing that, so what we did initially was to take this so-called misnomer initial data, which corresponds to two momentarily stationary black holes. So these are two black holes that someone brings, puts there for you, let's go of them, no initial momentum, and, you know, they attract each other, and you eventually collide head on. The next thing we attempted was to try to study the case of two black holes pushed towards each other, so you give them some boost towards each other. That had not been studied numerically. The only numerical simulation at that time, in 1994 and 1995, was this Misner case that had been done by the Illinois group. SMAR had done it like 20 years ago, but then people had refined the code, and now they have a code that they really thought they had under control and was reliable. The boosted case hadn't been done yet, so we started working on that. The problem we have there is that the initial data for such a case, That is, this Misner initial data is a very clever construction that works for stationary black holes. If you want to do it boosted, there's no exact solution. So we had two alternatives. We could try to do a numerical solution of the initial value problem, which is not impossible. I mean, for an axisymmetric case like that, even people like us can do it. You don't need, you know. These days, a lot of numerical expertise. It was a problem that 10, 15 years ago was the forefront of numerical relativity. Greg Cook and Jim York and others were working on this. But now, you know, anyone can do it because you can read their papers and see how to do it. But somehow it occurred to us that, first of all, doing that numerically and then taking that numerical data and somehow extracting initial data for this perturbation formalism was cumbersome enough that we may want to try something else. was to solve the initial value problem approximately. In the end, if we want two black holes that are closed, we can also make the approximations that are closed when we're solving the initial value problem. So we found approximate solutions for the initial value problem, evolved them with this, produced waveforms and energies. This was done mostly by a grad student here by the name of John Baker. And when we were doing this, we discovered something rather peculiar, That is, when you push the two black holes towards each other, for a while, they radiate less than if you just let them go, which is a little bit counterintuitive.

7:30 One would think if you're banging two things against each other, it would radiate more, right? So we were a little bit puzzled by that, going back and forth with John trying to understand what was going on. In the meantime, Richard Price was collaborating with Andrew Abrahams, who in turn was kind of more in touch with the numerical people than what we were. and through him we heard that the Illinois group were actually doing simulations for this case at the same time and they were also encountering that the thing radiate less and they were also very puzzled as to what was going on. Now the fact that we discovered that each other completely independently were finding the same thing led everyone to believe that this was a real effect and what really is happening is that these particular families of initial data we're using when you push the two black holes to each other, the horizon tends to jump out. So although in principle you would have more energy to radiate, so to speak, the horizon engulfs more of it. So there's kind of a competition effect. And for a while initially, when you're pushing them slowly, the horizon thing wins and the thing radiates less, considerably less, like an order of magnitude less. But then if you start pushing them harder and harder, the radiation is a function of the initial momentum goes up, recovery itself. initially is, is kind of significant. It's not referred commonly as the Baker dip because John was the first one to kind of notice that. Um, in the meantime, however, so, so, you know, the natural project there would have been to, well, now do collision of black holes with spin and then, you know, take two in-spiraling black holes. You won't be able to do the in-spiral, but you could take two black holes head-on, not quite a line, and do this, this kind of last thing not many orbits but just a little final thing with some angular momentum as long as the angular momentum is small we could treat the thing as a distortion or Schwarzschild black hole which is what we're doing we're not doing perturbation occur at the moment so one could have done all this but we decided to not do it because what we felt was these perturbative results unless you can tell or they're going to be valid they're kind of meaningless. Perturbation theory is consistent in itself. It doesn't tell you where it doesn't approximate reality anymore. So we found it of little value to just go and crank the handle and compute all these things because we want to be able to tell people, should you trust

10:00 this for this range of parameters, that range of parameters, whatever. In fact, the fact that the Misner case kind of surprised us that the thing worked much better, so to speak, that one would have expected at the beginning, that is, led us to believe that we needed some sort of way of quantifying this. Because, I mean, perturbation theory clearly works when perturbations are small, and that's what we all learned since college, basically. But the issue that in Route 30 is a little bit more complicated, because your perturbations can be large in a region that is of no physical interest to you. So, for instance, inside the horizon. And therefore, you wouldn't say that perturbation theory is failing in that case, perturbations are large, but in a region that is not causally connected with you. You need something better than just saying perturbations are small. So what we decided to do was to become ultra-conservative and say, well, really perturbation theory, the way it works is first-order approximation, the linearized theory we're doing is a good approximation when the second-order corrections are small. If not, it's not. So the way to decide this issue is to go and work out the second-order perturbations and see if they're small. there is that, at least to our knowledge, no one had worked out the second-order perturbation of a black hole. So we had to go and work it out from scratch. For this, we got involved with some collaborators that my ex-PhD advisor from Argentina, his name is Gleiser, Reinaldo Gleiser, and a postdoc that is working with him, his name is Oscar Nicasio, and the two of them, Richard and me, started hacking up with the second-order perturbations of black holes. Now, the formulas started getting quite massive, and we had to, and there are all sorts of subtle technical issues having to do with gauges, how you fix coordinate invariants to second-order, how you even extract formulas for the energy asymptotically to second-order. The story is really very long and detailed. I mean, we thought, well, you know, we just do everything to second-order, and six months we're done. It's been almost two years by now. I think we're done for the Misner case, but for other cases we're still discussing a little bit, a few of the subtle issues. So this program of trying to kind of put error bars to our formalism, I mean, telling when prehistoric perturbations actually work or not, has taken considerably longer than expected.

12:30 But on the other hand, if you look at the results we get, let me show you a picture here. Maybe I can keep a copy because we have the name of all the people involved, but these are two waveforms. These are waveforms. Separation is if you divide by the Schwarzschild radius of each black hole, it's 6.6. This I'm dividing by the total mass of the space-time, which is kind of twice, so it's 3.6. So this is fairly well separated. If you want, this is energy versus initial separation. Here you have an analogogram, 6.6. So you see that these are the numerical points. This is the first order of approximation. So you see this works well up to, you know, around here. This is a log plot, so, you know, this is already like 50% out of there. This is a second order thing. First plus second. So it's telling you that here the thing is breaking down, which is correct. But now what is kind of spectacular is to look at the waveforms at 6.6. Black dots are the numerical results. This is first order. And this other one is first plus second. So, you see, the effort kind of pays off in the sense that you get a much better approximation to what's going on. So we were kind of pleased by those results there. Some note of historical interest is I visited Kip sometime, I think it was in the summer last year, August last year, and he was giving a talk about this, and he, and the Japanese Japanese people were there. I don't remember who. Certainly, these people who work on the stuff you are aware of, like post-Newtonian stuff, spinning particles, no, the name escaped me for just a moment. Of the Japanese people? Well, there's Shibata, Tagashi, Tanaka. I think it was Shibata who was there. Yeah. Well, let me tell you precisely the acknowledgement in one of our papers.

15:00 Sasaki and Nakamura were there. And they and Kip pointed out that a Japanese person by the name of Tomita in the 70s had actually worked out the second-order perturbations of black hole. This was after we were done, basically, with this. It turns out that what he had done was very different than what we were doing. He was using Newman-Penro's kind of formulas, and so his results could have been adapted to our kind of language, but the effort would probably have been equivalent to kind of redoing everything from scratch. Plus, what he was trying to do, and this is historically very interesting, is in the 70s, at the beginning of the 70s, people really didn't know black holes existed. Price and his thesis had kind of proved that if you perturb them, perturbations die off and they're stable. But people still have the controversy saying, well, you know, what if that is just linear order? What if you throw in higher order effects and some instability creeps up? So to me, they actually had worked out the second order perturbations to prove actually that. He wanted to prove that black holes didn't exist. And he actually did it. he'd computed, I don't remember the details, some quantities at the horizon of a black hole to second order and found that they diverged. So in his opinion, black holes didn't exist. Well, it turns out that he had fallen into pitfalls that appear in perturbation theory. It turns out, I haven't studied this in enormous detail, but the general consensus seems to be that what he was computing at the horizon are not quite gauging varying quantities. Therefore, the fact that it diverged is not very meaningful. But he got kind of confused about that in the 70s, and his work was kind of forgotten after that. Moreover, since he was interested in looking at things at the horizon, he hadn't worked out any of the asymptotic formulas that give you the radiant energy into first and second order. That ends up being a major chunk of the work, so our work wasn't lost, but this was kind of interesting. His work was sitting there dormant and no one had paid attention to it. so I'll give you a copy of this it's just referred here and added in proof because we just got it in by the time we were publishing this anyway, in between what we have been trying to do is a postdoc who's visiting here, the name is Hans-Peter Nolert from Tübingen in Germany and John Baker had looked at the collision of

17:30 spinning black holes so just two black holes are individually hit each other head-on. So the whole thing has axisymmetry, you just align the spins like this. And if you put them like this, there's the net zero net angular momentum, so you can treat the whole thing as a perturbation of short, which is fairly straightforward to do from here. They have done that calculation by now to linear order. And the four of us, second order front, we are studying right now how to do the boost problem. We are virtually finished, except for certain little controversies of conceptual nature that is the meaning of what we did but the formalism is in place and and basically the work is done we have even a pre-print written that we haven't released yet because we want to iron out these last difficulties i'm flying to south america in two weeks to try to finish this um doing the spinning case to second order would also be i think no problem it's something we can do in the next few months And what we're trying to do now is this kind of, what we call pseudo-inspire. We don't want to call it a spiral because there's really not many orbits, but just this. Now, there is a couple of things that happened. This we discussed at length when Hans-Peter Nolart was visiting here with Pablo Laguna. Pablo and his group in astronomy, including Philip Papadopoulos and William Cribbon, who were with him, the post-doc and the grad student last year. He probably told me a little bit about this. for evolving the perturbations of a curved black hole, the Tucholsky equation. The idea was that, well, you know, they just write this code. When they're done, we take our initial data, put it in there, and do this sort of in spiral. But then we started running into problems of both conceptual and technical nature. First of all, conceptually, what happened was that this family of initial data for two black holes that go and hit each other with angular momentum, somehow, or let me put it this way. When you take those families of initial data, two black holes that hit each other with some angular momentum, if you take them real close and stuff, they look very much like a single rotating black hole, which is, okay, that's what it should be. But it turns out that the initial data of these families, which are the Bowen and York family of initial data, holes, if you evolve that, you don't get the Kerr space-time.

20:00 You get the Kerr space-time plus some radiation that goes out. The way in which this explicitly manifests itself in the initial data is that the initial data you produce has spatial sections of the metric that are conformally flat. And Kerr, to our knowledge, doesn't have any slicing that we know of where the spatial metric is conformally flat. Now that's a big problem because in the perturbation formalism You're doing perturbations around curve, so your spatial sizes are definitely not conformally flat. Now you're going to bring out this initial data that is conformally flat, how are you going to match it? So that, we still don't know very well what to do about it. That's the kind of conceptual problem. The solution we decided to do or to pursue right now is to just ignore the problem, basically. Say, well, our background is conformally flat, our initial data is not, so what? The difference we just treat as a perturbation. This may, the pitfall of that might be that we are introducing artificially large perturbations by not matching appropriately the initial data, but we'll try it and we'll see what the result is and learn from that basically. Even from that perspective, just give initial data for the Tucholsky equation that is just given a metric and a intrinsic curvature to find the Tucholsky function and its time derivative, It's a highly non-truvial exercise in Algebra. John Baker and another grad student named Gaurav Khanna are right now looking at that. They're going to succeed eventually, but they're wrangling with the Algebra and Computer Algebra quite a bit. The technical difficulties we encountered was that, at least in these families of bone and York initial data, when you crank up a lot the angular momentum, it turns out that all perturbations get cranked up too. So you might have thought that by working on a curved background, you would have absorbed most of the angular momentum into the background and be left with a few perturbations. Well, that's not true. If you have a lot of angular momentum, your perturbations are also large. So the whole thing is questionable in the sense that if that is the case, why don't just use perturbations in Schwarzschild? You'll be forced to keep the angular momentum smaller in any case. In Schwarzschild, because, you know, your background is not rotating in this other case because the perturbations have to be small. But we're debating that back and forth. It might be that, yes, using curry doesn't buy you a whole order of magnitude more in accuracy, but maybe it buys you a pack of two or something like that. So we think it's worthwhile pursuing when we're pursuing that.

22:30 And eventually, presumably, someone will have to work out the second order of that. I don't even want to think about that. But I guess that's the status of this program right now. We have, I think, for these boosted and spinning head-on collisions, we have a lot of control. We might have second-order results for all that within a year, I'm sure. For the in-spiraling case, we'll have first-order results on a curve background also within a year. And I think all this is a body of knowledge that people who are doing numerical relativity can use when they want to calibrate codes or just check if their codes are working. Better yet, you know, you are very well familiar with the work like people like Scott Hughes and Anna Flanagan and stuff. They have done work concerning, you know, detectability of in-spiraling waveforms without knowing the waveforms at all. That is, you know, this paper, the preprint that came out this year early on, they have a second one right now. They talk about the in-spiral, the ring-down, the merger regions. For the in-spiral and the ring-down, they have analytic formula from postentonian and from, you know, just quasi-normal ringing. For the merger, they have nothing. And yet they say, well, let's assume, you know, whatever spectrum is flat within certain frequencies and let's estimate. So my expectation is, if that already is useful, you know, if we can provide some sort of approximate waveforms that might be good within a factor or two, probably that's better. Depending on what you want to do with LIGO, but if you just want to detect or if after detection you want to narrow down what sort of object, having the approximate waveforms to certain factors may not be completely negligible in interest. And given that the numerical effort is taking a long time, this might be useful for a while. So, that is, if you want, the less ambitious kind of view one can take on this whole approach. The other thing is all these head-on collisions seem to proceed in the following way. Initially, when the things are just moving towards each other, they produce very little gravitational radiation. When they get close to each other, the horizon jumps up, engulfs everything, and there really is no merger region. That is, you make a transition from a region with no gravitational radiation, everything like post-Newtonian, to a region where everything is a single horizon. Couldn't it be that, you know, when two black holes in spiral towards each other and they get to a certain distance, the horizon jumps out, engulfs everything,

25:00 and the mythical merger region where all this interesting stuff is going to happen is clouded behind a horizon? We don't know. But I think that's not an attitude that should be completely discarded. I mean, Kip would bet everything that that's not true, and I think he probably will be right. But it's something we should contemplate, that horizons are a blessing in a sense, that they hide all this stuff and allow us to treat this thing so easily. So if they just move out a little bit more, they may, you know, spare us a lot of headaches in the intermediate region. That's something we're currently, you know, studying. And I think not a lot of effort has gone into studying, for instance, these families of initial data, what the horizons exactly do. I mean, Bowen and York, and actually Greg Cook and Jim York, and then Greg Cook and Andrew Abraham did some studies of this. But I think it's partial. I mean, people need to play more with these kind of initial data. Study apparent horizons, if you want, very simple to study. And see if, just quantitatively, you know, how much of that interesting region is clouded by one of these horizons. Because it might be that it's more than what we expect, and then maybe the whole attack on the problem should be different. shouldn't try to shoot to have a very accurate numerical code for doing many orbits, but just maybe something to guide us from when post-Newtonian breaks down towards a region where the horizon jumps out and engulfs us, and there we can take over with another approximation. I don't know. Interesting. And do you think that, or do you hope that it may be possible, using perturbation methods in the nearly inspiring case to get a reasonable picture of whether the horizon is likely to pay in this way, jumping over. We have to accumulate more evidence before we can say that. I mean, surely, if you just take it at face value, no, I mean, perturbation theory can't do this for you. But, you know, if you play around with things, you gain some intuitive feeling, maybe you can present the nominal boundaries of what this formalism is about. So we don't know at the moment. We need to play more. it to play with things like, you know, finding apparent horizons and stuff, it's effort and time-consuming. And we're a small group with not much funding, so it's just an issue of time per person, basically, that we can involve. If you think of what we have accomplished, I mean,

27:30 building a second-order formalism and applying it to all these cases and, and, you know, doing the head-on collisions with spins and without spins it is significant in so far as the fact that you know I've only had one postdoc here working on this and just a bunch of collaborators that are collaborating on a voluntary basis as opposed to you know the numerical effort for instance is a much larger effort so if you just compare scales when they ask me why did you do this well I didn't I suppose that's an interesting aspect of the state of the field at the moment. From my point of view, the fact that now you have, well, you have efforts like the Grand Challenge Alliance, which are on a kind of scale that's pretty unheard of for the rest of the theorists. Right. But also that what they're trying to do is pretty unheard of. Yeah, that's right. Sure. It's a big, big problem. I mean, do you see it in any way being difficult as the field matures further for groups that are not part of such big alliances or for people interested in analytics? If you want, we are an example, that's probably not true, that, you know, you can come up with a fresh idea from the outside and maybe alliances are typically good to tackle a problem that is well-defined and just needs a lot of effort, which, you know, probably Client Black Holes wasn't quite when this alliance was started, but it's getting more and more to be that way. That is, I think the progress they have achieved is significant, and maybe it's still not quite through today, but I'm sure within a few years it's an issue of, you know, putting enough people to work into this in a focused way and to get done. So whenever a problem reaches that stage in maturity, I think it's worthwhile, you know, pursuing it this way. On an arbitrary problem, of course, tossing money at it is not totally So how do you be if the flying black holes will be curing cancer or whatever, it's just the... So it's only going to be in certain instances that you're likely to find expensive efforts involved. It's also, I mean, the sociology and the dynamics of all this is very interesting, in the sense that you inject money, well then there are all these postdoctoral positions that crop up.

30:00 Because, you know, a field that was dormant for a few years, and where there weren't any post-doctoral positions would attract many students. So then you go and hire a lot of people and, you know, get them going. And a few years down the line, maybe the funding finishes, like this is the case, you know, for this particular effort. Then what do these post-docs do? So these kind of spurts of money that go in and out of fields rather quickly are a little bit dangerous in that aspect. that fields don't change ideobatically and therefore difficult to manage. I mean, if you go out now and ask, you know, you say, well, I want a postdoc that works in your marketable authority and does this and that and that, there aren't that many people around. Put an ad and you get a hundred applications of which maybe two or three are what you want. Not quite. Also, I mean, these large efforts become very complex from the point of view of people involved in the sense that, you know, postdoc that is whose job is to kind of manage a code that someone else wrote in collaboration with someone else doesn't have much of a chance of developing a career of its own and it is a fact that some of these people are having trouble finding jobs in spite of the fact that they have a very valuable work so it's complex