Interview with Stuart Shapiro

0:00 It's turning, and it's 3 o'clock on September 4th, and I'm talking to Professor Stu Shapiro. So, I guess this morning you gave me a lot of very useful information about some of the recent neutron star work. So that's what maybe we could start off now with your finder of that book. Well I'm part of a large effort, as you probably know, called the Binary Black Hole Grand Challenge Alliance, which is a National Science Foundation sponsored project to bring together computational relativists and computer scientists and relativists in general from over eight or nine institutions to try to solve what is arguably the most outstanding unsolved problem in classical called general relativity, the two-body problem. It's almost incredible to think that the two-body problem is yet unsolved, but indeed it is because of the non-linearity of Einstein's equations, the complications of dealing with many coupled non-linear partial differential equations, and the obvious nightmare that inherent in a black hole spacetime is an interior singularity, a region of spacetime where many of the physical quantities blow up to infinity, like the curvature. And so any numerical integration dealing with black holes has to figure out how to deal with these infinities, which otherwise tend to cause a computer code to overflow or under flow and blow up. How do you integrate with infinities? And to make a long story short, first, I think it's true today that despite the considerable

2:30 effort that's gone into solving this problem, in particular the binary black hole problem where the black holes are in some kind of quasi-equilibrium circular orbit in spiral slowly together due to gravitational waves, despite that effort, this problem is unsolved. Namely, we do not now have a computer code which can evolve two black holes for even one single orbital period without that code crashing because of instability. but that is not to say we have not made enormous progress on this problem we have advanced first of all the calculation of the head-on collision between two black holes a calculation pioneered years ago by larry smarr and his colleagues we now have resolved that problem in many different ways very accurately one way for example that i've been involved in black holes which are formed by the collapse of matter. So one starts with two distributions of matter. Hi. Sorry, just two quick rules. Great. She can. I don't think our kids are going to be around. Well, he's trying to, knowing that Adrian's going away, he's trying to make plans. And we gave him license to encourage him. Even encouragement. Jennifer Shannon has just arrived. She has a meeting with the head of the department. She will come to see you when she gets out in the meeting. So would you like... I was spying on her. No, but she's not available now. Okay, we're just chatting about the history of the... He's eager to get the computer set up, so... This is a good time when Jennifer's around. Make sure she does it on Donald.

5:00 On Donald? On Donald first, and then on... And I'll be catching her away. She will come looking for you, but she lives just in the bell room, behind the bell room, so you can walk through an eye out. Okay, thank you. I thought, but she's looking for you. He doesn't know what he looked like, because you just disappeared around the corner, as I was called. So, I was telling you that we have made progress. In particular, I was describing the elementary problem with two black holes colliding head-on. And some of the new features of that calculation are that we can now solve that problem by taking two globs of matter, in the case that I've worked on, two clusters of non-interacting particles, if you like, two star clusters, which are far apart initially. We follow their collapse on their own centers. So these clusters are undergoing gravitational collapse to form black holes, and then they move toward each other, feeling their distant gravitation in fields, and one watches the two black holes merge into one, and they have seen pictures of this process used. I guess this is a blind example of the two clusters that are collapsing, and you can see their tidal interactions leads to this hourglass-like event horizon. And then the event horizon goes to a single horizon which encompasses the collapsing material. And we've calculated gravitational waves from this event, and more significantly we've used this example in the Grand Challenge to probe the geometry of the event horizon. We've extended some of the theorems, some of the global theorems that were proven about null generators of horizons by doing simulations of this kind, showing that the computer is a useful tool for analyzing geometry, not just getting out of numerical waveforms, but

7:30 in fact, if you want to explore some of the properties of global properties of space-time, it can be helpful to discuss that. However, this was merely a stopping place in the larger picture. And the larger picture, of course, is to take two of these black holes and put them in binary orbit and integrate that problem, and that's been considerably more difficult. Eventually, even this code of the head-on collision crashes because the similarities become too strong. And the idea of following two stars in binary orbit with tracking their slow in spiral for many orbital periods is now beyond the capabilities of current algorithms and machine. But now what have we learned in that problem? Well, we've learned, first of all, how to do at least primitive parallel computations to take advantage of the new parallel architecture. So there's been a lot of software development for distributing machines. We think we've learned how to attach good outer boundary conditions on this calculation, conditions that describe the appropriate outgoing wave character of radiation. But I think it's fair to say that the nightmare of the singularities remain. The most promising way is to take a scissors, in effect, and cut the black holes out of the computational grid and replace the holes by a suitable boundary condition at the horizon, the so-called apparent horizon boundary condition. And that way you never have to deal with these infinities that are interior to the black hole. That has worked out very well in spherical symmetry for spherical collapse. We know how to do that. Unfortunately, generalizing that to 3D has been a problem, and it has not been resolved.

10:00 There are some new suggestions about how to do numerical relativity to accommodate that problem. You know, most of numerical relativity is done in the ADM 3 plus 1 decomposition. And Einstein's equations, of course, propagate information with the speed of light, their hyperbolic to hyperbolic system, but there are gauge terms that arise in the ADM formulation which do not propagate at the speed of light. they can even propagate faster than the speed of light some of these gauge quantities are determined by solving elliptic equations not hyperbolic equations so there's almost instantaneous information about changes in these gauge quantities across event horizons that means that the causal structure of our equations is somewhat obfuscated by the ADM formulation. And one wants a very tight causal coupling if one is going to take a scissors and cut out a horizon. Because what is a horizon? A horizon is a one-way membrane in which information only travels in. and in order to develop a difference scheme a way of dealing with the partial differential equations by finite differencing in which information is properly propagating along light cones and only goes inside a horizon and does not come out one wants a set of equations in which the characteristics are essentially along light tones. The characteristics travel at the speed of light. All the equations and all the characteristics, including all the terms, no gauge terms that propagated weird speeds, with eight calls of speeds. So there's been a new reformulation of Einstein's equation called the hyperbolic formulation, The only characteristics are essentially those that travel at the speed of light.

12:30 And there's some experimentation that has now begun to tackle these problems in that formulation. And there is no instant ratification that I can report. But in spherical symmetry, we've achieved some considerable success and integrating single black holes without encountering instabilities. And now the difficulty is to look at two black holes. So that's sort of a status report. But I think it's fair to say, and would be wrong to suggest otherwise, we do not now have a code that can solve this problem. It's a very difficult problem. And we hope that there will be interest and resources available for us to continue our work. The Grand Challenge, per se, terminates in a year. And we are among those who are seeking resources to continue that effort. And talent. The resources are not just dollars, but new insight, new people. And I'm really excited about it, and certainly one of the motivations, not the prime motivation, apart from its theoretical importance as an unsolved problem, is LIGO, GEO, Virgo, the gravity wave detectors. After all, the binary black hole problem is reported to be the most promising source for gravity waves for detection by the laser parameters under construction, and we'd like to have waveforms available to experiment for so they can do their matched filter analysis and do black hole spectroscopy. for great gold. We don't think we need our code to determine the black hole masses. That is pretty much a solved problem once you have the distant in-spiral wave form for which post-continental higher order analysis is adequate at a few percent level.

15:00 And it may be possible to get spins from that distant in-spiral, provided one takes adequate use of modulation in the wave amplitudes due to processional effects. Right. Well, they may be coupled. If the spins are very low, then one can get the masses to high accuracy without worrying about stuff. But if the spins are substantial, if they're anywhere near maximal curve, then it's a coupled problem. And yet, even that problem, I think, could ultimately be cracked by a suitable post-Newtonian analysis that we're going to go to. However, some of the real questions, or other questions that people want to know the answer to, is whether this whole space-time structure that we have prediction for, the curve structure, the horizon, the geometry that we're building in the strong field regime, that's correct. And the only way to really see that is to build away the amplitude during the final coalescence and merger stage and see whether that's what's observed. So, given the masses and spins from the asymptotic in spiral, we would then have, given the no-hair theorem, that's all we need, we then have a unique means of predicting the wave amplitude. We could do the calculation in principle and compare, and whether that will all work out is the great hope of this enterprise. that's still the hope. And as you know, people involved in both sides of the story, like Kit Thorne, who is deeply immersed in the experimental program, as well as having a very good oversight theoretical all aspects of theoretical problem themselves changed their minds over the years as to who will get the answers first and I think he has a bet arguing that the wave will be detected before it's understood theoretically

17:30 and he may very well be right very well be right much of our interest as I mentioned morning was channeled to the neutron star problem, as opposed to the black hole problem, not because we're not absolutely fascinated by the black hole problem and want to solve it, but because of the nightmares with the horizons. In some sense, for us, a neutron star is a black hole without an event horizon. It is an object that has a strong gravitational field in spirals in a binary. It has all of the same, many of the same virtues for strong field gravity that a binary black hole system has without the nightmare of the central singularity and allows for a regular interior solution. So in some sense we might learn how to probe field binary systems, most easily by looking at the neutron star problem first. Or at least simultaneously. So that's the direction that we are easing into here. How does that work relate to the work of the neutron star elements? Well, like I mentioned to you this morning, I think the analogy of the binary neutron star problem is somewhat like the supernova problem, which has been a computational problem that's been around ever since my career began and before, over 20, 25 years, a problem which has required computational input from many different groups in order to arrive at some idea of how a supernova can, on the one hand, blow off its mantle, and on the other hand, leave behind a compact remnant, like the neutron star. That's a story in which there has been computational failure repeatedly,

20:00 in the sense that the material, as in most computations over the years, collapsed above the neutron star maximum mass and imploded to form a black hole. and it's been only by the marriage of many different ideas and many different co-builders that we've reached the point now that we think we understand how a supernova works, how the neutrino-driven Raleigh-Taylor instabilities, for example, tend to blow out the outer regions while preserving that inner neutron star core. and that's taken many groups many years and many codes and I don't think the binary neutron star problem is likely to be much easier. I think it's going to require different input in different groups. Our own work on that problem has began through Newtonian calculations. We've done the binary neutron star problem in Newtonian theory. hydrodynamically. We've done it in various approximations, including simple ellipsoidal calculations as well as full hydrodynamics. We've added post-glutonian radiation reaction to it. We have a pretty good idea of what this problem is all about. And we want to couple that insight with our ability to do numerical relativity to bring those two together We hope to share insights with other groups doing this, including the Binary Black Hole Grand Challenge. Our approaches are probably different, given our different worldlines in arriving at this point. within the binders I call you mentioned the neutron star having different groups pursuing different paths with the do you think that's has been served well served by having an alliance within the alliance people still well that's an interesting thing That's an interesting question.

22:30 Let me put it in a larger context. When this alliance was first triggered by the International Science Foundation, there was a mandate to do numerical relativity in a new way. Prior to the Grand Challenge Alliance, numerical relativity was done by small teams, working fairly independently, getting together from now and then and sharing ideas, but working basically on individual codes and projects in small groups. I myself worked with Saul Tchaikovsky at Cornell for many years. And the way that worked in a small team was very different from how it works in the Alliance. In a small team working with Saul, the two of us would write every line of code ourselves. We would sometimes distribute our effort on different modules. but by the time we were done with a code each of us was intimately familiar with every line of portrait and that was an extremely useful fact because if one of us had some inspiration in the evening or the next morning or in the shower or on a trip, we could call the other and say, why don't we insert on line 25 where we deal with this gauge condition this way? Why don't we change this and add this? And the other person would know exactly what we were talking about. The change would be implemented instantaneously and we could experiment. And we marched forward in numerical relativity that way for something in the Class 619-78, working our way from simple spherical systems to more complicated two-dimensional axi-symmetric systems. The trouble is when you get to 3D, the problem becomes ever more complicated. The ability to stuff the problem into a machine and integrate it is itself a formidable obstacle.

25:00 One has to learn how to do parallel computing. One has to learn how to take use of adaptivity in the grids. These are such specialized issues and yet involve such enormous amounts of coding overhead that it's sometimes necessary to bring in specialized teams to build those pieces of software for the physicist's use. So, as one went to 3D, it was felt absolutely necessary to merge efforts because it would be impossible for two people or just three people alone to build the kinds of codes that were necessary. Now, is that a true statement? I'm not sure. I'm not sure that is really the case. Eventually, I hope it won't be the case. Eventually, I hope there will be enough software that we will have high-level numerical recipes that will enable us to integrate a couple non-linear partial-to-punnel equations without having to devote separate effort to this software overhead code management on parallel machines. Even then, of course, people may argue, well, but look, this is a very complicated problem. It's got outer boundary conditions, inner boundary conditions, interior regions of the code. Why not have teams focus on just those areas? That's what we've done in the alliance. And each team has made some considerable degree of progress it does tend in this mode to reduce the chance for breakthrough I think by segmenting the problem up in little pieces there's less opportunity for one person or two people to come up with a fundamental breakthrough because

27:30 often that breakthrough does involve insight into the whole problem as a whole, how it's tackled. And the history of memorabilitivity, at least the most of the successes that I'm aware of were done by individuals or small teams, not large collaborations. But on the other hand, no one has cracked this problem yet, so we'll know at the end whether it's a large team approach or the small team approach which was more successful it's certainly more difficult to work in a large alliance it's considerably more difficult the degree of coordination has to be much tighter holding up other groups and they're not adopting styles and coding in a precise way and they're not moving at a rate that's needed and expected by other teams and it's difficult also there may be and have been need for taking When there have been two paths or more paths to follow, we've had to make executive decisions, speculations as to which one we should take, and it's very difficult to retreat across those decisions that have been made, perhaps shown to be not adequate or not really adequate. When you're working with a small team, you can sort of move around more quickly, your handling time. It's just very different. I have not fully, you're looking for DRASA. Am I? Yes. Are you the new person? Yes. And this is Jennifer. So I wanted to let you know too that the patching wasn't successful and I've got the consultant from SGI, well we're actually having the connection problem, but anyway I'm going to have him just log in to the machines the problem. Wow, you are... No, no, I just... I've gone beyond his only... I don't know what to do anymore. So the guy from SGI called... Why is he not coming? He can do it remotely. He just has to log in. He doesn't need to physically come from Chicago here, right? I see.

30:00 Anyway, but the thing is, is I'm just going to... Do you know what the problems are? No, no, we've been doing the telephone tag thing. You know, I call, leave message... Yeah, but he can't log in. No, I can give him an account. He can log in. No, what I'm saying is he cannot just log in without being fully debriefed as to what's wrong? I'll talk to him. Of course I'll talk to him. Before he logs in. Yeah, I'll talk to him, explain the problem, but then I'll let him log in and observe it himself and say what to do because I can't think of anything else. Would you strongly suggest that he come down here? I don't think it's necessary for him to come down to look at the problem. I mean, there's no point in his driving three hours and driving back three hours. That won't help us. I mean, he needs to work with his mind. It doesn't have to physically be here. I mean, in this case, I think that he can look at it solve it or not solve it. But I am going to tell him that you're not going to buy any more computers and you want to return these if this problem doesn't get solved. I mean that's really the key here. He won't tamper with this so that it interferes with our use. No, no. He'll just look and then if he wants any tampering, then he'll instruct me how to do it. He'll say, you must do this or this or this. He won't actually do it himself. Are these people reliable? Well, this SGI can solve them. They ought to be, right? I don't know. I've never had a problem before. I've never had a problem this bad, okay? I never had a problem that not going to shoot down. Do warn him that there's ongoing work right now. Oh, yes. I'm only giving him a user account. He can't do anything. Read only? I see. Read only. Okay, and then I would tell you, I'll tell you whatever the answer is, okay? So the two things, please debrief him thoroughly before even he does that. Threaten him, as you've described. And, um, if he can't deal with it, we need a solution. If he can't deal with it, we're sending the computers back. Maybe there's a SWAT team that can deal with this. This is a solved problem, I'm sure. We just need to find the person, the person to... I have a feeling he may suggest to me that we should have them all running the same operating system. You know how we were talking about... Uh, so I guess we were talking about the, uh... There's a colloquium and 3.5 is a T, so I... Okay. Probably exit in about five minutes. Okay. Uh, so what were we saying last? Uh, well... The sociological contrast, practical contrast between working in a large team and working either as an individual or in a small group.

32:30 I would say that it's much easier to work in a small room, it's certainly much easier to have a complete overview of the entire problem, to have sudden insights and to implement that quickly, and so far for me it's also been more fruitful. That is to say, hey, progress achieved with a small group, they're more fruitful than the progress achieved with a large group. But that could be very well a small group with working on lower-scale problems. And once we crack with bigger problems, I will immediately recognize the virtues of the larger team I don't have that recognition at the current time. Well, you were saying that the current term of the alliance ends next year, so do you think that it will be continued in a similar form? Yes, we are applying for new funding to continue this, but we are, there are a couple smaller subsets of the Grand Challenge Alliance that are going to apply more tightly together and work more independently. Finally, my former colleagues at Cornell and my new team here at Illinois are likely to join together, probably with colleagues at North Carolina, and pursue some of these issues in a what won't type in way, and we were able to do that in the border lines. That's our plan. I'm going to be pursuing the hyperbolic equation. I'm going to be pursuing both ADM and hyperbolic, both Black Hole and the Trinstock. And we hope to try to take sort of a many-fingered approach to this, where wherever we can make

35:00 great strides, we want to move quickly, and where we are slow and sluggish, we may retreat. But we're going to adapt a slightly broader attack on these two problems together. I think now we've assembled a real brain trust as well as a huge supply of software knowledge and actual code to go on to the next step. But we will not be afraid to pick away at this problem with small models and Newtonian analogs and post-Newtonian approximations. I like a diverse attack on a problem. I do not like to define it regionally as a problem that we're going to do with the full Einstein equations in this particular gauge come hell or high water. I'm going to try to get at the answer any way I can. In fact, I wrote a paper about a year ago. I had to give a keynote address at the PISA conference sponsored by the Brubel collaboration. and the paper was titled Calculating Gravitational Waveforms by Any Means Necessary. And that's sort of my working slogan on this problem. But there are many approaches, and I have to take the difficult problem. And it would be foolish, I think, to restrict my attention to the one. Maybe the wrong one. So will the more tight-knit group between yourself and the North Carolina group still be loosely allied with other groups? Well, that all hasn't been worked out, and this is an ongoing discussion, but we're a good fraction of the Grand Challenge Alliance.

37:30 It's not really that it's a very small breakaway operation, it's a good large fraction and a good portion of the actual code builders are here. But we're going to try a slightly different approach to try to crack this. Well, that's probably a good place to stop for today. Thank you. Thank you.

40:00 Thank you. Thank you. Thank you. Thank you.

42:30 Thank you. Thank you. Thank you. Thank you.