Interview with Wai-Mo Suen

0:00 Now it's going, and it's the 18th of March at about 1.20 in the afternoon, and I'm talking to Waimo Soon, and also the device seems to be hearing us, so we can start away. Well, let me see. Since I mentioned that repetition is not bad, why don't we actually go back more or less to the beginning and talk about the projects that you're working on, the main subject, projects that you're working on at the moment, you mentioned that you're interested both in the binary neutron star problem and the binary black hole problem. Yes. In the former case, the neutron stars you're working with in the part of the Grand Challenge For the black hole case, you mean? Or in the neutron star case. In the neutron star case, we are one of the five institutes in this NASA Grand Challenge project. And in the black hole case, in the last few years, there have been more kind of affiliated, working together with the NSF Black Hole Grand Challenge, Richard Messner's group. Were you a co-PI on that? I am officially some kind of associate member or something of that sort. Yeah. However, I'm not clear exactly what that means. It means that the main significance is probably that I'm not getting money from her pocket. In the last two years, we have been working more on a different code. While the Richard Masters Grand Challenge is working on a separate code, on the New Translate Grand Challenge, I mean Blackhold work, this cactus code, together with our collaborator in POSDEM. That, of course, contain a vacuum part that can be used to study black holes, and also a source term that we put in, hydrodynamic source, that we can then use for simulating neutron stars. And one of the things I understand about the binary black hole grand challenge is that at the moment they seem to be splitting up into two subgroups moving in different directions.

2:30 The Texas-Pittsburgh group looking at the ADM formulas and the Cornell-North Carolina, maybe Illinois group looking at hyperbolic formulas. But in the CACTUS code, you kind of keep your options open with that. It can handle both different... I guess it's a different type of hyperbolic formulas. Yes. In the Cactus Code, we have the flexibility of switching our evolution system. Now, at this point, we are investigating with two formulations in it. One is the standard ADM. The other is a hyperbolic formulation based on a work by Carlos Bonner and Joanna Sohl, so-called BM system. we do have a plan to put in more, put in other systems. They all function as thorns that we can plug into the code. So we have an ADM thorn, we have a born and sold thorn. Interesting. So because even the formalisms by which you solve the Einstein equations are treated as thorns or subprogressive thing, you actually can, there's no theoretical limit to the number of approaches you can facilitate. Right, precisely. So do you have a favorite approach in mind at the moment, or is this more a question of, at least in that regard? In fact, the ADM formulation has been around for a long, long time. We know it's a robust formulation that can be used in many aspects, but we also know that it is very limited. We have only limited knowledge about this mechanical structure. The newer direction in the micro-reactivity is to go to hyperbolic formulations, for which we have a very clear, a better understanding of the mechanical structure of the equations, writing them out in hyperbolic forms. But there are many hyperbolic formulations around at this point. And the one that we call in is one of them. It's not necessarily the best one, and we do intend to explore more. And we have been doing, in fact, a stability analysis

5:00 of different kinds of hyperbolic systems on an analytic level at this point. And we would like to actually call up more hyperbolic formulation and test them. Of course, there are many different facets to the problem of solving binary motion numerically beyond just the basic solution of the Einstein equations for the motion of the source, and there are other issues, especially if you're interested in gravitational radiation. which kind of area of work at the moment do you think the greatest challenges in principle lie to well let's say for the sake of argument to the solution of what I think was the original stated goal of the black hole grand challenge that is to produce accurate estimates of the gravitational wave signal from a binary black hole I was wondering where do the greatest problems lie towards achieving that goal? Well, there are many problems that I can see. I cannot single out one single biggest problem. Depending on whether you're talking about the neutron star co-license problem or Breckle problem, we are facing different sets of difficulties in these two problems. For a Breckle case, obviously one major difficulty is how to handle the singularity, Breckle singularity. we put forth a proposal that we called apparent horizon boundary condition, which basically is really cutting away the singular structure. We replace it by a boundary condition. that approach is adopted by the Bracco-Gran challenge they are now experimenting with it both in the ADM formulation and the hyperbolic formulation and this is also an approach that we are taking of course

7:30 pushing forward it does not mean that the problem hasn't been solved but at least it provides direction of solving this very difficult problem of having a singularity in the space time another very major problem in getting the waveform out is that Einstein theory is a gauge theory right and there are many coordinate degree of freedom the handling of the coordinate degree of freedom is a major aspect in numerical relativity. So these are the, I would say, two biggest problems in the black hole case. For the neutron star case, it does not have the problem of singularity, it has the difficulty of interfacing with a hydrodynamic source. Of course, numerical hydrodynamic, so-called computational fluid dynamic, has been studied for many, many years, a lot of effort going through that. And we would be able to make use of a lot of these efforts. And also, in fact, the hyperbolic formulation of Einstein theory was partly motivated by the success of the hydrodynamic treatment. Modern hydrodynamic methods use hyperbolic base, based on hyperbolic formulation. So that at least is one motivation that we also want to write Einstein's equation in the hyperbolic form, so that we can make use of the same numerical technique in treating them. And in fact, perhaps it's worth mentioning that there's another motivation in going to hyperbolic is that in hyperbolic formulation, we have a better control of the flow of information. As I mentioned to you earlier, there's one major, one pleasantly popular idea of treating black hole is the apparent horizon bound condition that we put forth some time ago. So in that formulation, you want to replace the interior for the boundary condition.

10:00 And that requires a very good control of information propagation. You want to make sure that information only propagates from the outside to the inside, but not otherwise. Of course, physical information can never propagate out, but you can have gauge information. You can have the miracle error coming out from the interior to exterior. In order for the apparent horizon boundary condition to work, you want to make sure that in your mathematical formulation, this information publication is under well control. And hyperbolic formulation seems to be the way to go. So it's because of this kind of thing we are more interested in hyperbolic formulations and we will spend more time investigating different hyperbolic formulations and their use in neutron star and black hole collisions. Now back to that problem of difficulties with the neutron star study. The difficulty there, instead of singularity, we now have a hydrodynamic source. But now the hydrodynamic source is coupled to the full GR, which is something that has not been studied before, and it's not to a great extent. As far as I know, there's probably only one effort in having a hydrodynamic source coupled to Fujiya. That is by a Japanese group, headed by Nagamara. He has been doing this for a long time. There are also other characteristics of treatment, but they either assume fixed background or or assumed, throw away part of the G-out information. It's like conformal flat assumption and things like this. So this is more or less an uncharted territory. We do not really know what is waiting for us there. At present, we are only playing with very simple systems, like a Freeman Robinson Walker universe, or dust collapse or static neutron stars

12:30 and lately we have been looking at two systems one is enacting a neutron star across the grid and also have a gravitational wave hitting a neutron star and see how a neutron star will scatter the gravitational wave passing through it we have recently produced some result, a premium result in this direction. So, the bottom line is that we do not know what's waiting for us there. I expect major difficulty. Yes, sure. And for the second problem, we talk about coordinate control difficulties. We will have similar coordinate control difficulties in the neutron star case also. Although neutron star may not be as strongly gravitating But I would expect with gravitational wave coming out of the system, the highly dynamical nature of gravitational wave would require very good coordinate control, just like in the Black Hole case. And moreover, neutron star can turn into a Black Hole later after they collides. So we will still have to face the same difficulty in handling a Black Hole in the neutron star project. About coordinate control, are you thinking including problems like the way the sort of grid that the calculations are done on gets thrown out of shape by, say, frame dragging? Yeah, frame dragging, or any gravitational effect, or some error in isodata, or error in renewable evolution, all of them can excite instability in the gauge mode. Yes. So there's a difficulty of keeping track of what exactly your coordinates are in a dynamical system. Yeah, I'd like to say that the biggest difficulty in GR, in numerical relativity, is singularity, or instability. There are four types of instability in numerical evolution. The first type is shared by all physical system, all physical simulation.

15:00 That is, you're in a numerical code, you have some numerical instability because of numerical method, that is common to all systems, but probably worse in GR because of the non-linearity of the theory. And also in GR, well, typically something that we kind of keep off on is that in relativity, Error propagates with the speed of light. So we have all sorts of instability because of the numerical error and numerical method and not the non-linearity of the system. This is shared by everybody. The second type of singularity or instability that comes in is in slicing up your space-time. Even if you begin with a very regular, nice looking slicing, but as time develops further, your slicing, since it responds to the system, would develop kings. and such king in the slicing of course would induce sharp feature in the Yvav quantity, the metric and with sharp features that cannot be resolved by any miracle grid you are dead, you have something growing up the third type is the coordinate, the three coordinate system that you lay down on your time slicing the coordinate themselves can get sheared, can collapse together and can fly apart just a bunch of spaghettis with free will, right? So it's difficult to control. And when things, crazy things happen, like a coordinate line banned too much. That actually happened in numerical evolution. We've seen that. A coordinate line originally strict, right? After evolving a while, it gets banned. When they fold up, of course, it will crash. So, these are the three coordinate singularities. These three types of singularities, or instability, we want to get rid of.

17:30 We want to use a good numerical method, we want to get rid of the first kind, we want to develop the good slicing and coordinate conditions to get rid of the second and third. But the additional difficulty with GR is that we have to distinguish these three types with the fourth type, namely the singularity, the true space-time singularity, which are guaranteed to happen by the singularity theorems for the strongly gravitating system that we want to deal with, collapsing to black hole and things like this. So how do we distinguish the fourth type is not a trivial problem. we have to distinguish this four and get rid of the first three while controlling the fourth with a scheme like AHBC, apparent horizon boundary condition that's interesting well I I know from talking to Ed Seidel issues with the apparent horizon boundary condition, of course, was finding, locating the apparent horizon, and that was something that you worked on in collaboration with his group. Yeah, we have developed, in fact, a field apparatus for doing this kind of problem. For studying black holes, there are two of us, two important characteristics of black hole. One is the event horizon, one is the apparent horizon. developed finders, what we call finders, for finding the event horizon, for finding the apparent horizon of black holes, and also developed tools to study the properties of the event horizon or apparent horizon found. There are some interesting developments in this direction in the last few years, both on getting the event horizon and also the apparent horizon, and studying their properties. In fact, we have a person writing this draft of this paper on my desk on using various tools to study event horizon. And one particularly interesting set of tools that we are now pushing

20:00 are the membrane paradigm tools. Something I'm sure you are familiar with the kowtow, right? We are studying the membrane quantities like the shear, the viscosity, and blah, blah, blah, of the event horizon and look at the temperature of the horizon, surface gravity, and things like this. Our idea is that as numerical relativity are getting more and more mature, we'll have data sets coming out And we will need physical picture that we put, that we can analyze the numerical data in terms of those physical pictures. And membrane paradigm seems to be particularly suitable for this in providing physical understanding to the numerical data. So we're now developing tools for using the membrane paradigm in numerical relativity. based on the event horizons that we can locate in the numerical space-time. Since you mentioned that one of the key aspects from the American point of view of dealing with the apparent horizon was to prevent, make sure that information only passed one way across the membrane, I was wondering if that is part of the reason why looking at it in terms of the membrane paradigm was useful as a help to making sure that the information, the numerical information only passes. We are not making use of the membrane paradigm as a boundary condition. We are not trying to do it that way. one can make use of the membrane paradigm in the sense of making the boundary condition. That is not precisely what we are doing. Rather, we are using the membrane paradigm as a tool for understanding the physics in Mao. In constructing the apparent horizon boundary condition,

22:30 or the main idea there is really to use a shift vector so that you can achieve something what I call a horizon condition without a horizon condition. That is, you make use of a shift to arrange the causal structure of your grid and you use a scheme that respects the causal structure. In that case, you can implement a bound condition without a bound condition. In some way. Interesting. Well, so I guess it would be interesting then to get back to something that we've already discussed a good bit, but just to go over the ground some more to this question of the problems faced in the field of numerical relativity by simply the scale of the challenges in solving problems like binary, back old binary neutron star, which now of course is an urgent problem because of LIGO and so on. And so the scale means that there's a dramatic change in scale in terms of the level of collaborations involved and so on, and we were discussing this to a considerable extent. And so you mentioned that your experiences working with the Black Hole Grand Challenge had led you and the Potsdam group, former NCSA group, to look for ways to develop an infrastructure for collaboration as part of your long-standing and continuing collaboration, including things like the Cactus Code, for instance. So I'll put it slightly deeper. In fact, we have been developing this collaborative tool even before we get involved in the Blackwell Grand Challenge work. It has evolved quite a lot, improving this collaborative tool.

25:00 But for the structure of the Cactus Code, it is built specifically for collaboration. It is in fact based on many previous generations of codes that we work together on. The first big code that we worked together on, Russia and NCCSA, we are working on this This so-called G-code is an ADM code that is of the sort of Einstein equation and use of black hole and gravitational wave and such. And so there's many co-workers working on it. And very soon we encounter the problem of someone writing something, breaking out a part of code, and the code branching into many directions, it's difficult to put together, to merge them together, and when we merge together we see that none of it would work, no one can ever work again for a long time, we fix it. So there are a lot of pain and experience into putting calls together. And it's because of those experiences that gradually led us to develop this collaborative infrastructure, also on the group level. In the past, we tried to do it like also CVS check-in, CVS check-out, and those things. but without the central collaborative structure as we are now doing in Cactus yeah so CVS is a is software that's designed to keep track of changes it's a commercial package I think you can get it for free oh yeah it's a free one In fact, we have tried many different versions of this system. We begin with something called RCS and then gradually move to CVS and we have also tried

27:30 other things like GRDoc as we call it, it's an automatic documentation system and we have project page developed for this. Right. The project page is based on a collaborative tool called the Coco Bond that Paul Walker wrote quite a long while ago. and it's not COCOBOT B-O-A-R-D COCOBOT Oh, so he developed a particular program for enabling the kind of project page environment where people could interact yes, right and that ties in with something else that you discussed that you mentioned earlier the importance of maintaining a kind of an open environment within the group where people would be sharing information right, right the Cocoa Bot is really central or the project page is really central to enable this. And also to, of course, good planning and good person-to-person relationship, being friends is also very important. It's almost like that you have to first become friends before you can be good collaborators. It's not easy. Yes, obviously, the personal interaction is most important. and this is a difficult part for us since as we talk about we all the many corporations are separated by oceans yes in Europe in Asia in India and it's not easy to fly around so because of that we are getting a lot of frequent flyer manages

30:00 I imagine so so in terms of the great distances between the groups what are the different ways that you overcome that through visits. Are there much interchange of postdocs and personnel between groups, say for instance between the Potsdam group now and... Yeah, the Potsdam group is still kind of newly established, right, just two years ago. So we do anticipate a lot of postdocs coming here, coming there, and travelling has been quite a bit since practically for the last year they are, say it's nearly a visit per month between two groups. Either we have someone send someone over there or they send someone over here. As I was here twice this year in St. Louis and I was there sometimes even for their group meeting. I was there for their January group meeting. Also, I often travel back to Asia for the corporate in Hong Kong. And a lot of traveling. Just a big overhead in doing science. Yes. So obviously that's a big level of visiting. What are the other most successful methods for maintaining collaboration? Email. Email is really crucial. Email and the project page, again, I cannot stop emphasizing the importance of that. So project page has that advantage of that. It's now developed We have a few of us working on the same project very often that, say, my post-doc down the hall would send something to the project page so that I can learn what it's doing by looking at the project page. And the same also happened in Postdam. I can see Postdam people even communicating among themselves with the project page. so it's really so even where people are geographically closed since project page also serves the purpose of

32:30 archive also if you have some crazy idea if you just send an email the email might get lost say a few months down the road you might not remember what is said but now it's all fully archived there and remind ourselves from time to time. That, in some sense, also helped a little bit in identifying credits. Since we have this full archive of the development that at least would give everybody involved a good summary or a good diary of what happened. and there would be less opinion would be less diverge with such a diary so you also serve the purpose of a diary and you mentioned in fact earlier that the problem of assigning credit is one of the big issues yes for big collaboration I guess assigning credit is something that we all tend to not mention it does matter especially there's young people many young people in the group and they need to continue develop their career further yes and it's important to get the recognition Edzardel also mentioned that this was an important consideration and when we discussed this earlier you said that one of the problems here was the different expectations that people from different backgrounds might have of how one would go about assigning credit for instance in the form of the order of the authors on the paper and so on and so that for instance as you say in NGR it's quite customary to go by alphabetical order whereas perhaps in astrophysics or other fields it's more common to pick out a first author which is a big deal and this tied into something that I was interested in what you said earlier the question of kind of a culture of collaboration that perhaps has been developed historically in areas like experimental physics especially in some areas of experiment where they've become accustomed to big collaborations but which still has to be developed

35:00 within GR perhaps not within theoretical physics even since theoretical physicists tend to be more solitary animals so for instance they have a tendency to want to go off on their own track which is something you mentioned earlier was a problem with the collaborations and then obviously they're not used to having as opposed to share the credit when it comes time to write papers. To go back to the project page again, it occurs to me, since you mentioned that people actually within the same building will communicate using the project page, that must have a quite deep and subtle advantage that it means that at some level the people geographically separate are still participating in the conversation that's going on in the other place because it's actually open and visible on the page. enhance a lot of feeling really being one big family instead of being two separate groups. If we always try to say first unify whatever we think here then it can easily develop into a sense of two groups whereas now if even inside we're completely open it certainly helps the feeling So in some sense you're actually consciously aiming for a situation where it's not just a very successful collaboration between two groups but that there really is one group that has to be separated by it Right, that would be the aim there will be the goal that we can function as one coherent entity and hopefully wishful if the whole GR community can function that way then the whole GR and the whole enterprise can go much faster and advance much better but that is probably not possible well you mentioned for instance that

37:30 even within the context of the Grand Challenge which is, well, I suppose that was close to getting the whole numerical relativity community together, if not the whole GR community. But you mentioned that, based on your experience with the project page and so on, you had recommended that to the Grand Challenge, but that Richard Mattson, I think he said, was saying, well, one can have a project page, but the problem is getting people to post to it. Yeah, I think that is really not that much the software. Of course, the software enables this kind of thing to happen, but it's really the mentality of the people or the culture. yes obviously the culture as you say the culture of collaboration is the key thing I mean it's interesting to see the technical attempts to at least produce the infrastructure of collaboration but ultimately of course the two things kind of tie into one another closely in the past when the project page first came into existence It is not as convenient, and therefore, even if we are very willing to share information in that regard, but if it is not convenient, it also will hurt. Now the project page evolved to a point that we can post, not to send email there, but we can post our results. Now we produce a graph, we produce a movie, we can all include into the posting. so that people over the ocean can click a button and see the movie that you produced for the problem. So technically the thing has advanced. Yes, so that certainly helped. So the project page is presumably something that people in the group would look at every day. Is it something that a lot of time is spent looking at each day? Does that sort of depend on? It is one of the most time-consuming things for me. I spend really a good part of my day going through the project page and seeing what people post. There can be, in a good day, there can be, say, 15 messages, 20 messages posted. It really takes time even to go through them, let alone comment on them and respond to them.

40:00 Yeah, that would obviously take time. And especially as we are so ambitious in trying to get so many projects going at the same time, that also adds to the complication. We have probably 15 to 20 projects up on the project page at this point. All generally connected with the combat binary problem? With the binary problems, with computer infrastructure, code development, with solarization tools, adaptive mesh refinement, so they are not just physics but also the computational aspect. How much interaction now? We have to go to the talk. Okay, there we go, and it's still the 18th of March, and it's now quarter to four, and I'm still talking with Wymalsu, and let me see. I'm not exactly sure where we were, but I suppose the... Well, let me just start off with one question that comes to mind. I suppose what have been the primary motivations for the increase in size in the collaborations in numerical relativity? I mean, what were, as it were, the original pinpricks, would encourage groups to come together? Was it primarily the fact that people would encounter problems which they felt they couldn't be solved by the answer? They were looking for people with other expertise? Or was it the question of a need to attract more funding because of the scales of the problem and the resources required? Or were there other factors, or was it easy to...?

42:30 Yeah, I think all of these factors are real. And like those, when applying for those Grand Challenge Grants, it would be impossible to try to get it with just one group without involving multi-institutes. And going multi-institutes is kind of the train at present. So that provides some motivation for doing this. And of course, the size of the problem is also very clear. driving this development, namely for Neutron Star Brand Challenge project, for example. There's so many different branches of physics involved. Yes, that's necessary to find. And also, it also has to do with the nature of the work, namely is computer-related, is computer code that we're building. if it is a theory work purely theory, paper and pencil then it doesn't make too much sense to put together 10 theories trying to do one calculation since it's difficult to separate I just think for one hour then I stop and give you a new thing on this carry on second hour that won't work whereas computer program is something that can be done by a team it's done by teamwork so it's also partly because of the nature of the work that such a collaboration can be built. So you mean that it lends itself to a, what's the well-known phrase, a kind of a division of labour? Yes, so that that can be done. Do you find, incidentally, you mentioned the trend towards multi-institute collaborations. Is that something that the funding agencies are kind of interested in? Yeah, there are, in fact, funding which specifically say that they encourage multi-institutes. That's interesting. But is there a particular problem, then, with international collaborations like the type that you have with Potsdam? Does that make it tricky if you want to apply for money together because you fall into different jurisdictions, or is that not really a problem? as an advantage, right?

45:00 Yeah, we go to the U.S. government agencies to get money. They go to the Germans. And those in Hong Kong get money from Hong Kong. It's an advantage. And you can still, when you go to the U.S. agency or they go to the German agency, you can still say, well, we have these collaborators in the institute. That's interesting. And, um, So I guess then, which is probably kind of the last question to you that I have, there's, just to go back to what, as I mentioned, is sort of the main topic of what I'm interested in, the connection between the problem of gravitational wave detection, specifically, and these issues. How much, I suppose I'm interested in how much how much LIGO has influenced this growth in numerical relativity well, so for starters, that I mean, one might imagine that the two-body problem being such a fundamental one for GR would have been tackled anyway probably by numerical methods as computers got more sophisticated perhaps but presumably LIGO has played a role. Yeah, and I will definitely play a fundamental role in this, in many regards. First of course is that now really not only give us an excuse but necessity to really do the calculation and get the waveform. possibility, but first a real detection

47:30 is of course exciting, you want to predict what it is, and also it's requiring so much accuracy that leads us to do a good job. Without such an accurate detection that is possible, it probably doesn't make sense to push like a CRIF, push P3N, right? A few years ago, people would think oh, this is crazy, why do you want to put a P3N? Just an automatic estimate would be things like this now we see the need for doing this calculation yes and the same can be said for numerical relativity now is now the need to for doing that so that are reasons that striving the development in numerical activity in this regard and of course also that because of the funding again because of such a big project, and now we can make use, we can therefore use it as a justification of why you need more funding, you need to give money to this area so that we can do the calculation and predict the results and understand the result. So that enabled this kind of work to be done in the first place by getting the money you from the agencies. So both it provides motivation, make it necessary, and also make it possible. And because of all these three reasons, you can see all the papers that... Yes, well, we'll be back in a few minutes. Okay. Can you hold on a few seconds? Oh, sure. Do you want me to come back in ten minutes? Okay. Thank you. So, in all the papers we publish, right, we keep saying, in a few years LIGO, blah, blah, blah, there's always in the first paragraph of all our papers. Yes, I know the feeling. So, tying in with the previous question, to a great extent, LIGO provided the occasion by which it became necessary and possible to move into this new type of bigger collaboration. Yes, yes. And do you see this as being a continuing process,

50:00 if, as you say, Ligo's had a big impact on his work also, pushing him towards what would have previously been thought of unheard of efforts for accuracy. But he foresaw possibly when that is done there not being any great need to go any further and there wouldn't be necessarily a continued stimulus to further work. Is that likely to be the case, do you feel, with numerical relativity or is it more a case that, as, for instance, when LIGO actually comes online, that it will continue to provide the occasion for future? Right. In fact, I would not think that this activity, the local activity, would, say, gradually fade away. In fact, I think it would be going uphill for still a long, long time to come. the objective that we state in our homepage describing our group is that we want to make generativity to become a practical tool for investigating astrophysics. under that title, of course, there are so many things. Quartational wave astronomy is one important aspect. High energy astrophysics is another, like gamma ray astronomy, x-ray astronomy. All of this are related to strong rotational field phenomena. Gamma ray bursts, for example, we expect it to be coming out from the strong rotational energy, and therefore there's not a strong field phenomena. And all these strong field phenomena, of course, require generativity as a tool to investigate. And when we have observational data coming in from high-end astronomy, from gravitational wave astronomy, it will push the need of using GR to a higher level that's really to use it to look at the real system instead of idealized system that can be treated with social metric and we'll write down and finish it, or plan wave analysis. Now we want to deal with realistic systems. And any realistic system, of course, you cannot do it with paper and pencil. So we have to do large-scale simulations, and therefore, because of this, I think there's a lot of driving force moving this area forward in a long time scale.

52:30 And also cosmology, of course, is another big area, cosmology by definition you need GR, and when we move beyond the simple Freedman model, Freedman universes, then when you compare with real observation, then you need numerical simulations also in that direction. So LIGO, a successful LIGO, which will open up observations of strong field systems would create a whole new realm of opportunity considering that previously there had been little access to strong field systems. So this would be a great opportunity for numerical relativity. and I guess this ties in with the fact that you were saying that you envisaged the Cactus Code as being something that would be made available to a wide community the demand for which would presumably be stimulated by the success of LIGO as a matter of fact I gather that with the Neutron Star Grand Challenge part of the a key part of the agreement with NASA is that at the end there will be a code provided which will have widely applicable use. Precisely. The title of our proposal to NASA was a multi-purpose 3D code for general characteristic astrophysics, basically. And the call license, the neutron star call license is just an application, a binine kind of thing. So we are really using the Neutron Star Grand Challenge, the Neutron Star Core License as a driver for the development of this code that we hope would be useful for the investigation of many generative astrophysics systems. and we are now putting forth a proposal saying that we want to add neutrino transport radiation transport in this code so that it can cover even bigger ground within astrophysics so that not even the GR community but also the astrophysics community can make use of this

55:00 and again LIGO will presumably, hopefully, stimulate demand for that if it's successful in detecting systems, crystalline systems, as you say. So, well, it's going to be exciting to see what happens. I think that's all the questions I could think of. Great.