Workshop on Numerical Relativity

Ngonyama, Krugersdorp Game Reserve

Michael Koppitz, Albert Einstein Institute

The Numerical Relativity 2001 workshop was organised as a sister-conference to GR16, allowing many of the participants of that conference to get involved in more in-depth discussions of the numerical side of their work. As an added bonus, the workshop was held at the Ngonyama Lion Lodge( in a game park near Johannesburg, with patrolling wildlife to ensure that delegates did not stray too far from the conference venue.

After an introduction by Nigel Bishop, the stage was handed over to the AEI/Golm group for the first session. Ed Seidel summarized work going on in the EU-Network ( collaboration on numerical relativity, and then focussed on work carried out at the AEI on colliding black holes. Denis Pollney summarized gauge conditions which have proven crucial to extending the life of evolutions both with and without excision. Carlos Lousto and Manuela Campanelli closed the session off with a descriptionthe Lazarus project, which combines full numerical studies of the plunge of two black holes with the perturbative treatment starting in the linear regime. They discussed the details of the idea, pointed out the inherent self-tests this method provides how well it passes this tests, and showed recent results obtained with this method, including the first full treatment of the binary black hole system starting from the ISCO down to the ring down of the final black hole. Later in the week, colliding black holes were also demonstrated by Richard Matzner (Texas/Austin), who demonstrated his group's grazing collision results.

Initial data methods were discussed over the afternoon. Peter Diener (AEI/Golm) presented his results using an adaptive mesh technique combined with a multi-grid solver to solve the initial data problem for two black holes with the Kerr-Schild approach. Nina Jansen (Tac/Copenhagen) used a similar solver to compare initial data sets in terms of the behavior of the ADM mass as a function of separation. Phillipe Grandclement (Observatoire de Paris/Meudon) presented a new approach to the initial data problem, using multi-domain spectral methods and a helical killing vector field to simplify the problem. Micheal Koppitz (AEI/Golm) summarized the efforts underway at the AEI to generate new sets of initial data for binary black hole systems, emphasizing the strong need for comparison between sets.

The important role of constraints in the evolution equations was emphasized in the interesting talks of Hisa-aki Shinkai (RIKEN/Japan) and Oscar Reula (Cordoba). Raymond Bursten, Anthony Lun, and Elizabeth Stark (Monash University) described their use of the electromagnetic parts of the Weyl tensor as well as the Bianchi identities, to improve certain aspects of the conventional 3+1 evolution system. Luis Lehner (British Columbia) also underlined the need for a better understanding of boundary problems and non-principal terms of the evolution equations.

Florian Siebel (MPI für Astrophysik/Germany) reported on fully relativistic evolution of a neutron star using characteristic methods, and Motoyuki Saijo (University of Illinois/Champaign) reported on simulations of fate of the collapse of super-massive stars. Marcelo Salgado (UNAM/Mexico) presented a scalar-tensor model for neutron star collapse. Shin'ichirou Yoshida (SISSA/Trieste) described numerical studies of rotation modes of differentially rotating neutron stars. John Miller (SISSA/Trieste) gave an illuminating presentation of the influence of shocks in domain significant to the r-mode instability.

The advantages of the technique of Padé approximants for post-Newtonian calculation were described by Bala Iyer (Raman Institute/Bangalore) Carsten Gundlach (Southampton) described the methods used for his studies of critical collapse of perfect fluids. Jose Martin-Garcia (Southampton) reported on a new formalism to calculate nonspherical linear perturbations around a general spherical background containing a perfect fluid. It is independent of the equation of state and can therefore model physically interesting problems. David Hobill (University of Calgary) presented recent studies of both sub-and super-critical Brill waves emphasising the creation and evolution of trapped surfaces for super-critical initial data. Mihai Bondarescu (AEI/Golm) presented his work on embeddings of 2d surfaces (in particular, apparent horizons) in Minkowski space.

On the technical front, Garielle Allen and Thomas Radke (AEI/Golm) gave a two hour introductory tutorial on the Cactus Computational Toolkit, its underlying idea and benefits of using it even for small scale computers and laptops. They explained how to obtain, compile and run Cactus and presented some of its features, especially its integration with visualization tools. During the open discussion session, adaptive mesh refinement (AMR) was identified as a urgent requirement for bringing numerical relativity into the realm of real physics problems, and it was good to see AMR work being carried out on a number of fronts. In addition to the work of Diener and Jansen already mentioned, Scott Hawley (AEI/Golm) presented his implementation of Berger-Oliger type mesh refinements. Dae-Il Choi (NASA Space Flight Center/Houston) showed AMR evolutions of strong Brill waves demonstrating how the refined grid followed the wave very well.

Alternative approaches to 3+1 were also discussed. Nigel Bishop (University of South Africa/Pretoria) reported on results obtained by evolving a neutron star orbiting around a Schwarzschild black hole using characteristic techniques. Ray d'Inverno (Southampton) summarized recent work on Cauchy-Characteristic matching techniques, in particular cosmic string evolutions and progress on an axisymmetric code. Ruth Williams (Cambridge) discussed discrete techniques involving space-times tessellated by polygons. Carlos Sopuerta (University of Portsmouth) suggested a technique of using a background metric to do the 3+1 split of Einstein's equations in situations where the system under study is sufficiently known already. Osvaldo Moreschi (Cordoba) described work on Robinson-Trautman space-times, for perturbations specified at null infinity. Jörg Frauendiener (Universität Tübingen/Tübingen) discussed boundary conditions, evolution schemes, and technical problems arising when implementing the conformal field equations.

Sash Husa (AEI/Golm) reported on the current status of the treatment of the conformal field equations and discussed some possible future strategies. (Notable attendees to this latter session were the conference site's resident hippos, who had until then refused to make an appearance but listened attentively to the final day's talks from across the pool.)

All in all it was an enjoyable week, not only for the physics that were discussed, but also the fun location and Nigel Bishop and the local organisers should be commended for putting it all together.

Denis Pollney was of great help in preparing this report.

Jorge Pullin