Numerical Relativity and Black Hole Collisions

at the 20th Texas Symposium on Relativistic Astrophysics

Pablo Laguna, Penn State

In spite of the low general attendance to the 20th Texas Symposium on Relativistic Astrophysics last December in Austin, Texas, the parallel session on numerical relativity and black hole collisions was not only oversubscribed and had to be extended one hour beyond the allocated time limit, but it also attracted a large audience. Eleven ten minute talks were given and two one minute poster advertisements.

Bernd Schmidt (AEI/Germany) presented results on the numerical evolution of the Kruskal spacetime using the conformal field equations. Specifically, he addressed initial data sets for the conformal field equations which describe spacelike hypersurfaces in the conformally extended Kruskal spacetime. These are data sets that have been evolved using the code for the conformal field equations developed by P. Huebner. Schmidt showed results from these simulations.

Sascha Husa (AEI/Germany) reported recent progress toward the global study of asymptotically flat spacetimes with numerical relativity. The development of a 3D solver for asymptotically Minkowski extended hyperboloidal initial data has rendered possible the application of Friedrich's conformal field equations to astrophysically interesting spacetimes. As a first application, he presented the future development of a hyperboloidal set of weak initial data, including future null and timelike infinity. Using this example, he sketched the numerical techniques employed and highlighted some of the unique capabilities of the numerical code. Husa briefly mentioned the implications of these results for future work on (multi) black hole spacetimes.

Pedro Marronetti (Texas/Austin) presented the first full numerical solutions of the initial data problem of two black holes based on a Kerr-Schild spacetime slicing. These new solutions provides more physically realistic solutions than the initial data based on conformally flat metric/maximal slicing methods. The singularity/inner boundary problems are circumvented by a new technique that allows the use of an elliptic solver on a Cartesian grid where no points are excised, simplifying enormously the numerical problem. After this presentation, Richard Matzner (Texas/Austin) showed a video of the simulation of grazing collisions of black holes performed by the Texas-Pittsburgh-Penn State collaboration.

Deirdre Shoemaker (Penn State) gave a presentation pointing out first that recent experience with numerically evolving the space-time of grazing collisions of black holes have provided valuable lessons about the difficulties that one might face in the more important case of a collision when the holes start far apart. She stressed that some of the difficulties can be successfully modeled and studied in attempting to understand how to evolve a single black hole. She then presented results from several studies that the Penn State group have performed attempting to evolve the ADM equations with various lapse/shift conditions for this problem.

E. Seidel and R. Takahashi (AEI/Germany) presented results from the full 3D evolution of two colliding black holes, with angular momentum, spin, and unequal mass. They emphasized that the AEI group has for the first time computed waveforms a grazing collision. The collision can be followed through the merger to form a single black hole, and through part of the ring-down period of the final black hole. The apparent horizons are tracked and studied, and physical parameters, such as the mass of the final black hole, are computed. The total energy radiated is shown to be consistent with the total ADM mass of the spacetime and the final black hole mass. Finally, Seidel discussed the implications of these simulations for gravitational wave astronomy.

Miguel Alcubierre and D. Pollney (AEI/Germany) discussed a series of techniques required for the numerical simulation of black hole spacetime. These techniques include the choice of an adequate formulation of the evolution equations, the choice of lapse and shift conditions, the choice of boundary conditions, and the use of black hole excision. They presented also the results of the three dimensional simulation of a distorted black hole where these techniques have been applied successfully, allowing us to obtain long-term stable, accurate simulations.

Carlos Lousto, John Baker and Manuela Campanelli (AEI/Germany) presented results from the coalescence of binary black holes from the innermost stable circular orbit down to the final single rotating black hole under the Lazarus framework. The Lazarus approach combines the full numerical approach to solve Einstein equations, applied in the truly nonlinear regime, and linearized perturbation theory around the final distorted single black hole at later times. Their results indicate a significantly higher amount of energy radiated (up to 4 or 5 They presented also waveforms lasting for over t 100M, and pointed out that their waveforms suggest an early nonlinear ringing.

Peter Diener (AEI/Germany) presented results from a work in progress on Binary black hole initial data, based on adding two Schwarzschild black holes in Kerr-Schild form. Using attenuation functions in order to force the constraint deviations to vanish near the singularities, he pointed out that it is possible to solve the constraint equations over the entire spatial grid.

S. Hawley (AEI/Germany) presented results of his study on critical phenomena in boson stars. Specifically, this study introduces a real field to perturb the boson star via a gravitational interaction which results in a significant transfer of energy. The resulting critical solutions not only are similar to those of unstable boson stars but also persist for a finite time before dispersing or forming a black hole.

John Whelan (Texas/Brownsville) presented results in which the quasi-stationary approximation is used to model a phase of the inspiral of a compact-object binary where the time scale for decay of the orbits is long compared to the orbital period, without imposing any weak-field approximations. These results were obtained by numerically solving for a stationary spacetime which approximates the slowly evolving one, maintaining equilibrium in the radiating system by imposing a balance of incoming and outgoing radiation at large distances. Such a radiation-balanced solution can serve as an alternative to existing techniques for constructing initial-value data for full-numerical "plunge" simulations.

Mark Miller (WashU) presented a new method for numerically constructing solutions to the constraint equations of general relativity that correspond to a single black hole in quasi-circular orbit with a single neutron star. By examining sequences of such solutions, he showed that it is possible to estimate the location of the innermost stable circular orbit for these systems, which will be used as the starting point for full 3D numerical simulations of binary black hole - neutron star coalescences.

Harald Dimmelmeier (Garching/Germany) reported on results from a new numerical relativistic hydrodynamical code for axisymmetric core collapse. He utilizes high-resolution shock capturing methods for the hydrodynamic equations, and Wilson and Mathews' approximation of a conformally flat spatial metric. The results presented were obtained from simulations of supernova core collapse and bounce, and rotating neutron star simulations. He showed gravitational radiation waveforms obtained by post-processing using the quadrupole formula.

Jorge Pullin