Relativistic hydrodynamic evolutions with black hole excision

Abstract

We present a numerical code designed to study astrophysical phenomena involving dynamical spacetimes containing black holes in the presence of relativistic hydrodynamic matter. We present evolutions of the collapse of a fluid star from the onset of collapse to the settling of the resulting black hole to a final stationary state. In order to evolve stably after the black hole forms, we excise a region inside the hole before a singularity is encountered. This excision region is introduced after the appearance of an apparent horizon, but while a significant amount of matter remains outside the hole. We test our code by evolving accurately a vacuum Schwarzschild black hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder dust collapse, and the collapse of nonrotating and rotating stars. These systems are tracked reliably for hundreds of M following excision, where M is the mass of the black hole. We perform these tests both in axisymmetry and in full 3+1 dimensions. We then apply our code to study the effect of the stellar spin parameter ${J/M}^{2}$ on the final outcome of gravitational collapse of rapidly rotating $n=1$ polytropes. We find that a black hole forms only if ${J/M}^{2}<1,$ in agreement with previous simulations. When ${J/M}^{2}>1,$ the collapsing star forms a torus which fragments into nonaxisymmetric clumps, capable of generating appreciable ``splash'' gravitational radiation.