Relativistic Hydrodynamic Evolutions with Black Hole Excision

TL;DR

This paper introduces a numerical code for simulating black hole formation and evolution in relativistic hydrodynamics, successfully modeling collapse scenarios and analyzing the impact of stellar spin on black hole creation and gravitational wave emission.

Contribution

The paper presents a new stable numerical method for evolving spacetimes with black holes and matter, including excision techniques and applications to rotating star collapse.

Findings

Black holes form only if J/M^2<1.

Rapidly rotating stars with J/M^2>1 form tori that fragment and emit gravitational waves.

The code accurately tracks black hole evolution in 3+1 dimensions.

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.