Grazing Collisions of Black Holes via the Excision of Singularities

TL;DR

This paper presents pioneering simulations of grazing black hole collisions with singularities excised, showing horizon merging and gravitational radiation estimates, advancing numerical relativity techniques.

Contribution

First successful simulations of grazing black hole collisions with singularity excision, including rotating cases and horizon dynamics.

Findings

Horizon merging occurs at approximately 3.8m after initial separation.

Estimated gravitational radiation is about 2.6% of total mass.

Simulations demonstrate stability issues after moderate evolution times.

Abstract

We present the first simulations of non-headon (grazing) collisions of binary black holes in which the black hole singularities have been excised from the computational domain. Initially two equal mass black holes $m$ are separated a distance $\approx10m$ and with impact parameter $\approx2m$. Initial data are based on superposed, boosted (velocity $\approx0.5c$) solutions of single black holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes are considered. The excised regions containing the singularities are specified by following the dynamics of apparent horizons. Evolutions of up to $t \approx 35m$ are obtained in which two initially separate apparent horizons are present for $t\approx3.8m$. At that time a single enveloping apparent horizon forms, indicating that the holes have merged. Apparent horizon area estimates suggest gravitational radiation of about 2.6% of the total mass. The evolutions end after a moderate amount of time because of instabilities.