High-velocity collision of two black holes

TL;DR

This study investigates high-velocity black hole collisions, revealing the impact parameter threshold for black hole formation and quantifying gravitational radiation energy and angular momentum loss.

Contribution

It introduces a new initial condition setup for boosted black holes and provides extrapolated results on collision outcomes at near-light speeds.

Findings

Impact parameter for black hole formation is approximately 2.5 times the gravitational radius.

20-30% of the system's mass energy is radiated away as gravitational waves.

60-70% of angular momentum is dissipated through gravitational radiation.

Abstract

We study nonaxisymmetric collision of two black holes (BHs) with a high velocity $v=|dx^i/dx^0|=0.6$--$0.9c$ at infinity, where $x^{\mu}$ denotes four-dimensional coordinates. We prepare two boosted BHs for the initial condition which is different from that computed by a simple moving-puncture approach. By extrapolation of the numerical results, we find that the impact parameter has to be smaller that $\approx 2.5GM_0/c^2$ for formation of a BH in the collision for $v \to c$, where $M_0 c^2$ is the initial total ADM mass energy of the system. For the critical value of the impact parameter, 20--30% of mass energy and 60--70% of angular momentum are dissipated by gravitational radiation for $v=0.6$--$0.9c$.