The Collision of Two Black Holes

TL;DR

This paper investigates head-on collisions of equal-mass black holes through numerical simulations, analytical estimates, and perturbation theory, revealing dominant mode spectra and confirming theoretical predictions with high accuracy.

Contribution

It provides the first comprehensive comparison between analytical, perturbative, and numerical methods for black hole collisions, validating models across different approaches.

Findings

Dominant final black hole modes observed

Excellent agreement between methods

Analytical estimates match numerical results

Abstract

We study the head-on collision of two equal mass, nonrotating black holes. We consider a range of cases from holes surrounded by a common horizon to holes initially separated by about $20M$, where $M$ is the mass of each hole. We determine the waveforms and energies radiated for both the $\ell = 2$ and $\ell=4$ waves resulting from the collision. In all cases studied the normal modes of the final black hole dominate the spectrum. We also estimate analytically the total gravitational radiation emitted, taking into account the tidal heating of horizons using the membrane paradigm, and other effects. For the first time we are able to compare analytic calculations, black hole perturbation theory, and strong field, nonlinear numerical calculations for this problem, and we find excellent agreement.