The Head-On Collision of Two Equal Mass Black Holes Peter Anninos

TL;DR

This paper investigates the head-on collision of two equal mass black holes through numerical simulations and analytic estimates, analyzing gravitational waveforms, energy emission, and horizon deformations.

Contribution

It provides new numerical results on gravitational waveforms and energy emission, and introduces an analytic approach incorporating finite size and horizon effects.

Findings

Total energy radiated is less than 0.002 M.

Dominant modes are the  and  gravitational waveforms.

Analytic estimates agree well with numerical results.

Abstract

We study the head-on collision of two equal mass, nonrotating black holes. Various initial configurations are investigated, including holes which are initially surrounded by a common apparent horizon to holes that are separated by about $20M$, where $M$ is the mass of a single black hole. We have extracted both $\ell = 2$ and $\ell=4$ gravitational waveforms resulting from the collision. The normal modes of the final black hole dominate the spectrum in all cases studied. The total energy radiated is computed using several independent methods, and is typically less than $0.002 M$. We also discuss an analytic approach to estimate the total gravitational radiation emitted in the collision by generalizing point particle dynamics to account for the finite size and internal dynamics of the two black holes. The effects of the tidal deformations of the horizons are analysed using the membrane paradigm of black holes. We find excellent agreement between the numerical results and the analytic estimates.