The Collision of Two Black Holes

TL;DR

The wave forms and energy output are computed, showing that normal modes of the final black hole are clearly excited, and the total gravitational radiation emitted is estimated analytically, considering tidal heating of horizons and other erects.

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.

Figures (3)

• Figure : The physical parameters of the six initial data sets studied are summarized. $M$ is the mass parameter defined in the text, $L/M$ is the proper distance between the throats, and we note whether or not one apparent horizon surrounds both holes.
• Figure : The physical parameters of the six initial data sets studied are summarized. $M$ is the mass parameter defined in the text, $L/M$ is the proper distance between the throats, and we note whether or not one apparent horizon surrounds both holes.
• Figure : The physical parameters of the six initial data sets studied are summarized. $M$ is the mass parameter defined in the text, $L/M$ is the proper distance between the throats, and we note whether or not one apparent horizon surrounds both holes.