Collisions of boosted black holes: perturbation theory prediction of gravitational radiation

TL;DR

This paper uses perturbation theory to predict gravitational radiation from colliding boosted black holes, showing good agreement with full numerical simulations for certain initial conditions.

Contribution

It introduces a perturbative approach to estimate gravitational waves from boosted black hole collisions, extending previous methods to time-asymmetric data.

Findings

Perturbation theory accurately predicts emitted energies.

Good agreement with numerical simulations for close, high-momentum black holes.

Provides a new analytical tool for black hole collision analysis.

Abstract

We consider general relativistic Cauchy data representing two nonspinning, equal-mass black holes boosted toward each other. When the black holes are close enough to each other and their momentum is sufficiently high, an encompassing apparent horizon is present so the system can be viewed as a single, perturbed black hole. We employ gauge-invariant perturbation theory, and integrate the Zerilli equation to analyze these time-asymmetric data sets and compute gravitational wave forms and emitted energies. When coupled with a simple Newtonian analysis of the infall trajectory, we find striking agreement between the perturbation calculation of emitted energies and the results of fully general relativistic numerical simulations of time-symmetric initial data.