The high-energy collision of two black holes

TL;DR

This paper investigates the head-on collision of two highly boosted black holes, comparing analytic, perturbative, and numerical methods, revealing that up to 14% of energy converts into gravitational waves at near-light speeds.

Contribution

It provides the first comprehensive comparison of analytic, perturbative, and numerical approaches for high-velocity black hole collisions, extending results to velocities up to 0.94c.

Findings

Approximately 14% of energy is radiated as gravitational waves at ultra-relativistic speeds.

The gravitational wave luminosity reaches about 10^-2 c^5/G, the highest observed in black hole mergers.

The study confirms the consistency of different theoretical approaches in modeling high-energy black hole collisions.

Abstract

We study the head-on collision of two highly boosted equal mass, nonrotating black holes. We determine the waveforms, radiated energies, and mode excitation in the center of mass frame for a variety of boosts. For the first time we are able to compare analytic calculations, black hole perturbation theory, and strong field, nonlinear numerical calculations for this problem. Extrapolation of our results, which include velocities of up to 0.94c, indicate that in the ultra-relativistic regime about (14\pm 3)% of the energy is converted into gravitational waves. This gives rise to a luminosity of order 10^-2 c^5/G, the largest known so far in a black hole merger.