The Efficiency of Gravitational Bremsstrahlung Production in the Collision of Two Schwarzschild Black Holes

TL;DR

This paper investigates the efficiency of gravitational wave emission during head-on collisions of Schwarzschild black holes, using numerical methods to analyze energy extraction and emission patterns.

Contribution

It introduces a numerical approach to model black hole collisions in Robinson-Trautman spacetimes and relates energy efficiency to non-extensive thermostatistics.

Findings

Efficiency relates to the final black hole mass and fits a non-extensive distribution.

Early emission shows a bremsstrahlung angular pattern, evolving to quadrupole form.

Final black hole mass exceeds the sum of initial masses.

Abstract

We examine the efficiency of gravitational bremsstrahlung production in the process of head-on collision of two boosted Schwarzschild black holes. We constructed initial data for the characteristic initial value problem in Robinson-Trautman spacetimes, that represent two instantaneously stationary Schwarzschild black holes in motion towards each other with the same velocity. The Robinson-Trautman equation was integrated for these initial data using a numerical code based on the Galerkin method. The final resulting configuration is a boosted black hole with Bondi mass greater than the sum of the individual mass of each initial black hole. Two relevant aspects of the process are presented. The first relates the efficiency $\Delta$ of the energy extraction by gravitational wave emission to the mass of the final black hole. This relation is fitted by a distribution function of non-extensive thermostatistics with entropic parameter $q \simeq 1/2$; the result extends and validates analysis based on the linearized theory of gravitational wave emission. The second is a typical bremsstrahlung angular pattern in the early period of emission at the wave zone, a consequence of the deceleration of the black holes as they coalesce; this pattern evolves to a quadrupole form for later times.