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

Abstract

In this paper, we examine the efficiency of gravitational bremsstrahlung production in the process of head-on collision of two boosted Schwarzschild black holes. We construct initial data for the characteristic initial value problem in Robinson-Trautman space-times, which represent two instantaneously stationary Schwarzschild black holes in motion toward each other with the same velocity. The Robinson-Trautman equation is integrated for these initial data using a numerical code based on the Galerkin method. The resulting final configuration is a boosted black hole with Bondi mass greater than the sum of the individual masses of the individual initial black holes. Two relevant aspects of the process are presented. The first relates the efficiency ∆ of the energy extraction by gravitational wave emission to the mass of the final black hole. This relation is fitted by a 2049 Int. J. Mod. Phys. D 2008.17:2049-2064. Downloaded from www.worldscientific.com by PURDUE UNIVERSITY on 04/12/15. For personal use only. 2050 R. F. Aranha et al.distribution function of nonextensive thermostatistics with entropic parameter q 1/2; the result extends and validates analysis based on the linearized theory of gravitational wave emission. The second aspect 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.

Black Holes Collision in General Robinson-Trautman Spacetimes: Wave Forms and the Efficiency of the Gravitational Wave Extraction

“…(10), generalizes the initial data established for the head-on collision presented in Ref. 7. The numerical integration of the field equations (2) and (3) provides a useful theoretical probe for studying the consequences of the non-frontal collision of two black holes.…”

“…Some of these aspects were addressed in Refs. [5][6][7][8][9][10][11] in the context of axial symmetry after the development of a numerical code for integrating the field equations.…”

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

“…[14,25,[27][28][29][30][31][32][33][34] and the references therein). The general theory of non-additive thermodynamics has also advanced significantly in the past few decades (see e.g.…”

A Zeroth Law Compatible Model to Kerr Black Hole Thermodynamics

“…The Bekenstein-Hawking black hole entropy also seems to be nonextensive because it is proportional to the area of the horizon instead of being proportional to the black hole volume (although the problem of how to compute the volume of a general black hole and how it is related to the horizon area is also a nontrivial question [6]). The nonextensive nature of black hole thermodynamics has been studied with many approaches and various methods [7][8][9][10][11][12][13][14][15][16], and in the present paper we also consider a simple model to the Kerr problem that we have already investigated in the Schwarzschild case [17]. The main idea behind this approach is to study the system in equilibrium while also requiring to satisfy the zeroth law of thermodynamics.…”