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

摘要

We examine the efficiency of gravitational bremsstrahlung production in theprocess of head-on collision of two boosted Schwarzschild black holes. Weconstructed initial data for the characteristic initial value problem inRobinson-Trautman spacetimes, that represent two instantaneously stationarySchwarzschild black holes in motion towards each other with the same velocity.The Robinson-Trautman equation was integrated for these initial data using anumerical code based on the Galerkin method. The final resulting configurationis a boosted black hole with Bondi mass greater than the sum of the individualmass of each initial black hole. Two relevant aspects of the process arepresented. The first relates the efficiency $\Delta$ of the energy extractionby gravitational wave emission to the mass of the final black hole. Thisrelation is fitted by a distribution function of non-extensive thermostatisticswith entropic parameter $q \simeq 1/2$; the result extends and validatesanalysis based on the linearized theory of gravitational wave emission. Thesecond is a typical bremsstrahlung angular pattern in the early period ofemission at the wave zone, a consequence of the deceleration of the black holesas they coalesce; this pattern evolves to a quadrupole form for later times.