Black-hole bremsstrahlung and the efficiency of mass-energy radiative transfer

Abstract

We present results from numerical evolution of a boosted black hole, perturbed nonlinearly by an axisymmetric distribution of matter in the realm of Robinson-Trautman spacetimes. Characteristic initial data for the system were constructed and the Robinson-Trautmann equation was integrated for these data using a numerical code based on the Galerkin-collocation method. The emission of gravitational waves by the system is typical of bremsstrahlung at early times, a consequence of the deceleration of the black hole as it interacts with the perturbation; part of the perturbation is radiated away and another part is absorbed into the hole. The angular pattern evolves to the quadrupole form for later times. The final configuration is a black hole in motion with larger (Bondi) rest mass and smaller boost parameter. The efficiency $\ensuremath{\Delta}$ of mass-energy extraction by gravitational wave emission was also computed. The relation of $\ensuremath{\Delta}$ to the mass of the remnant black hole satisfies a nonextensive thermostatistics distribution with entropic index $q\ensuremath{\simeq}1/2$. The result extends analytical evaluations based on the linearized theory of gravitational wave emission. For each initial boost parameter, there always exists a (large) value of the perturbation parameter ${A}_{0}$ for which the momentum of the remnant black hole has opposite sign to that of the unperturbed black hole, due to the strong deceleration during the process of gravitational wave emission. The temporal wave form is that of an initial burst and we evaluate that for a large range of ${A}_{0}$ the process corresponds to a high power output in the initial dominant pulse.