The non-linear perturbation of a black hole by gravitational waves. I. The Bondi-Sachs mass loss

Abstract

In previous work [3] we presented a numerical framework to study the impact of gravitational waves on an initially static or stationary system by solving a particular initial boundary value problem for Friedrich's generalised conformal field equations. This allows us to (at least in principle) follow the evolution for infinitely long physical time and to infinitely large distances. Here, we present the first results from simulations of the response of an initially static Schwarzschild black hole to strong gravitational waves coming in from a large sphere surrounding the black hole. We follow the ensuing non-linear distortions of the space-time and the scattered gravitational waves out to null-infinity ℐ+ obtaining a semi-global evolution. We observe a particular oscillating behaviour of the gravitational field which seems to be related to the onset of quasi-normal ringing. We also verify numerically that the Bondi-Sachs massloss formula is satisfied in our simulation by computing the relevant asymptotic quantities directly on ℐ+ based on the general expressions for the Bondi-Sachs energy-momentum, news and flux derived in a recent paper [10]. This provides a strong check on the accuracy of our numerical computations.