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

TL;DR

This paper numerically investigates how a Schwarzschild black hole responds to an incoming gravitational wave pulse, analyzing the non-linear scattering effects and verifying the Bondi-Sachs mass loss formula at null infinity.

Contribution

It introduces a well-posed numerical setup using conformal field equations to study non-linear black hole scattering by gravitational waves, enabling direct analysis at null infinity.

Findings

Verification of the Bondi-Sachs mass loss formula.

Observation of scattered gravitational waves at null infinity.

Insights into non-linear black hole response to gravitational waves.

Abstract

The excitation of a black hole by infalling matter or radiation has been studied for a long time, mostly in linear perturbation theory. In this paper we study numerically the response of a Schwarzschild black hole to an incoming gravitational wave pulse. We present a numerically well-posed initial boundary value problem for the generalized conformal field equations in which a wave profile for the ingoing wave is specified at an outer time-like boundary which then hits an initially static and spherically symmetric black hole. The non-linear interaction of the black hole with the gravitational wave leads to scattered radiation moving back out. The clean separation between initial state and incoming radiation makes this setup ideal to study scattering problems. The use of the conformal field equations allows us to trace the response of the black hole to null infinity where we can read off the scattered gravitational waves and compute the Bondi-Sachs mass and the gravitational flux through $\mathscr{I}$. In this way we check the Bondi-Sachs mass loss formula directly on null infinity. We also comment on comparisons with quasinormal modes.