Asymptotics of Schwarzschild black hole perturbations

TL;DR

This paper numerically investigates linear gravitational perturbations of Schwarzschild black holes using hyperboloidal surfaces, emphasizing the importance of including the asymptotic region for accurate gravitational radiation analysis.

Contribution

It introduces a hyperboloidal approach with a compactifying radial coordinate for time-domain simulations of black hole perturbations, enhancing the study of gravitational radiation.

Findings

Successful numerical solution of Regge-Wheeler-Zerilli equations in the hyperboloidal framework

Demonstrated the significance of including the asymptotic region in simulations

Potential applications in broader black hole perturbation studies

Abstract

We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge-Wheeler-Zerilli equations in time domain using hyperboloidal surfaces and a compactifying radial coordinate. We stress the importance of including the asymptotic region in the computational domain in studies of gravitational radiation. The hyperboloidal approach should be helpful in a wide range of applications employing black hole perturbation theory.