Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

TL;DR

This paper develops a hyperboloidal initial value approach to study gravitational perturbations of Schwarzschild spacetime, enabling accurate extraction of gravitational waveforms at null infinity, with potential extension to Kerr black holes.

Contribution

It introduces a hyperboloidal compactification method for solving the Bardeen-Press equation, improving waveform accuracy at null infinity compared to traditional boundary methods.

Findings

Hyperboloidal approach yields more accurate gravitational waveforms.

Method is efficient and can be extended to Kerr spacetime.

Access to null infinity improves gravitational wave analysis.

Abstract

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access to the gravitational waveform at null infinity in a general setup. We argue that this hyperboloidal approach leads to a more accurate and efficient calculation of the radiation signal than the common approach where a timelike outer boundary is introduced. The method can be generalized to study perturbations of Kerr spacetime using the Teukolsky equation.