General theories of linear gravitational perturbations to a Schwarzschild Black Hole

TL;DR

This paper employs a covariant approach to analyze linear gravitational perturbations around Schwarzschild black holes across various gravity theories, examining how modifications to General Relativity influence quasi-normal modes.

Contribution

It provides a comprehensive covariant formulation of quadratic actions for perturbations in scalar-tensor, vector-tensor, and single-tensor gravity models around Schwarzschild black holes.

Findings

Explicit covariant quadratic actions derived for different gravity models.

Unified analysis of odd and even parity perturbations.

Insights into how alternative gravity theories affect black hole quasi-normal modes.

Abstract

We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes of perturbed black holes may be affected by modifications to General Relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyse odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.