A new look on black hole perturbations in modified gravity

TL;DR

This paper introduces a systematic method to analyze linear perturbations of nonrotating black holes in Horndeski's modified gravity, focusing on asymptotic behaviors to facilitate quasinormal mode calculations and reveal scalar sector pathologies.

Contribution

It presents a novel approach to extract asymptotic behaviors of black hole perturbations directly from the differential system, bypassing Schrödinger-like equations, and applies it to identify issues in the scalar sector.

Findings

Method enables direct asymptotic analysis of perturbations.

Facilitates numerical computation of quasinormal modes.

Identifies pathologies in the scalar sector of the solution.

Abstract

We study the linear perturbations about a nonrotating black hole solution of Horndeski's theory, using a systematic approach that extracts the asymptotic behaviour of perturbations (at spatial infinity and near the horizon) directly from the first-order radial differential system governing these perturbations instead of finding Schr\"odinger-like equations for their dynamics. We illustrate this method in the case of a specific black hole solution. The knowledge of the asymptotic behaviours of the perturbations paves the way for a numerical computation of the quasinormal modes. Finally, the asymptotic form of the modes also signals some pathologies in the scalar sector of the solution considered here.