A new look on black hole perturbations in modified gravity

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 Schrödinger-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.

Contribution to the 2022 Gravitation session of the 56th Rencontres de Moriond