Black hole stability under odd-parity perturbations in Horndeski gravity

TL;DR

This paper investigates the stability of static spherically symmetric black holes in Horndeski gravity under odd-parity perturbations, deriving conditions for stability and applying them to known solutions.

Contribution

It derives a master equation for odd-parity perturbations in Horndeski gravity and establishes algebraic conditions for black hole stability based on the positivity of three functions.

Findings

Stability conditions are similar to no-ghost and Laplacian instability criteria.

Stability reduces to an algebraic problem involving three functions.

Results are applied to various known black hole solutions.

Abstract

We study the stability under linear odd-parity perturbations of static spherically symmetric black holes in Horndeski gravity. We derive the master equation for these perturbations and obtain the conditions of no-ghost and Laplacian instability. In order for the black hole solutions to be stable, we study their generalized "Regge-Wheeler potential". It turns out that the problem is reduced to an algebraic problem where three functions characterizing the black hole should be positive outside the horizon to prove the stability. We found that these conditions are similar to the no-ghost and Laplacian instability conditions. We apply our results to various known solutions.