Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations

TL;DR

This paper investigates the stability of black holes with scalar hair in shift-symmetric Horndeski theories, finding many solutions unstable but identifying some stable under odd-parity perturbations.

Contribution

It provides a detailed mode stability analysis of odd-parity perturbations for hairy black holes in these theories, highlighting stability conditions.

Findings

Many black hole solutions are unstable due to ghost or gradient instabilities.

Some classes of solutions are stable under linear odd-parity perturbations.

The analysis constrains the viability of certain hairy black hole models.

Abstract

We analyze the mode stability of odd-parity perturbations of black holes with linearly time-dependent scalar hair in shift-symmetric Horndeski theories. We show that a large class of black hole solutions in these theories suffer from ghost or gradient instability, while there are some classes of solutions that are stable under linear odd-parity perturbations in the context of mode analysis.