Odd-parity perturbations in the most general scalar-vector-tensor theory

TL;DR

This paper investigates the stability of static spherically symmetric black holes within the most general scalar-vector-tensor theories by deriving conditions for stability against odd-parity perturbations.

Contribution

It provides the first comprehensive analysis of odd-parity perturbations and stability conditions in the broadest class of scalar-vector-tensor theories.

Findings

Derived second-order action for perturbations

Established no-ghost and Laplacian instability conditions

Analyzed specific cases for stability criteria

Abstract

In the context of the most general scalar-vector-tensor theory, we study the stability of static spherically symmetric black holes under linear odd-parity perturbations. We calculate the action to second order in the linear perturbations to derive a master equation for these perturbations. For this general class of models, we obtain the conditions of no-ghost and Laplacian instability. Then, we study in detail the generalized Regge-Wheeler potential of particular cases to find their stability conditions.