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

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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.