Odd-parity stability of hairy black holes in $U(1)$ gauge-invariant scalar-vector-tensor theories

Abstract

In scalar-vector-tensor theories with $U(1)$ gauge invariance, it was recently shown that there exists a new type of hairy black hole (BH) solutions induced by a cubic-order scalar-vector interaction. In this paper, we derive conditions for the absence of ghosts and Laplacian instabilities against odd-parity perturbations on a static and spherically symmetric background for most general $U(1)$ gauge-invariant scalar-vector-tensor theories with second-order equations of motion. We apply those conditions to hairy BH solutions arising from the cubic-order coupling and show that the odd-parity stability in the gravity sector is always ensured outside the event horizon with the speed of gravity equivalent to that of light. We also study the case in which quartic-order interactions are present in addition to the cubic coupling and obtain conditions under which black holes are stable against odd-parity perturbations.

15 pages, 3 figures

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• Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity
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• Even-parity stability of hairy black holes in $U(1)$ gauge-invariant scalar-vector-tensor theories
• Exploring Self-Gravitating Cylindrical Structures in Modified Gravity: Insights from Scalar-Vector-Tensor Theory
• Linear instability of hairy black holes in Horndeski theory
• Linear perturbations of dyonic black holes in the lowest-order $U(1)$ gauge-invariant scalar-vector-tensor theories