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

TL;DR

This paper establishes stability conditions for odd-parity perturbations of hairy black holes in scalar-vector-tensor theories with $U(1)$ gauge invariance, ensuring their physical viability and consistency with light-speed gravity.

Contribution

It derives general stability conditions for odd-parity perturbations in $U(1)$ gauge-invariant scalar-vector-tensor theories, including cubic and quartic interactions, for the first time.

Findings

Odd-parity stability is guaranteed outside the horizon for cubic interactions.

Gravity propagates at the speed of light in these black hole solutions.

Additional quartic interactions can be stable under certain conditions.

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.