Black holes in quartic-order beyond-generalized Proca theories

TL;DR

This paper explores black hole solutions in beyond-generalized Proca theories with quartic-order couplings, demonstrating that gravitational wave speeds match light speed near black holes and that these solutions are free from certain instabilities.

Contribution

It introduces black hole solutions with vector hairs in beyond-generalized Proca theories and shows gravitational wave speeds are equal to light speed under specific conditions.

Findings

Gravitational wave speed equals light speed near black holes.

Existence of exact and numerical black hole solutions with vector hairs.

Black holes are free from ghost and Laplacian instabilities.

Abstract

The generalized Proca theories with second-order equations of motion can be healthily extended to a more general framework in which the number of propagating degrees of freedom remains unchanged. In the presence of a quartic-order nonminimal coupling to gravity arising in beyond-generalized Proca theories, the speed of gravitational waves $c_t$ on the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological background can be equal to that of light $c$ under a certain condition. By using this condition alone, we show that the speed of gravitational waves in the vicinity of static and spherically symmetric black holes is also equivalent to $c$ for the propagation of odd-parity perturbations along both radial and angular directions. As a by-product, the black holes arising in our beyond-generalized Proca theories are plagued by neither ghost nor Laplacian instabilities against odd-parity perturbations. We show the existence of both exact and numerical black hole solutions endowed with vector hairs induced by the quartic-order coupling.