# Hairy black-hole solutions in generalized Proca theories

## TL;DR

This paper introduces exact and numerical black-hole solutions in generalized Proca theories, highlighting the potential for gravitational wave observations to detect vector hair deviations from General Relativity.

## Contribution

It provides the first exact solutions and numerical evidence for black holes with vector hair in second-order generalized Proca theories, expanding understanding of alternative gravity models.

## Key findings

- Existence of exact black-hole solutions with vector hair.
- Numerical evidence for regular black holes with primary hair.
- Significant deviations from GR near the horizon detectable via GWs.

## Abstract

We present a family of exact black-hole solutions on a static spherically symmetric background in second-order generalized Proca theories with derivative vector-field interactions coupled to gravity. We also derive non-exact solutions in power-law coupling models including vector Galileons and numerically show the existence of regular black holes with a primary hair associated with the longitudinal propagation. The intrinsic vector-field derivative interactions generally give rise to a secondary hair induced by non-trivial field profiles. The deviation from General Relativity is most significant around the horizon and hence there is a golden opportunity for probing the Proca hair by the measurements of gravitational waves (GWs) in the regime of strong gravity.