AdS$_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling

TL;DR

This paper constructs a novel three-dimensional Einstein-Gauss-Bonnet vector-tensor theory using Weyl geometry regularization, leading to new AdS$_3$ black hole solutions with primary Proca hair, including charged and stealth variants.

Contribution

It introduces a regularized Gauss-Bonnet vector-tensor theory in 3D and derives new black hole solutions with primary Proca hair, expanding the understanding of vector-tensor gravities.

Findings

Found asymptotically AdS$_3$ black holes with primary Proca hair.

Constructed regular and charged black hole solutions.

Identified stealth BTZ black hole solutions.

Abstract

We construct a consistent three-dimensional Einstein-Gauss-Bonnet theory as a vector-tensor theory within the generalized Proca class by employing a regularization procedure based on the Weyl geometry, which was introduced recently in \link{2504.13084}. We then obtain an asymptotically AdS$_3$, static, and circularly symmetric black hole solution with primary Proca hair. Afterward, we investigate the effect of the scalar-tensor Gauss-Bonnet coupling constructed previously by different regularization schemes. We further generalize these solutions by incorporating an electric charge. As special cases, we find a regular black hole solution in addition to charged and uncharged stealth BTZ black hole solutions.