Black Holes and Abelian Symmetry Breaking

TL;DR

This paper explores exact black hole solutions in vector-tensor theories with broken Abelian symmetry, revealing new regular configurations and extending solutions to rotating and higher-dimensional cases.

Contribution

It provides the first comprehensive analysis of regular black holes in vector-tensor theories with symmetry breaking, including static, rotating, and higher-dimensional solutions.

Findings

Regular black hole solutions with vector charges are found.

Solutions include static, slowly-rotating, and higher-dimensional black holes.

The geometry depends on vector charges and symmetry-breaking parameters.

Abstract

Black hole configurations offer insights on the non-linear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector-tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector-tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarization, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.