Static and rotating solutions for Vector-Galileon theories

TL;DR

This paper constructs static and rotating black hole solutions with non-trivial vector fields in Vector-Galileon theories, including extensions to higher dimensions, revealing new stealth solutions with potential implications for modified gravity models.

Contribution

It introduces a class of static and rotating black hole solutions with non-trivial vector fields in Vector-Galileon theories, including higher-dimensional extensions.

Findings

Existence of stealth solutions with (Anti) de Sitter or Kerr metrics.

Construction of backreacting black holes with nonlinear electrodynamics.

Extension of solutions to arbitrary dimensions.

Abstract

We consider a particular truncation of the generalized Proca field theory in four dimensions for which we construct a static and axisymmetric rotating black hole "stealth solutions", namely solutions with (Anti) de Sitter or Kerr metric but non-trivial vector field. The static configuration is promoted to a backreacting black hole with asymptotic (Anti) de Sitter behavior by turning on a nonlinear electrodynamic source given as a fixed power of the Maxwell invariant. Finally we extend our solutions to arbitrary dimensions.