Static and rotating solutions for vector-Galileon theories

Abstract

We consider a particular truncation of the generalized Proca field theory in four dimensions for which we construct static and axisymmetric rotating black hole "stealth solutions," namely solutions with (anti) de Sitter or Kerr metric but nontrivial 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.