Static and rotating solutions for vector-Galileon theories

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.