Lovelock black holes with a nonlinear Maxwell field

Abstract

We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in $n(\ensuremath{\ge}5)$ dimensions. The spacetimes are given as a warped product ${\mathcal{M}}^{2}\ifmmode\times\else\texttimes\fi{}{\mathcal{K}}^{n\ensuremath{-}2}$, where ${\mathcal{K}}^{n\ensuremath{-}2}$ is a $(n\ensuremath{-}2)$-dimensional constant curvature space. We establish a generalized Birkhoff's theorem by showing that it is the unique electrically charged solution with this isometry and for which the orbit of the warp factor on ${\mathcal{K}}^{n\ensuremath{-}2}$ is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Chern-Simons case.