Lovelock black holes with a nonlinear Maxwell field

TL;DR

This paper derives new electrically charged black hole solutions in higher-dimensional Einstein-Gauss-Bonnet gravity with nonlinear electrodynamics, establishing their uniqueness and extending the analysis to full Lovelock gravity including Chern-Simons cases.

Contribution

It provides explicit solutions for Lovelock black holes with nonlinear Maxwell fields and proves a generalized Birkhoff's theorem for these configurations.

Findings

Derived explicit black hole solutions in higher dimensions

Proved uniqueness of these solutions under certain symmetries

Extended analysis to full Lovelock gravity including Chern-Simons cases

Abstract

We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in $n (\ge 5)$ dimensions. The spacetimes are given as a warped product $M^2 \times K^{n-2}$, where $K^{n-2}$ is a $(n-2)$-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 $K^{n-2}$ is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Chern-Simons case.