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 ${\mathcal{M}}^2\times {\mathcal{K}}^{n-2}$, where ${\mathcal{K}}^{n-2}$ 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 ${\mathcal{K}}^{n-2}$ is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Chern-Simons case.

• Received 17 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.044012