Lovelock black holes with a nonlinear Maxwell field

We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in n(5) dimensions. The spacetimes are given as a warped product M2×Kn-2, where Kn-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 Kn-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.