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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 M^2K^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.
Maeda et al. (Tue,) studied this question.