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Motivated by possible applications within the framework of anti-de Sittergravity/Conformal Field Theory (AdS/CFT) correspondence, charged black holeswith AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in Ddimensions, and whose electric field is described by a nonlinearelectrodynamics (NED) are studied. For a topological static black hole ansatz,the field equations are exactly solved in terms of the electromagnetic stresstensor for an arbitrary NED Lagrangian, in any dimension D and for arbitrarypositive values of Gauss-Bonnet coupling. In particular, this procedurereproduces the black hole metric in Born-Infeld and conformally invariantelectrodynamics previously found in the literature. Altogether, it extends toD>4 the four-dimensional solution obtained by Soleng in logarithmicelectrodynamics, which comes from vacuum polarization effects. Fall-offconditions for the electromagnetic field that ensure the finiteness of theelectric charge are also discussed. The black hole mass and vacuum energy asconserved quantities associated to an asymptotic timelike Killing vector arecomputed using a background-independent regularization of the gravitationalaction based on the addition of counterterms which are a given polynomial inthe intrinsic and extrinsic curvatures.

Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space