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

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##### Locator

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##### Fulltext (public)

1009.5763

(Preprint), 307KB

PRD83_024011.pdf

(Any fulltext), 279KB

##### Supplementary Material (public)

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##### Citation

Miskovic, O., & Olea, R. (2011). Conserved charges for black holes in Einstein-Gauss-Bonnet
gravity coupled to nonlinear electrodynamics in AdS space.* Physical Review D,* *83*(2):
024011. doi:10.1103/PhysRevD.83.024011.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-10A2-1

##### Abstract

Motivated by possible applications within the framework of anti-de Sitter
gravity/Conformal Field Theory (AdS/CFT) correspondence, charged black holes
with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D
dimensions, and whose electric field is described by a nonlinear
electrodynamics (NED) are studied. For a topological static black hole ansatz,
the field equations are exactly solved in terms of the electromagnetic stress
tensor for an arbitrary NED Lagrangian, in any dimension D and for arbitrary
positive values of Gauss-Bonnet coupling. In particular, this procedure
reproduces the black hole metric in Born-Infeld and conformally invariant
electrodynamics previously found in the literature. Altogether, it extends to
D>4 the four-dimensional solution obtained by Soleng in logarithmic
electrodynamics, which comes from vacuum polarization effects. Fall-off
conditions for the electromagnetic field that ensure the finiteness of the
electric charge are also discussed. The black hole mass and vacuum energy as
conserved quantities associated to an asymptotic timelike Killing vector are
computed using a background-independent regularization of the gravitational
action based on the addition of counterterms which are a given polynomial in
the intrinsic and extrinsic curvatures.