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A calculation of the entropy of static, electrically charged, black holeswith spherical, toroidal, and hyperbolic compact and oriented horizons, in Dspacetime dimensions, is performed. These black holes live in an anti-de Sitterspacetime, i.e., a spacetime with negative cosmological constant. To find theentropy, the approach developed by Solodukhin is followed. The method consistsin a redefinition of the variables in the metric, by considering the radialcoordinate as a scalar field. Then one performs a 2+(D-2) dimensionalreduction, where the (D-2) dimensions are in the angular coordinates, obtaininga 2-dimensional effective scalar field theory. This theory is a conformaltheory in an infinitesimally small vicinity of the horizon. The correspondingconformal symmetry will then have conserved charges, associated with itsinfinitesimal conformal generators, which will generate a classical Poissonalgebra of the Virasoro type. Shifting the charges and replacing Poissonbrackets by commutators, one recovers the usual form of the Virasoro algebra,obtaining thus the level zero conserved charge eigenvalue L_0, and a nonzerocentral charge c. The entropy is then obtained via the Cardy formula.Comment: 21 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Conformal entropy from horizon states: Solodukhin’s method for spherical, toroidal, and hyperbolic black holes in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>-dimensional anti-de Sitter spacetimes

Conformal entropy from horizon states: Solodukhin’s method for spherical, toroidal, and hyperbolic black holes inD-dimensional anti-de Sitter spacetimes