Einstein black holes, free scalars and AdS/CFT correspondence
Abstract
We investigate AdS/CFT correspondence for two families of Einstein black holes in d > 3 dimensions, modelling the boundary CFT by a free conformal scalar field and evaluating the boundary two-point function in the bulk geodesic approximation. For the d > 3 counterpart of the nonrotating BTZ hole and for its Z2 quotient, the boundary state is thermal in the expected sense, and its stress-energy reflects the properties of the bulk geometry and suggests a novel definition for the mass of the hole. For the generalised Schwarzschild-AdS hole with a flat horizon of topology Rd-2, the boundary stress-energy has a thermal form with energy density proportional to the hole ADM mass, but stress-energy corrections from compactified horizon dimensions cannot be consistently included at least for d=5.
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