Surface counterterms and boundary stress-energy tensors for asymptotically non–anti–de Sitter spaces

Abstract

For spaces which are not asymptotically anti--de Sitter space where the asymptotic behavior is deformed by replacing the cosmological constant by a dilaton scalar potential, we show that it is possible to have well-defined boundary stress-energy tensors and finite Euclidean actions by adding appropriate surface counterterms. We illustrate the method by the examples of domain-wall black holes in gauged supergravities, three-dimensional dilaton black holes, and topological dilaton black holes in four dimensions. We calculate the boundary stress-energy tensor and Euclidean action of these black configurations and discuss their thermodynamics. We find new features of topological black hole thermodynamics.