Quantum Properties of Topological Black Holes
  We examine quantum properties of topological black holes which are asymptotically anti--de Sitter. First, massless scalar fields and Weyl spinors which propagate in the background of an anti--de Sitter black hole are considered in an exactly soluble two--dimensional toy model. The Boulware--, Unruh--, and Hartle--Hawking vacua are defined. The latter results to coincide with the Unruh vacuum due to the boundary conditions necessary in asymptotically adS spacetimes. We show that the Hartle--Hawking vacuum represents a thermal equilibrium state with the temperature found in the Euclidean formulation. The renormalized stress tensor for this quantum state is well--defined everywhere, for any genus and for all solutions which do not have an inner Cauchy horizon, whereas in this last case it diverges on the inner horizon. The four--dimensional case is finally considered, the equilibrium states are discussed and a luminosity formula for the black hole of any genus is obtained. Since spacelike infinity in anti--de Sitter space acts like a mirror, it is pointed out how this would imply information loss in gravitational collapse. The black hole's mass spectrum according to Bekenstein's view is discussed and compared to that provided by string theory. 
Dietmar Klemm and Luciano Vanzo (University of Trento, Italy)