QUANTUM-PROPERTIES OF TOPOLOGICAL BLACK-HOLES - ART. NO. 104025

We examine quantum properties of topological asymptotically anti-de Si tter black holes. First, massless scalar fields and Weyl spinors which propagate in the background of an anti-de Sitter black hole are consi dered in an exactly soluble two-dimensional toy model. The Boulware, U nruh, and Hartle-Hawking vacua are defined. The latter coincides with the Unruh vacuum due to die boundary conditions necessary in asymptoti cally AdS spacetimes. We show that the Hartle-Hawking vacuum represent s a thermal equilibrium state with the temperature round in the Euclid ean 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 div erges on the inner horizon. The four-dimensional case is finally consi dered, the equilibrium states are discussed and a luminosity formula f or the black hole of any genus is obtained. Since spacelike infinity i n 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 compa red to that provided by string theory. [S0556-2821(98)07220-8].