BLACK-HOLES AND CAUSAL-STRUCTURE IN ANTI-DE SITTER ISOMETRIC SPACETIMES

The observation that the (2 + 1)-dimensional BTZ black hole can be obt ained as a quotient space of anti-de Sitter space leads one to ask wha t causal behaviour other such quotient spaces can display. In this pap er we answer this question in 2 + 1 and 3 + 1 dimensions when the iden tification group has one generator. Among other things we find that th ere does not exist any 3 + 1 generalization of the rotating BTZ hole. However, the non-rotating generalization exists and exhibits some unex pected properties; for example, it turns out to be non-static and to p ossess a non-trivial apparent horizon.