Black holes and causal structure in anti-de Sitter isometric spacetimes

The observation that the (2 + 1)-dimensional BTZ black hole can be obtained as a quotient space of anti-de Sitter space leads one to ask what causal behaviour other such quotient spaces can display. In this paper we answer this question in 2 + 1 and 3 + 1 dimensions when the identification group has one generator. Among other things we find that there does not exist any 3 + 1 generalization of the rotating BTZ hole. However, the non-rotating generalization exists and exhibits some unexpected properties; for example, it turns out to be non-static and to possess a non-trivial apparent horizon.