Quotients of ${\mathrm{AdS}}_{p+1\mathrm{}}\times {\mathrm{S}}^q:$ Causally well-behaved spaces and black holes

Starting from the recent classification of quotients of Freund-Rubin backgrounds in string theory of the type ${\mathrm{AdS}}_{p+1\mathrm{}}\times {\mathrm{S}}^q$ by one-parameter subgroups of isometries, we investigate the physical interpretation of the associated quotients by discrete cyclic subgroups. We establish which quotients have well-behaved causal structures, and of those containing closed timelike curves, which have interpretations as black holes. We explain the relation to previous investigations of quotients of asymptotically flat spacetimes and plane waves, of black holes in AdS spacetimes, and of Gödel-type universes.