Making anti-de Sitter black holes

It is known from the work of Bañados et al that a spacetime with event horizons (much like the Schwarzschild black hole) can be obtained from (2 + 1)-dimensional anti-de Sitter space through a suitable identification of points. We point out that this can be done in 3 + 1 dimensions as well. In this way we obtain black holes with event horizons that are tori or Riemann surfaces of genus higher than one. They can have either one or two asymptotic regions (with non-standard topology). Locally, the spacetime is isometric to anti-de Sitter space.