Anti-de Sitter quotients, bubbles of nothing, and black holes

Abstract

In 3+1 dimensions there are anti-de Sitter quotients which are black holes with toroidal event horizons. By analytic continuation of the Schwarzschild-anti-de Sitter solution (and appropriate identifications) one finds two one parameter families of spacetimes that contain these quotient black holes. One of these families consists of B-metrics ("bubbles of nothing"), the other of black hole spacetimes. All of them have vanishing conserved charges.

Anti-de Sitter quotients: when are they black holes?

“…Actually there is a third way to perform the analytic continuation, so that the toroidal black hole does appear as a member of a one parameter family of black holes. This will be described in a separate publication [15].…”