Multi-Black-Holes in 3D and 4D anti-de Sitter Spacetimes

Abstract

The (single) black hole solutions of Ba\~nados, Teitelboim and Zanelli (BTZ) in 2+1 dimensional anti-de Sitter space are generalized to an arbitrary number $n$ of such black holes. The resulting multi-black-hole (MBH) spacetime is locally isometric to anti-de Sitter space, and globally it is obtained from the latter as a quotient space by means of suitable identifications. The MBH spacetime has $n$ asymptotically anti-de Sitter exterior regions, each of which has the geometry of a single BTZ black hole. These exterior regions are separated by $n$ horizons from a common interior region. This interior region can be described as a ``closed" universe containing $n$ black holes. Similar configurations in 3+1 dimensions, with horizons of toroidal and higher genus topologies, are also presented.