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

TL;DR

This paper generalizes BTZ black hole solutions to multiple black holes in 2+1 and 3+1 dimensional anti-de Sitter spaces, describing their geometric structure and topologies.

Contribution

It introduces multi-black-hole solutions in anti-de Sitter space for arbitrary numbers of black holes in 2+1 and 3+1 dimensions, expanding the understanding of their global geometries.

Findings

Multi-black-hole spacetimes are locally isometric to anti-de Sitter space.

Exterior regions resemble single BTZ black holes with horizons separating them.

Configurations include toroidal and higher genus horizon topologies.

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.