Time-Symmetric Initial Data for Multi-Body Solutions in Three Dimensions

TL;DR

This paper constructs time-symmetric initial data for two-body solutions in 3D anti-de Sitter gravity, revealing geometric and horizon properties, and showing conditions for black hole coexistence in open and closed universes.

Contribution

It provides explicit constructions of initial data for multi-body black hole solutions in 3D anti-de Sitter space, highlighting geometric structures and horizon conditions.

Findings

Two black holes cannot exist separately in an open universe without a third horizon.

In a closed universe, two black holes can coexist with an additional image mass.

Apparent horizons are identified as closed geodesics in the constructed geometry.

Abstract

Time-symmetric initial data for two-body solutions in three dimensional anti-deSitter gravity are found. The spatial geometry has constant negative curvature and is constructed as a quotient of two-dimensional hyperbolic space. Apparent horizons correspond to closed geodesics. In an open universe, it is shown that two black holes cannot exist separately, but are necessarily enclosed by a third horizon. In a closed universe, two separate black holes can exist provided there is an additional image mass.