Explicit solutions for Point Particles and Black Holes in spaces of constant curvature in 2+1-D Gravity

TL;DR

This paper derives explicit solutions for point particles and black holes in 2+1-dimensional gravity with constant curvature, covering various cosmological constant scenarios and spatial topologies.

Contribution

It provides explicit solutions for gravitational fields involving particles and black holes in 2+1D gravity with different cosmological constants.

Findings

Explicit solutions for 1 or 2 particles in 2+1D gravity.

Explicit solutions for 1 black hole and black-hole vacuum states.

Different spatial topologies depending on the cosmological constant.

Abstract

In this paper we consider space-times containing matter expanding or contracting according to a time-dependent scale factor. Cosmologies with vanishing, positive or negative cosmological constant are considered. In the case of vanishing or negative cosmological constant open and closed spatial surfaces are solutions while in the case of positive cosmological constant only closed surfaces exist. The gravitational field is solved explicitly in the case of 1 or 2 particles, 1 black-hole, and 1 black-hole vacuum state.