Compact Three Dimensional Black Hole: Topology Change and Closed Timelike Curve (minor changes)

TL;DR

This paper introduces a compactified 3D black hole solution, explores its extended spacetime with topology change and closed timelike curves, revealing a transition from a double torus to multiple spheres.

Contribution

It presents a new compactified 3D black hole model with analytical continuation and demonstrates topology change and closed timelike curves in the extended spacetime.

Findings

Topology change from double torus to spheres with punctures

Existence of closed timelike curves in extended regions

Analytical continuation beyond coordinate singularity

Abstract

We present a compactified version of the 3-dimensional black hole recently found by considering extra identifications and determine the analytical continuation of the solution beyond its coordinate singularity by extending the identifications to the extended region of the spacetime. In the extended region of the spacetime, we find a topology change and non-trivial closed timelike curves both in the ordinary 3-dimensional black hole and in the compactified one. Especially, in the case of the compactified 3-dimensional black hole, we show an example of topology change from one double torus to eight spheres with three punctures.