Simple solutions to the Einstein Equations in spaces with unusual topology

TL;DR

This paper explores simple vacuum solutions to Einstein's equations in five-dimensional spaces with unusual topologies, revealing multiple black hole and black string phases, and discussing their properties and phase transitions.

Contribution

It introduces new solutions by adapting existing metrics to novel topologies, highlighting the coexistence of different black object phases in higher-dimensional spaces.

Findings

Multiple black hole and black string phases can exist in these topologies

Adapted old metrics yield new solutions to Einstein's equations

Discussion of horizon topology and phase transitions

Abstract

We discuss simple vacuum solutions to the Einstein Equations in five dimensional space-times compactified in two different ways. In such spaces, one black hole phase and more then one black string phase may exist. Several old metrics are adapted to new background topologies to yield new solutions to the Einstein Equations. We then briefly talk about the angular momentum they may carry, the horizon topology and phase transitions that may occur.