The Three-Dimensional BTZ Black Hole as a Cylindrical System in Four-Dimensional General Relativity

TL;DR

This paper demonstrates how to convert a three-dimensional BTZ black hole into a four-dimensional cylindrical black hole, akin to transforming a point particle into a cosmic string, within the framework of general relativity.

Contribution

It introduces a method to embed the BTZ black hole into four-dimensional spacetime as a cylindrical black hole, expanding understanding of lower-dimensional black holes in higher-dimensional contexts.

Findings

BTZ black hole can be transformed into a four-dimensional black string

The transformation parallels the conversion of a point particle into a cosmic string

Provides a new perspective on embedding lower-dimensional black holes in higher dimensions

Abstract

It is shown how to transform the three dimensional BTZ black hole into a four dimensional cylindrical black hole (i.e., black string) in general relativity. This process is identical to the transformation of a point particle in three dimensions into a straight cosmic string in four dimensions.