Higher dimensional flat embeddings of black strings in (2+1) dimensions

TL;DR

This paper constructs higher-dimensional flat embeddings of (2+1)-dimensional black strings, including charged and uncharged cases, revealing their relation to other black hole solutions in a unified Minkowski space framework.

Contribution

It provides explicit global flat embeddings for (2+1) black strings in (3+1) and (3+2) dimensions, linking charged black strings to charged de Sitter black holes.

Findings

Charged black string embedded in (3+2) Minkowski space

Uncharged black string embedded in (3+1) Minkowski space

Charged black string shares embedding structure with charged de Sitter black hole

Abstract

We obtain (3+1) and (3+2) dimensional global flat embeddings of (2+1) uncharged and charged black strings, respectively. In particular, the charged black string, which is the dual solution of the Banados-Teitelboim-Zanelli black holes, is shown to be embedded in the same global embedding Minkowski space structure as that of the (2+1) charged de Sitter black hole solution.