Higher dimensional flat embeddings of (2+1) dimensional black holes

TL;DR

This paper constructs higher-dimensional flat embeddings for various (2+1)-dimensional black holes, including BTZ and de Sitter types, revealing differences in their embedding structures.

Contribution

It provides new higher-dimensional flat embeddings for static, rotating, and charged BTZ and de Sitter black holes, highlighting differences in their GEMS structures.

Findings

Charged dS black hole embedded in (3+2) GEMS

Charged BTZ black hole embedded in (3+3) GEMS

Distinct embedding structures for dS and AdS black holes

Abstract

We obtain the higher dimensional global flat embeddings of static, rotating, and charged BTZ black holes. On the other hand, we also study the similar higher dimensional flat embeddings of the (2+1) de Sitter black holes which are the counterparts of the anti-de Sitter BTZ black holes. As a result, the charged dS black hole is shown to be embedded in (3+2) GEMS, contrast to the charged BTZ one having (3+3) GEMS structure.