Classification of global minimal embeddings for nonrotating black holes

TL;DR

This paper classifies minimal global embeddings of spherically symmetric black hole metrics into ambient spaces, proving known embeddings are unique for certain black holes and discovering new embeddings for others.

Contribution

It provides a classification of possible embeddings based on symmetry realization and introduces a new global embedding for Reissner-Nordstrom-de Sitter black holes.

Findings

Known embeddings for Schwarzschild, Schwarzschild-de Sitter, Reissner-Nordstrom are unique.

New global embedding constructed for Reissner-Nordstrom-de Sitter.

Impossible to construct such embeddings for Schwarzschild-anti-de Sitter.

Abstract

We consider the problem of the existence of global embeddings of metrics of spherically symmetric black holes into an ambient space with the minimal possible dimension. We classify the possible types of embeddings by the type of realization of the metric symmetry by ambient space symmetries. For the Schwarzschild, Schwarzschild-de Sitter, and Reissner-Nordstrom black holes, we prove that the known global embeddings are the only ones. We obtain a new global embedding for the Reissner-Nordstrom-de Sitter metrics and prove that constructing such embeddings is impossible for the Schwarzschild-anti-de Sitter metric. We also discuss the possibility of constructing global embeddings of the Reissner-Nordstrom-anti-de Sitter metric.