Classification of minimum global embeddings for nonrotating black holes

We consider the problem of the existence of global embeddings of metrics of spherically symmetric black holes into an ambient space with the minimum 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–Nordström black holes, we prove that the known global embeddings are the only ones. We obtain a new global embedding for the Reissner–Nordström–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–Nordström–anti-de Sitter metric.