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–Nordstr¨om 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–antide Sitter metric. We also discuss the possibility of constructing global embeddings of the Reissner–Nordstrom–anti-de Sitter metric.
Original languageEnglish
Pages (from-to)1547-1556
JournalTheoretical and Mathematical Physics
Volume185
Issue number1
DOIs
StatePublished - 2015

    Research areas

  • gravity theory, isometric embedding, embedding theory, black hole, additional dimension

ID: 3973435