TY - JOUR

T1 - Classification of minimum global embeddings for nonrotating black holes

AU - Sheykin, A.A.

AU - Paston, S.A.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - gravity theory

KW - isometric embedding

KW - embedding theory

KW - black hole

KW - additional dimension

U2 - 10.1007/s11232-015-0364-1

DO - 10.1007/s11232-015-0364-1

M3 - Article

VL - 185

SP - 1547

EP - 1556

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -