Explicit isometric embeddings of black holes geometry with non-singular matter distribution

Abstract

The work is devoted to the construction of explicit embeddings for the metrics of the black holes, formed by nonsingular matter distribution. One of the possible examples of such type of solutions is regular black holes. Using the existing classification of minimal symmetric embeddings of the Schwarzschild metric as a base, we construct embeddings for regular black holes with de Sitter interior. Another simple example is black hole, formed by collapsing homogeneous spherically symmetric cloud of dustlike matter. We discuss embeddings for two variants of such black holes -the one with the eternally existing horizon, when dust ball never leaves the interior of the horizon, and another variant with the dynamically forming horizon.