This article is cited in 15 papers

Embeddings for solutions of Einstein equations

S. A. Paston^a, A. A. Sheikin

^a Saint Petersburg State University, St. Petersburg, Russia

Abstract: We study isometric embeddings of some solutions of the Einstein equations with sufficiently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimal embeddings of the Schwarzschild metric obtained using this method and show how the method can be used to construct all minimal embeddings for the Friedmann models. We classify all the embeddings in terms of realizations of symmetries of the corresponding solutions.

Keywords: theory of gravity, isometric embedding, embedding theory, Schwarzschild metric embedding, asymptotically flat embedding, extra dimension.

DOI: 10.4213/tmf8494

 English version: Theoretical and Mathematical Physics, 2013, 175:3, 806–815

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