TY - JOUR

T1 - Embeddings for solutions of Einstein equations

AU - Paston, S.A.

AU - Sheykin, A.A.

PY - 2013

Y1 - 2013

N2 - We study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimum 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.

AB - We study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimum 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.

KW - theory of gravity

KW - isometric embedding

KW - embedding theory

KW - Schwarzschild metric embedding

KW - asymptotically flat embedding

KW - extra dimension

U2 - 10.1007/s11232-013-0067-4

DO - 10.1007/s11232-013-0067-4

M3 - Article

VL - 175

SP - 806

EP - 815

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -