Embeddings for Schwarzschild metric: classification and new results

Details Embeddings for Schwarzschild metric: classification and new results Embeddings for Schwarzschild metric: classification and new results

2012-02-06

arxiv.org/abs/1202.1204v1

Class. Quantum Grav. 29 (2012) 095022

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 19 pages

Scientific paper

10.1088/0264-9381/29/9/095022

We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings of the Schwarzschild metric which have the symmetry of this solution, and all such embeddings in a six-dimensional ambient space (i.e. a space with a minimal possible dimension) are constructed. Four of the six possible embeddings are already known, while the two others are new. One of the new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be of use in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space.

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