Dynamically generated embeddings of spacetime

Details Dynamically generated embeddings of spacetime Dynamically generated embeddings of spacetime

2005-03-23

arxiv.org/abs/gr-qc/0503103v2

Class.Quant.Grav. 22 (2005) 5005-5014

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

(8 pages, 1 figure). A section on Cauchy Stability of the embedding was added. (To appear in Class. Quant. Grav.)

Scientific paper

10.1088/0264-9381/22/23/006

We discuss how embeddings in connection with the Campbell-Magaard (CM) theorem can have a physical interpretation. We show that any embedding whose local existence is guaranteed by the CM theorem can be viewed as a result of the dynamical evolution of initial data given in a four-dimensional spacelike hypersurface. By using the CM theorem, we establish that for any analytic spacetime, there exist appropriate initial data whose Cauchy development is a five-dimensional vacuum space into which the spacetime is locally embedded. We shall see also that the spacetime embedded is Cauchy stable with respect these the initial data.

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