Deformations of the embedded Einstein spaces

Details Deformations of the embedded Einstein spaces Deformations of the embedded Einstein spaces

Mar 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978gregr...9..257k&link_type=abstract

General Relativity and Gravitation, Volume 9, Issue 3, pp.257-270

Physics

3

Scientific paper

We discuss a method of studying the stability of solutions of Einstein's equations, which can be outlined as follows: Consider an embedding of a given Einstein spaceV 4 into a pseudo-Euclidean spaceE {/p,q N } (N > 4,p + q =N) (p,q) describing the signature of the spaceE {/p,q N }. Then all the geometrical objects ofV 4 can be expressed in terms of the embedding functions,Z A (x i ),A = 1, 2,...,N, i = 0, 1, 2, 3. Then let us deform the embedding:Z A →Z A +ɛυ A , ɛ being an infinitesimal parameter. The Einstein equations can be developed then in the powers ofɛ; we study the equations arising by requirement of the vanishing of the first- or second-order terms. Some partial results concerning the de Sitter, Einstein, and Minkowskian spaces are given.

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