Deformations of the embedded Einstein spaces

  • Richard Kerner
Chapter V. Riemannian Spaces — General Relativity
Part of the Lecture Notes in Mathematics book series (LNM, volume 570)


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 space V4 into a pseudo-Euclidean space E p,q N (N>4, p+q=N),(p,q) describing the signature of the space E p,q N . Then all the geometrical objects of V4 can be expressed in terms of the embedding functions, ZA(xi), A=1,2,...,N,i=0, 1,2,3.

Then let us deform the embedding: ZA → ZA+εvA, ε being an infinitesimal parameter. The Einstein equations can be developed then in the powers of ε; 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.


Einstein Space Suitable Topology Symmetric Tensor Field Nonrotating Star Infinitesimal Parameter 
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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Richard Kerner
    • 1
  1. 1.Département de Mécanique RelativisteUniversité Pierre et Marie CurieParisFrance

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