ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
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Deformations of embedded Einstein spaces; pp. 313–325

Full article in PDF format | doi: 10.3176/proc.2010.4.10

Authors
Richard Kerner, Salvatore Vitale

Abstract
Many important Einsteinian space-times can be globally embedded into a pseudo-Euclidean flat space of higher dimension N. In this paper we analyse in detail the geometrical properties of infinitesimal deformations of embedded Einstein spaces. Embeddings are defined by N functions zA(xμ), A = 1, 2, …, N, μ = 0, 1, 2, 3. Their infinitesimal deformations can be developed in a power series of small parameter ε as follows: zA → zA = zA + ε vA + ε2 wA + … . All geometrical quantities can be then expressed in terms of embedding functions zA and their deformations vA, wA, etc. Then we require the deformations to keep Einstein equations satisfied up to a given order in ε. This method can be used to construct approximate solutions of Einstein’s equations, and was first introduced in 1978 by one of the authors (RK).
References

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