Abstract. We show how approximate radiative solutions of Einstein's equations can be constructed using small deformations of Einstein spacetimes embedded into a pseudo-Euclidean flat space of higher dimension. Infinitesimal deformations are seen then as vector fields in E^N. All geometrical quantities can be then expressed in terms of embedding functions z^A and their deformations . Then we require the deformations to keep Einstein equations satisfied up to a given order in ε. The system obtained is then analyzed in particular cases of the Minkowski and Schwarzschild manifolds taken as a starting point, and solutions of deformations of Einstein's equations displaying radiative behavior are found up to the third order of expansion in small parameter ε.

PACS numbers: 04.25.−g, 04.20.Cv, 04.30.−w

Print publication: Issue 23 (7 December 2009)
Received 15 April 2009, in final form 28 September 2009
Published 6 November 2009