Gravitational waves as deformations of embedded Einstein spaces

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 nu(A), z(A) -> (z) over tilde (A) = z(A) + epsilon nu(A) + epsilon(2) omega(A) + center dot center dot center dot. Then we require the deformations to keep Einstein equations satisfied up to a given order in epsilon. 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 epsilon.