  The formulation of General Relativity in which the 4-dimensional space-time
is embedded in a flat host space of higher dimension is reconsidered. New
classes of embeddings (modeled after Nash's classical free embeddings) are
introduced. They present the important advantage of being deformable and
therefore physically realistic. Explicit examples of embeddings whose
deformations DO describe gravitational waves around their respective
backgrounds are given for several space-times, including the Schwarzschild
black hole. New variational principles which give back Einstein's General
Relativity are proposed. In this framework, the 4-D space-time is a membrane
moving in a flat host space.
