An hyperbolic system of P.D.E. relevant in general relativity

Abstract

Assuming as starting point the validity of the Einstein-Rosen metric we study the hyperbolic system of P.D.E. to which the Einstein’s field equations can be reduced. We prove using the implicit function theorem in Banach spaces, the existence and uniqueness of gravitational waves of small amplitude. A class of solutions, not necessarily small, is also constructed. In the last Section a theorem of existence and uniqueness is given for the corresponding stationary problem.