Radiation field for Einstein vacuum equations

Abstract

The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions to the Einstein Vacuum equations, which are close to Minkowski space, at null infinity. By imposing harmonic gauge, the Einstein Vacuum equations reduce to a system of quasilinear wave equations on R"j". We show that if the space dimension n > 5 the Moller wave operator is an isomorphism from Cauchy data satisfying the constraint equations to the radiation fields satisfying the corresponding constraint equations on small neighborhoods of suitable weighted b-type Sobolev spaces.