Radiation field for Einstein vacuum equations with spacial dimension $n\geq 4$

Abstract

In this paper, the radiation field is defined for solutions to Einstein vacuum equations which are close to Minkowski space-time with spacial dimension $n\geq 4$. The regularity properties and asymptotic behavior of those Einstein vacuum solutions are established at the same time. In particular, the map from Cauchy intial data to the radiation field is proved to be an isomorphism when restricting to a small neighborhood of Minkowski data in suitable weighted b-Sobolev spaces.