A massa em termos dos tensores de Einstein e Newton e aplicações.

Abstract

It is shown that the mass and the center of mass of an asymptotically flat Riemannian manifold with noncompact boundary can be computed as the limit, as r goes to infinity, of the integral, over the coordinate sphere of radius r, of expressions in terms of the Einstein and Newton tensors of the manifold. The expression obtained for the mass is then used to give a new proof, for noncompact Euclidean graphs, of the positive mass theorem and the Penrose inequality.