  It is shown that the mass of an asymptotically flat manifold with a
noncompact boundary can be computed in terms of limiting surface integrals
involving the Einstein tensor of the interior metric and the Newton tensor
attached to the second fundamental form of the boundary. This extends to this
setting previous results by several authors in the boundaryless case. The
method outlined below, which is based on a coordinate-free approach due to
Herzlich, also applies to asymptotically hyperbolic manifolds, again with a
noncompact boundary, for which a similar notion of mass has been recently
considered by Almaraz and the first named author, and both cases will be
discussed here.
