A positive mass theorem for asymptotically flat manifolds with a   non-compact boundary
  We prove a positive mass theorem for $n$-dimensional asymptotically flat manifolds with a non-compact boundary if either $3\leq n\leq 7$ or if $n\geq 3$ and the manifold is spin. This settles, for this class of manifolds, a question posed in a recent paper by the first author in connection with the long-term behavior of a certain Yamabe-type flow on scalar-flat compact manifolds with boundary. 
Sergio Almaraz, Ezequiel Barbosa, Levi Lopes de Lima
math.DG gr-qc math.AP