A positive mass theorem for low-regularity metrics
  We prove a positive mass theorem for continuous Riemannian metrics in the Sobolev space $W^{2, n/2}_{\mathrm{loc}}(M)$. We argue that this is the largest class of metrics with scalar curvature a positive a.c. measure for which the positive mass theorem may be proved by our methods. 
James D. E. Grant, Nathalie Tassotti
math.DG gr-qc math-ph math.MP