Evaluation of the ADM mass and center of mass via the Ricci tensor
  We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the same. 
Pengzi Miao and Luen-Fai Tam
math.DG gr-qc