On the validity of the definition of angular momentum in general   relativity
  We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero angular momentum vector are presented. We also discuss the Beig-\'O Murchadha-Regge-Teitelboim center of mass and study analogous examples in the Schwarzschild spacetime. 
Po-Ning Chen, Lan-Hsuan Huang, Mu-Tao Wang, Shing-Tung Yau
math.DG gr-qc