Total angular momentum for asymptotically flat manifolds is defined. Positive mass theorem for initial (spin) data set (M, g(ij), p(ij)) with nonsymmetric p(ij) is proved. As an application, we establish positive mass theorems involving total linear momentum and total angular momentum. This gives an answer to a problem of S. T. Yau in his Problem Section [Ya2] and a partial answer to his recent conjecture on the relationship among total energy, total linear momentum, total angular momentum and entropy of black hole.
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