Angular Momentum and Positive Mass Theorem
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Submission date: 23. Jan. 1999
published in: Communications in mathematical physics, 206 (1999) 1, p. 137-155
DOI number (of the published article): 10.1007/s002200050700
Total angular momentum for asymptotically flat manifolds is defined. Positive mass theorem for initial (spin) data set (M, gij, pij) with nonsymmetric pij 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 (Seminar on Differential Geometry, Annals of Math. Stud. 102, Princeton Univ. Press, Princeton, 1982) 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.