A definition of total energy-momenta and the positive mass theorem on asymptotically hyperbolic 3-manifolds. I. (English) Zbl 1073.83019
This paper begins with a brief but nicely written survey of the positivity of mass problem and points out certain difficulties are still present in the spinor approach to this problem and regarding boundary terms. Section 2 and 3 discuss the definition of the total energy-momenta and sort out some mathematical preliminaries. A spinor proof of the positivity of mass is given in section 4. In section 5, the author shows that his definition of total energy coincides with the Bondi mass at least in a certain case and in certain time slices of the Kerr-AdS space-time. The interested reader may wish to consult three other papers by the same author [Angular momentum and positive mass theorem, Commun. Math. Phys. 206, No. 1, 137–155 (1999; Zbl 1007.83014); Strongly asymptotically hyperbolic spin manifolds, Math. Res. Lett. 7, No. 5–6, 719–727 (2000; Zbl 0979.53054); Remarks on the total angular momentum in general relativity, Commun. Theor. Phys. 39, No. 5, 521–524 (2003)].
Reviewer: Graham S. Hall (Aberdeen)
MSC:
| 83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |
| 83C80 | Analogues of general relativity in lower dimensions |
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