Witten, Edward A new proof of the positive energy theorem. (English) Zbl 1051.83532 Commun. Math. Phys. 80, No. 3, 381-402 (1981). Summary: A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by R. Schoen and S. T. Yau [Commun. Math. Phys. 65, 45–76 (1979; Zbl 0405.53045)].) The relevance of these results to the stability of Minkowski space is discussed. Cited in 10 ReviewsCited in 468 Documents MSC: 83C99 General relativity 58J50 Spectral problems; spectral geometry; scattering theory on manifolds Citations:Zbl 0405.53045 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Trautman, A.: Conservation laws in general relativity. In: Gravitation: an introduction to current research, Witten, L. (ed.). New York: Wiley 1962; [2] Misner, C., Thorne, K.S., Wheeler, J.A.: Gravitation. San Francisco: W. H. Freeman 1973; [3] Weinberg, S.: Gravitation and cosmology. New York: Wiley 1972 · Zbl 0256.05105 [4] Arnowitt, R., Deser, S., Misner, C.W.: Phys. Rev.117, 1595 (1960);118, 1100 (1960);122, 997 (1961); The dynamics of general relativity. In: Witten, L. op.cit · Zbl 0091.21203 · doi:10.1103/PhysRev.117.1595 [5] Weber, J., Wheeler, J.A.: Rev. Mod. Phys.29, 509 (1957) · Zbl 0078.43204 · doi:10.1103/RevModPhys.29.509 [6] Araki, H.: Ann. Phys. (N.Y.)7, 456 (1959); · Zbl 0087.23002 · doi:10.1016/0003-4916(59)90054-5 [7] Brill, D.: Ann. Phys. (N. Y.)7, 466 (1959); · doi:10.1016/0003-4916(59)90055-7 [8] Arnowitt, R., Deser, S., Misner, C.: Ann. Phys. (N.Y.)11, 116 (1960) · Zbl 0091.43801 · doi:10.1016/0003-4916(60)90129-9 [9] Brill, D., Deser, S.: Ann. Phys. (N.Y.)50, 548 (1968) · doi:10.1016/0003-4916(68)90131-0 [10] Brill, D., Deser, S., Faddeev, L.: Phys. Lett.26 A, 538 (1968) · doi:10.1016/0375-9601(68)90533-1 [11] Leibovitz, C., Israel, W.: Phys. Rev. D1, 3226 (1970); [12] Misner, C.: In: astrophysics and general relativity, Chretien, M., Deser, S., Goldstein, J. (ed.). New York: Gordon and Breach 1971 [13] Geroch, R.: Ann. N.Y. Acad. Sci.224, 108 (1973); Proc. Symp. Pure Math.27, 401 (1975) · Zbl 0942.53509 · doi:10.1111/j.1749-6632.1973.tb41445.x [14] O’Murchadha, N., York, J.W., Jr.: Phys. Rev. D10, 2345 (1974) [15] Jang, P.S.: J. Math. Phys.17, 141 (1976) · doi:10.1063/1.522793 [16] Leite, M.: Ph.D. Dissertation, MIT (1977) (unpublished) [17] Choquet-Bruhat, Y.: C.R. Acad. Sci.280, 169 (1975); [18] Cantor, M., Fischer, A., Marsden, J., O’Murchadha, N., York, J.W., Jr.: Commun. Math. Phys.49, 187 (1976) · Zbl 0336.53015 · doi:10.1007/BF01608741 [19] Choquet-Bruhat, Y., Marsden, J.: C.R. Acad. Sci.282, 609 (1976); Commun. Math. Phys.51, 283 (1976) [20] Deser, S., Teitelboim, C.: Phys. Rev. Lett.39, 249 (1977) · doi:10.1103/PhysRevLett.39.249 [21] Grisaru, M.: Phys. Lett.73 B, 207 (1978) · doi:10.1016/0370-2693(78)90837-7 [22] Schoen, P., Yau, S.T.: Commun. Math. Phys.65, 45 (1979) · Zbl 0405.53045 · doi:10.1007/BF01940959 [23] Jang, P.S.: J. Math. Phys.19, 1155 (1978) · doi:10.1063/1.523776 [24] Schoen, P., Yau, S.T.: Phys. Rev. Lett.43, 1457 (1979); Commun. Math. Phys. (to appear) · doi:10.1103/PhysRevLett.43.1457 [25] Schoen, P., Yau, S.T.: Phys. Rev. Lett.42, 547 (1979) · doi:10.1103/PhysRevLett.42.547 [26] Gibbons, G.W., Hawking, S.W., Perry, M.J.: Nucl. Phys. B138, 141 (1978); · doi:10.1016/0550-3213(78)90161-X [27] Hawking, S.W.: Phys. Rev. D18, 1747 (1978); [28] Page, D.N.: Phys. Rev. D18, 2733 (1978); [29] Gibbons, G.W., Pope, C.N.: Commun. Math. Phys.66, 267 (1979) · doi:10.1007/BF01197188 [30] Coleman, S.: Phys. Rev. D15, 2929 (1977); [31] Coleman, S., Callan, C.G., Jr.: Phys. Rev. D16, 1762 (1977) [32] Perry, M.: Princeton Preprint, to appear in 1980 Nuffield workshop proc.; [33] Gross, D.J., Perry, M., Yaffe, L.: Princeton Preprint (to appear) [34] Witten, E.: Princeton Preprint (to appear) [35] Lichnerowicz, A.: C.R. Acad. Sci. (Paris) A?B,257, 7 (1963); [36] Hitchin, N.: Adv. Math.14, 1 (1974) · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8 [37] Ehlers, J., Kundt, W.: In Witten, L.: op.cit. · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8 [38] Geroch, R.: J. Math. Phys.11, 343 (1970) · Zbl 0199.28303 · doi:10.1063/1.1665067 [39] Cremmer, E., Scherk, J.: Nucl. Phys. B103, 399 (1976) · doi:10.1016/0550-3213(76)90507-1 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.