Communications in Mathematical Physics

, Volume 80, Issue 3, pp 381–402 | Cite as

A new proof of the positive energy theorem

  • Edward Witten


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 Schoen and Yau.) The relevance of these results to the stability of Minkowski space is discussed.


Neural Network Statistical Physic General Relativity Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Trautman, A.: Conservation laws in general relativity. In: Gravitation: an introduction to current research, Witten, L. (ed.). New York: Wiley 1962;Google Scholar
  2. 1a.
    Misner, C., Thorne, K.S., Wheeler, J.A.: Gravitation. San Francisco: W. H. Freeman 1973;Google Scholar
  3. 1b.
    Weinberg, S.: Gravitation and cosmology. New York: Wiley 1972Google Scholar
  4. 2.
    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.citGoogle Scholar
  5. 3.
    Weber, J., Wheeler, J.A.: Rev. Mod. Phys.29, 509 (1957)Google Scholar
  6. 4.
    Araki, H.: Ann. Phys. (N.Y.)7, 456 (1959);Google Scholar
  7. 4a.
    Brill, D.: Ann. Phys. (N. Y.)7, 466 (1959);Google Scholar
  8. 4b.
    Arnowitt, R., Deser, S., Misner, C.: Ann. Phys. (N.Y.)11, 116 (1960)Google Scholar
  9. 5.
    Brill, D., Deser, S.: Ann. Phys. (N.Y.)50, 548 (1968)Google Scholar
  10. 6.
    Brill, D., Deser, S., Faddeev, L.: Phys. Lett.26 A, 538 (1968)Google Scholar
  11. 7.
    Leibovitz, C., Israel, W.: Phys. Rev. D1, 3226 (1970);Google Scholar
  12. 7a.
    Misner, C.: In: astrophysics and general relativity, Chretien, M., Deser, S., Goldstein, J. (ed.). New York: Gordon and Breach 1971Google Scholar
  13. 8.
    Geroch, R.: Ann. N.Y. Acad. Sci.224, 108 (1973); Proc. Symp. Pure Math.27, 401 (1975)Google Scholar
  14. 9.
    O'Murchadha, N., York, J.W., Jr.: Phys. Rev. D10, 2345 (1974)Google Scholar
  15. 10.
    Jang, P.S.: J. Math. Phys.17, 141 (1976)Google Scholar
  16. 11.
    Leite, M.: Ph.D. Dissertation, MIT (1977) (unpublished)Google Scholar
  17. 12.
    Choquet-Bruhat, Y.: C.R. Acad. Sci.280, 169 (1975);Google Scholar
  18. 12a.
    Cantor, M., Fischer, A., Marsden, J., O'Murchadha, N., York, J.W., Jr.: Commun. Math. Phys.49, 187 (1976)Google Scholar
  19. 13.
    Choquet-Bruhat, Y., Marsden, J.: C.R. Acad. Sci.282, 609 (1976); Commun. Math. Phys.51, 283 (1976)Google Scholar
  20. 14.
    Deser, S., Teitelboim, C.: Phys. Rev. Lett.39, 249 (1977)Google Scholar
  21. 15.
    Grisaru, M.: Phys. Lett.73 B, 207 (1978)Google Scholar
  22. 16.
    Schoen, P., Yau, S.T.: Commun. Math. Phys.65, 45 (1979)Google Scholar
  23. 17.
    Jang, P.S.: J. Math. Phys.19, 1155 (1978)Google Scholar
  24. 18.
    Schoen, P., Yau, S.T.: Phys. Rev. Lett.43, 1457 (1979); Commun. Math. Phys. (to appear)Google Scholar
  25. 19.
    Schoen, P., Yau, S.T.: Phys. Rev. Lett.42, 547 (1979)Google Scholar
  26. 20.
    Gibbons, G.W., Hawking, S.W., Perry, M.J.: Nucl. Phys. B138, 141 (1978);Google Scholar
  27. 20a.
    Hawking, S.W.: Phys. Rev. D18, 1747 (1978);Google Scholar
  28. 20b.
    Page, D.N.: Phys. Rev. D18, 2733 (1978);Google Scholar
  29. 20c.
    Gibbons, G.W., Pope, C.N.: Commun. Math. Phys.66, 267 (1979)Google Scholar
  30. 21.
    Coleman, S.: Phys. Rev. D15, 2929 (1977);Google Scholar
  31. 21a.
    Coleman, S., Callan, C.G., Jr.: Phys. Rev. D16, 1762 (1977)Google Scholar
  32. 22.
    Perry, M.: Princeton Preprint, to appear in 1980 Nuffield workshop proc.;Google Scholar
  33. 22a.
    Gross, D.J., Perry, M., Yaffe, L.: Princeton Preprint (to appear)Google Scholar
  34. 23.
    Witten, E.: Princeton Preprint (to appear)Google Scholar
  35. 24.
    Lichnerowicz, A.: C.R. Acad. Sci. (Paris) A–B,257, 7 (1963);Google Scholar
  36. 24a.
    Hitchin, N.: Adv. Math.14, 1 (1974)Google Scholar
  37. 25.
    Ehlers, J., Kundt, W.: In Witten, L.: op.cit.Google Scholar
  38. 26.
    Geroch, R.: J. Math. Phys.11, 343 (1970)Google Scholar
  39. 27.
    Cremmer, E., Scherk, J.: Nucl. Phys. B103, 399 (1976)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Edward Witten
    • 1
  1. 1.Joseph Henry LaboratoriesPrinceton UniversityPrincetonUSA

Personalised recommendations