Proof of the positive mass theorem. II (original) (raw)

Abstract

The positive mass theorem states that for a nontrivial isolated physical system, the total energy, which includes contributions from both matter and gravitation is positive. This assertion was demonstrated in our previous paper in the important case when the space-time admits a maximal slice. Here this assumption is removed and the general theorem is demonstrated. Abstracts of the results of this paper appeared in [11] and [13].

Access this article

Log in via an institution

Subscribe and save

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Arnowitt, R., Deser, S., Misner, C.: Phys. Rev.118, 1100 (1960b)
    Article Google Scholar
  2. Brill, D., Deser, S.: Ann. Phys.50, 548 (1968)
    Article Google Scholar
  3. Hawking, S., Ellis, S.: Cambridge: Cambridge University Press 1973
  4. Hoffman, D., Spruck, J.; CPAM27, 715–727 (1974)
    Google Scholar
  5. Jang, P.S.: On the positivity of energy in general relativity (to be published)
  6. Michael, J., Simon, L.: CPAM26, 361–379 (1973)
    Google Scholar
  7. Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966
    Google Scholar
  8. Schoen, R., Simon, L., Yau, S.T.: Acta Math.134, 275–288 (1975)
    Google Scholar
  9. Schoen, P., Yau, S.T.: Commun. Math. Phys.65, 45–76 (1979)
    Article Google Scholar
  10. Schoen, R., Yau, S.T.: The energy and the linear momentum of space-times in general relativity. Commun. Math. Phys. (to appear)
  11. Schoen, R., Yau, S.-T.: Phys. Rev. Lett.43, 159–183 (1979)
    Article Google Scholar
  12. York, J.: Energy and momentum of the gravitational field (to appear)
  13. Yau, S.-T.: The total mass and the topology of an asymptotically flat spacetime. In: The Chern Symposium 1979. Berlin, Heidelberg, New York: Springer 1980
    Google Scholar

Download references

Author information

Authors and Affiliations

  1. University of California, Berkeley, 94720, Berkeley, CA, USA
    Richard Schoen
  2. Institute for Advanced Study, 08540, Princeton, NJ, USA
    Shing-Tung Yau

Authors

  1. Richard Schoen
    You can also search for this author inPubMed Google Scholar
  2. Shing-Tung Yau
    You can also search for this author inPubMed Google Scholar

Additional information

Communicated by A. Jaffe

Rights and permissions

About this article

Cite this article

Schoen, R., Yau, ST. Proof of the positive mass theorem. II.Commun.Math. Phys. 79, 231–260 (1981). https://doi.org/10.1007/BF01942062

Download citation

Keywords