Foundations of Physics

, Volume 15, Issue 5, pp 605–616 | Cite as

Logarithmic asymptotic flatness

  • Jeffrey Winicour
Part II. Invited Papers Dedicated To Peter G. Bergmann


We present a general family of asymptotic solutions to Einstein's equation which are asymptotically flat but do not satisfy the peeling theorem. Near scri, the Weyl tensor obeys a logarithmic asymptotic flatness condition and has a partial peeling property. The physical significance of this asymptotic behavior arises from a quasi-Newtonian treatment of the radiation from a collapsing dust cloud. Practically all the scri formalism carries over intact to this new version of asymptotic flatness.


Radiation Dust General Family Asymptotic Behavior Asymptotic Solution 
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  1. 1.
    P. G. Bergmann,Phys. Rev. 124, 274 (1961).Google Scholar
  2. 2.
    P. G. Bergmann, Preface to “Quantization of Generally Covariant Field Theories,” ARL Technical report 63–56 (1963).Google Scholar
  3. 3.
    H. Bondi, M. G. J. Van der Burg, and A. W. K. Metzner,Proc. R Soc. London Ser. A 269, 21 (1962).Google Scholar
  4. 4.
    R. K. Sachs,Phys. Rev. 128, 2851 (1962).Google Scholar
  5. 5.
    R. Penrose,Phys. Rev. Lett. 10, 66 (1963).Google Scholar
  6. 6.
    R. Geroch, inAsymptotic Structure of Space-Time, F. P. Esposito and L. Witten, eds. (Plenum Press, New York, 1977).Google Scholar
  7. 7.
    A. Ashtekar and R. O. Hansen,J. Math. Phys. 19, 1542 (1978).Google Scholar
  8. 8.
    M. Alexander and P. G. Bergmann, inProceedings of the Third Annual Marcel Grossman Meeting, Hu Ning, ed. (Science Press, Princeton, 1983).Google Scholar
  9. 9.
    R. Geroch,J. Math. Phys. 9, 450 (1968).Google Scholar
  10. 10.
    D. Eardley and R. K. Sachs,J. Math. Phys. 14, 209 (1973).Google Scholar
  11. 11.
    P. Sommers,J. Math. Phys. 19, 549 (1978).Google Scholar
  12. 12.
    R. Beig and B. G. Schmidt,Commun. Math. Phys. 87, 65 (1982).Google Scholar
  13. 13.
    J. Centrella and A. L. Mellot,Nature (London) 305, 196 (1983).Google Scholar
  14. 14.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler, inGravitation (W. H. Freeman, San Francisco, 1973).Google Scholar
  15. 15.
    R. Penrose,Proc. R. Soc. London Ser. A 284, 159 (1965).Google Scholar
  16. 16.
    E. T. Newman and R. Penrose,J. Math. Phys. 3, 566 (1962).Google Scholar
  17. 17.
    J. M. Bardeen and W. H. Press,J. Math. Phys. 14, 7 (1973).Google Scholar
  18. 18.
    J. Porill and J. M. Stewart,Proc. R. Soc. London Ser. A 376, 451 (1981).Google Scholar
  19. 19.
    B. G. Schmidt and J. M. Stewart,Proc. R. Soc. London Ser. A 367, 503 (1979).Google Scholar
  20. 20.
    R. A. Isaacson, J. S. Welling, and J. Winicour, “An Extension of the Einstein Quadrupole Formula,”Phys. Rev. Lett. 53, 1870 (1984).Google Scholar
  21. 21.
    W. E. Couch and R. J. Torrence,J. Math. Phys. 13, 69 (1972).Google Scholar
  22. 22.
    S. Novak and J. N. Goldberg,Gen. Relativ. Gravit. 13, 79 (1981).Google Scholar
  23. 23.
    S. Novak and J. N. Goldberg,Gen. Relativ. Gravit. 14, 655 (1982).Google Scholar
  24. 24.
    S. Persides,J. Math. Phys. 20, 1731 (1979).Google Scholar
  25. 25.
    L. Tamburino and J. Winicour,Phys. Rev. 150, 1039 (1965).Google Scholar
  26. 26.
    A. Ashtekar,J. Math. Phys. 22, 2285 (1981).Google Scholar
  27. 27.
    J. N. Goldberg and R. P. Kerr,J. Math. Phys. 5, 172 (1964).Google Scholar
  28. 28.
    E. T. Newman and R. Penrose,Proc. R. Soc. London Ser. A 305, 175 (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Jeffrey Winicour
    • 1
  1. 1.Department of Physics and AstronomyUniversity of PittsburghPittsburgh

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