General Relativity and Gravitation

, Volume 30, Issue 3, pp 473–495 | Cite as

Yang's Gravitational Theory

  • Brendan S. Guilfoyle
  • Brien C. Nolan


Yang's pure space equations generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations with common energy-momentum tensors.



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yang, C. N. (1974). Phys. Rev. Lett.33, 445.Google Scholar
  2. 2.
    Pavelle, R. (1974). Phys. Rev. Lett.33, 1461.Google Scholar
  3. 3.
    Pavelle, R. (1975). Phys. Rev. Lett.34, 1114.Google Scholar
  4. 4.
    Thompson, A. H. (1975). Phys. Rev. Lett.35, 320.Google Scholar
  5. 5.
    Thompson, A. H. (1975). Phys. Rev. Lett.34, 507.Google Scholar
  6. 6.
    Ni, W.-T. (1975). Phys. Rev. Lett.35, 319.Google Scholar
  7. 7.
    Chen-lung, C., Han-ying, G., Shi, C., and Zuo-xiu, H. (1976). Acta Astr. Sinica17, 147.Google Scholar
  8. 8.
    Chen-lung, C., Han-ying, G., Shi, C., and Zuo-xiu, H. (1977). Chinese Astronomy1, 292.Google Scholar
  9. 9.
    Aragone, C., and Restuccia, A. (1978). Gen. Rel. Grav.9, 409.Google Scholar
  10. 10.
    Mielke, E. W. (1981). Gen. Rel. Grav.13, 175.Google Scholar
  11. 11.
    Baekler, P., Hehl, F. W., and Mielke, E. W. (1982). In Proc. II Marcel Grossmann meeting in General Relativity, R. Ruffini, ed. (North Holland Publishing Company, Amsterdam), p. 413.Google Scholar
  12. 12.
    Maluf, J. (1988). Class. Quantum Grav.5, L81.Google Scholar
  13. 13.
    Maluf, J. (1991). J. Math. Phys.32, 1556.Google Scholar
  14. 14.
    Szczyrba, V. (1987). Phys. Rev. D36, 351.Google Scholar
  15. 15.
    van Putten, M. H. P. M. (1994). In Proc. November 6-8 Meeting of the Grand Challenge Alliance on Black Hole Collisions, E. Seidel, ed. (NCSA).Google Scholar
  16. 16.
    Kundt, W. (1961). Z. Phys. 163, 77.Google Scholar
  17. 17.
    Herlt, E., Kramer, D., MacCallum, M. and Stephani, H. (1980). Exact Solutions of Einstein's Equations, E. Schmutzer, ed. (Cambridge University Press, Cambridge).Google Scholar
  18. 18.
    Penrose, R., and Rindler, W. (1982). Spinors and Spacetime(Cambridge University Press, Cambridge).Google Scholar
  19. 19.
    Hall, G. S. (1982). The Classification of Second Order Symmetric Tensors in General Relativity Theory(Banach Center Publications, Vol. 12. Polish Scientific Publishers, Warsaw).Google Scholar
  20. 20.
    Lichnerowicz, A. (1967). Relativistic Hydrodynamics and Magnetohydrodynamics(Benjamin, New York).Google Scholar
  21. 21.
    Foures-Bruhat, Y. (1952). Acta Math.88, 141.Google Scholar
  22. 22.
    Hughes, T., Kato, T., and Marsden, J. (1976). Arch. Rat. Mech. and Anal.63, 276.Google Scholar
  23. 23.
    Choquet-Bruhat, Y., and York, J. (1997). In Gravitation, Electromagnetism and Geometric Structures, G. Ferrarese, ed. (Pythagora Editrice, Bologna).Google Scholar
  24. 24.
    Kerner, R. (1974). Ann. Inst. H. PoincaréXX.3, 279.Google Scholar
  25. 25.
    Eardley, D. M., and Moncrief, V. (1982). Commun. Math. Phys.83, 171.Google Scholar
  26. 26.
    Eardley, D. M., and Moncrief, V. (1982). Commun. Math. Phys.84, 193.Google Scholar
  27. 27.
    Klainerman, S., and Machedon, M. (1995). Ann. Math.142, 39.Google Scholar
  28. 28.
    Hawking, S. W., and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time(Cambridge University Press, Cambridge).Google Scholar
  29. 29.
    Choquet-Bruhat, Y., and Paneitz, S. M., and Segal, I. E. (1983). J. Funct. Anal.53, 112.Google Scholar
  30. 30.
    Yang, Y. (1990). J. Math. Phys.31, 1237.Google Scholar
  31. 31.
    Choquet-Bruhat, Y., Christodoulou, D., and Francavi glia, M. (1978). Ann. Inst. H. Poin caréXXIX.3, 241.Google Scholar
  32. 32.
    Guilfoyle, B. (1997). “The Cauchy initial value problem for Yang-Mills metrics”. PhD thesis, University of Texas at Austin.Google Scholar
  33. 33.
    Krasiński, A. (1997). In homogeneous cosmological models(Cambridge University Press, Cambridge).Google Scholar
  34. 34.
    Ellis, G. F. R. (1971). In Proc. International School of Physics “Enrico Fermi,” XLVII-General Relativity and Cosmology (Varenna, 30 June-12 July 1969), B. K. Sachs, ed. (Academic Press, New York).Google Scholar
  35. 35.
    Pavelle, R. (1976). Phys. Rev. Lett.37, 961.Google Scholar
  36. 36.
    Trautman, A. (1979). Bull. Acad. Polon. Sci. Series 9, Sci. Phys. Astronom.27, 7.Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Brendan S. Guilfoyle
  • Brien C. Nolan

There are no affiliations available

Personalised recommendations