General Relativity and Gravitation

, Volume 27, Issue 2, pp 223–231 | Cite as

Bianchi and Weyl equations as sufficient equations for Einstein spaces

  • S. Brian Edgar


When the Bianchi equation and the wave equation for the Weyl spinor are written in the form which they take for Einstein spaces, but with the symmetric 4-spinorΦ ABCD considered arbitrary and with the background space unspecified, ∇ EA′ ΦEBCD=0; (□+12λ)Φ ABCD −6Φ(AB EF (Φ CD )EF =0 it is shown that — in general — for this pair of equations to be consistent, the background space has to be an Einstein space, and the symmetric 4-spinorΦ ABCD has to be the Weyl spinor of this space.


Wave Equation Differential Geometry Einstein Space Weyl Spinor Background Space 
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  1. 1.
    Penrose, R., and Rindler, W. (1984).Spinors and Spacetime (Cambridge University Press, Cambridge), vol. 2.Google Scholar
  2. 2.
    Szekeres, P. (1963).Proc. Roy. Soc. Lond. 274A, 206.Google Scholar
  3. 3.
    Kilmister, C. W., and Newman, D. J. (1961).Proc. Cambridge Phil. Soc. 57, 851.Google Scholar
  4. 4.
    Stephenson, G. (1958).Nuovo Cimento 9, 263.Google Scholar
  5. 5.
    Yang, C. N. (1974).Phys. Rev. Lett. 33, 445.CrossRefGoogle Scholar
  6. 6.
    Szczyrba, V. (1987).Phys. Rev. D 36, 351.Google Scholar
  7. 7.
    Thompson, A. H. (1962).A Set of Alternative Field Equations for General Relativity. Ph.d. thesis, University of London.Google Scholar
  8. 8.
    White, P. (1969).The Role of the Bianchi Identities in General Relativity. Ph.d. thesis, University of London.Google Scholar
  9. 9.
    Bell, P., and Szekeres, P. (1972).Int. J. Theor. Phys. 6, 111.CrossRefGoogle Scholar
  10. 10.
    Buchdahl, H. A. (1958).Nuovo Cimento 10, 96.Google Scholar
  11. 11.
    Buchdahl, H. A. (1962).Nuovo Cimento 25, 486.Google Scholar
  12. 12.
    Newman, E. T., and Penrose, R. (1962).J. Math. Phys. 3, 566.CrossRefGoogle Scholar
  13. 13.
    Chandrasekhar, S. (1983).The Mathematical Theory of Black Holes (Clarendon Press, Oxford).Google Scholar
  14. 14.
    Edgar, S. B. (1990).J. Math. Phys. 31, 131.CrossRefGoogle Scholar
  15. 15.
    Geroch, R., Held, A., and Penrose, R. (1973).J. Math. Phys. 14, 874.CrossRefGoogle Scholar
  16. 16.
    Teukolsky, S. A. (1972).Phys. Rev. Lett. 29, 1114.CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • S. Brian Edgar
    • 1
  1. 1.Department of MathematicsUniversity of LinköpingLinköpingSweden

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