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General Relativity and Gravitation

, Volume 5, Issue 1, pp 25–47 | Cite as

Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

  • Robert W. Lind
Research Articles

Abstract

The problem of finding algebraically special solutions of the vacuum Einstein-Maxwell equations is investigated using the spin coefficient formalism of Newman and Penrose. The general case, in which the degenerate null vectors are not hypersurface orthogonal, is reduced to a problem of solving five coupled differential equations that are no longer dependent on the affine parameter along the degenerate null directions.

It is shown that the most general regular, shearfree, nonradiating solution of these equations is the Kerr-Newman metric.

Keywords

Differential Equation Differential Geometry Special Solution Null Vector Couple Differential Equation 
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.

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References

  1. 1.
    Newman, E.T. and Penrose, R. (1962).J. Math. Phys.,3, 566.Google Scholar
  2. 2.
    Newman, E.T. and Unti, T. (1962).J. Math. Phys.,3, 891.Google Scholar
  3. 3.
    Lind, R., Messmer, J. and Newman, E.T. (1972).Phys. Rev. Lett.,28, 857.Google Scholar
  4. 4.
    Lind, R., Messmer, J. and Newman, E. T. (1972).J. Math. Phys.,13, 1879.Google Scholar
  5. 5.
    Lind, R. Messmer, J. and Newman, E. T. (1972).J. Math. Phys.,13, 1384.Google Scholar
  6. 6.
    Aronson, B., Lind, R., Messmer, J. and Newman, E.T. (1971).J. Math. Phys.,12, 2462.Google Scholar
  7. 7.
    Robinson, I. and Trautman, A. (1962).Proc. Roy. Soc.,A265, 462.Google Scholar
  8. 8.
    Newman, E.T. and Tamburino, L.A. (1962).J. Math. Phys.,3, 902.Google Scholar
  9. 9.
    Newman, E.T. and Posadas, R. (1969).Phys. Rev.,187, 1784.Google Scholar
  10. 10.
    Kerr, R.P. (1963).Phys. Rev. Lett.,11, 237.Google Scholar
  11. 11.
    Talbot, C.J. (1969).Commun. Math. Phys.,13, 45.Google Scholar
  12. 12.
    Debney, G.C., Kerr, R.P. and Schild, A. (1969).J. Math. Phys.,10, 1842.Google Scholar
  13. 13.
    Robinson, I. and Robinson, J. R. (1969).Int. J. Theor. Phys.,2, 231–242.Google Scholar
  14. 14.
    Robinson, I., Robinson, J.R. and Zund, J. D. (1969).J. Math. Mech.,18, 881.Google Scholar
  15. 15.
    Robinson, I., Schild, A. and Strauss, H. (1969).Int. J. Theor. Phys.,2, 243–245.Google Scholar
  16. 16.
    Newman, E.T., Couch, E., Chinnapared, K., Exton, A., Prakash, A. and Torrence, R. (1965).J. Math. Phys.,6, 918.Google Scholar
  17. 17.
    Newman, E.T. and Penrose, R. (1966).J. Math. Phys.,7, 863.Google Scholar
  18. 18.
    Goldberg, J.N., MacFarlane, A.J., Newman, E.T., Rohrlich, F. and Sudarshan, C.G. (1967).J. Math. Phys.,8, 2155.Google Scholar
  19. 19.
    Goldberg, J. N. and Sachs, R. (1962).Acta Phys. Pol.,22, Supplement, 13.Google Scholar
  20. 20.
    Lind, R.W. (1970). (Thesis), (University of Pittsburgh).Google Scholar
  21. 21.
    Forsyth, A.R. (1959).Theory of Differential Equations, Vol.5, (Dover Publications, Inc., New York), chapter III.Google Scholar
  22. 22.
    Held, A., Newman, E.T. and Posadas, R. (1970).J. Math. Phys.,11, 3145.Google Scholar
  23. 23.
    Derry, L., Isaacson, R. and Winicour, J. (1969).Phys. Rev.,185, 1647.Google Scholar

Copyright information

© Plenum Publishing Company Limited 1974

Authors and Affiliations

  • Robert W. Lind
    • 1
  1. 1.Department of PhysicsSyracuse UniversitySyracuse

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