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Spacetimes with killing tensors

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Abstract

For Einstein-Maxwell fields for which the Weyl spinor is of type {2, 2}, and the electromagnetic field spinor is of type {1, 1} with its principal null directions coaligned with those of the Weyl spinor, the integrability conditions for the existence of a certain valence two Killing tensor are shown to reduce to a simple criterion involving the ratio of the amplitude of the Weyl spinor to the amplitude of a certain test solution of the spin two zero restmass field equations. The charged Kerr solution provides an example of a spacetime for which the criterion is satisfied; the chargedC-metric provides an example for which it is not.

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References

  1. Penrose, R.: Structure of space-time. In: DeWitt, C., Wheeler, J. A. (Eds.): Battelle Rencontres. New York: W. A. Benjamin Inc. 1968.

    Google Scholar 

  2. Kozarzewski, B.: Acta Phys. Polon.27, 775 (1965).

    Google Scholar 

  3. Walker, M., Penrose, R.: Commun. math. Phys.18, 265 (1970).

    Google Scholar 

  4. Hughston, L. P., Penrose, R., Sommers, P., Walker, M.: Commun. math. Phys.27, 303 (1972).

    Google Scholar 

  5. Kinnersley, W. M.: TypeD gravitational fields (unpublished thesis, California Institute of Technology), (1969).

  6. Carter, B.: Phys. Rev.174, 1559 (1968).

    Google Scholar 

  7. Kinnersley, W. M., Walker, M.: Phys. Rev. D2, 1359 (1970).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics: Joseph Henry Laboratories, Princeton University, Princeton, New Jersey, USA

    Lane P. Hughston

  2. Division of Mathematics and Mathematical Physics, The University of Texas at Dallas, Dallas, Texas, USA

    Lane P. Hughston

  3. Magdalen College, Oxford, England

    Lane P. Hughston

  4. Center for Relativity Theory, The University of Texas at Austin, Austin, Texas, USA

    Paul Sommers

Authors
  1. Lane P. Hughston
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  2. Paul Sommers
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Additional information

This piece of work was completed, in part, during the authors' summer 1972 stays at The University of Texas at Dallas, Division of Mathematics and Mathematical Physics, the Max-Planck-Institut für Physik und Astrophysik in München, and the Black Hole session of the Ecole d'été de Physique Théorique in Les Houches; supported, in part, by the National Science Foundation, Grants GP-8868, GP-3463 9X, GP-20023, and GU-1598; the Air Force Office of Scientific Research, Grant 903-67; the National Aeronautics and Space Administration, Grant 44-004-001; the Westinghouse Corporation; the Clark Foundation; and the Rhodes Trust.

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Hughston, L.P., Sommers, P. Spacetimes with killing tensors. Commun.Math. Phys. 32, 147–152 (1973). https://doi.org/10.1007/BF01645652

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  • DOI: https://doi.org/10.1007/BF01645652

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