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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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