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Expansion-free Kerr-Schild fields

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Lettere al Nuovo Cimento (1971-1985)

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References

  1. R. P. Kerr andA. Schild:Atti del Convegno sulla Relatività Generale: Problemi dell’Energia e Onde Gravitazionali (Firenze, 1965), p. 173. This treatment assumedl μ had nonzero complex expansion but did allow zero complex expansion for another eigendirection different froml μ.

  2. G. Debney, R. P. Kerr andA. Schild:Journ. Math. Phys.,10, 1842 (1969).

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  3. Tetrad components of objects are denoted by Latin letters, whereas co-ordinate components are denoted by Greek letters. The tensor calculus on tetrad components is very nearly that of the classical type, with some notable exceptions involving symmetric and antisymmetric operations. See, for example, ref. (2).

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  4. See, for example, ref. (2).

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  5. J. N. Goldberg andR. K. Sachs:Acta Phys. Polon.,22, 13 (1962).

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  6. See, for exmaple,S. Sternberg:Lectures on Differential Geometry (Englewood Cliffs, N. J., 1964), p. 134.

  7. Note that, even though the transformation (15) is noninertial,\(\alpha \alpha + \varrho v = \zeta \bar \zeta + uv\).

  8. The splitting ofg μν =η μν +l μ l ν into two parts is invariant with respect to co-ordinate transformations.

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  1. G. Debney

    Present address: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Va

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    1. G. Debney
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    Debney, G. Expansion-free Kerr-Schild fields. Lett. Nuovo Cimento 8, 337–341 (1973). https://doi.org/10.1007/BF02724591

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