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Single kerr-schild metrics: A double view

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Abstract

Real-vacuum single Kerr-Schild (ISKS) metrics are discussed and new results proved. It is shown that if the Weyl tensor of such a metric has a twist-free expanding principal null direction, then it belongs to the Schwarzschild family of metrics — there are no Petrov type-II Robinson-Trautman metrics of Kerr-Schild type. If such a metric has twist then it belongs either to the Kerr family or else its Weyl tensor is of Petrov type II. The main part of the paper is concerned with complexified versions of Kerr-Schild metrics. The general real ISKS metric is written in double Kerr-Schild (IDKS) form. TheH andl potentials which generate IDKS metrics are determined for the general vacuum ISKS metric and given explicitly for the Schwarzschild and Kerr families of metrics.

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Authors and Affiliations

  1. Mathematics Department, Monash University, 3168, Victoria, Clayton, Australia

    C. B. G. McIntosh & M. S. Hickman

  2. Department of Mathematics, Canterbury University, Christchurch, New Zealand

    M. S. Hickman

Authors
  1. C. B. G. McIntosh
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  2. M. S. Hickman
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McIntosh, C.B.G., Hickman, M.S. Single kerr-schild metrics: A double view. Gen Relat Gravit 20, 793–811 (1988). https://doi.org/10.1007/BF00758901

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  • DOI: https://doi.org/10.1007/BF00758901

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