Abstract
In this paper the theory of integrable double Kerr-Schild (IDKS) spaces is examined. The vacuum field equations are shown to reduce to the single equation of Plebański and Robinson [20]. These metrics are given essentially in terms of one potentialH. First-order perturbations ofH lead to metric (gravitational) perturbations of vacuum algebraically degenerate spaces in a direct manner and give results in agreement with those of Cohen and Kegeles [6, 7, 8], Stewart [9], Teukolsky [5], Torres del Castillo [12, 13], and others. Higher-order perturbations ofH are also obtained with the view that, in the limit, these solutions should yield (new) exact vacuum solutions. The success of this construction lies in the (complex) geometric structure of IDKS spaces. This structure induces a natural splitting of the field equations which allows a potentialization of the perturbation (as well as the vacuum metric itself). It also allows massless spin 1/2 and 1 fields to be examined on the IDKS background in a similar manner.
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Hickman, M.S., McIntosh, C.B.G. Complex relativity and real solutions. IV. Perturbations of vacuum Kerr-Schild spaces. Gen Relat Gravit 18, 1275–1290 (1986). https://doi.org/10.1007/BF00763452
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DOI: https://doi.org/10.1007/BF00763452