Complex relativity and real solutions. IV: Perturbations of vacuum Kerr- Schild spaces
[For the review of part III, cf. Zbl 0579.53054.] In this paper the theory of integrable double Kerr-Schild spaces (IDKS) is examined. The vacuum field equations are shown to reduce to the single equation of \textit{J. F. Plebański} and \textit{I. Robinson} [Phys. Rev. Lett 37, 493 (1976)]. These metrics are given essentially in terms of one potential H. First-order perturbations of H lead to metric (gravitational) perturbations of vacuum algebraically degenerate spaces in a direct manner and give results in agreement with those of \textit{J. M. Cohen} and \textit{L. S. Kegeles} [Phys. Lett. A 47, 261 (1974); ibid. 54, 5 (1975), and Phys. Rev. D 19, 1641-1664 (1979)], \textit{B. G. Schmidt} and \textit{J. M. Stewart} [Proc. R. Soc. Lond., Ser. A 367, 503-525 (1979; Zbl 0425.35064)], \textit{S. A. Teukolsky} [Astrophys. J. 185, 635 (1973)], \textit{G. F. Torres del Castillo} [J. Math. Phys. 24, 590-596 (1983; Zbl 0513.53025), and ibid. 25, 342-346 (1984)], and others. Higher-order perturbations of H 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.
scientific article; zbMATH DE number 3986108