Complex relativity and real solutions. IV: Perturbations of vacuum Kerr- Schild spaces
type: Item
instance of: scholarly article
title: Complex relativity and real solutions. IV: Perturbations of vacuum Kerr- Schild spaces
zbMATH Open document ID: 0609.53025
DOI: 10.1007/BF00763452
author: M. S. Hickman
author: Colin B. G. McIntosh
published in: General Relativity and Gravitation
publication date: 1986-01-01T00:00:00Z
review text: [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.
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 83C20
zbMATH DE Number: 3986108
zbMATH Keywords: perturbation of solutions
zbMATH Keywords: Kerr-Schild spaces
zbMATH Keywords: field equations
zbMATH Keywords: vacuum solutions
MaRDI profile type: Publication
cites work: Zero rest-mass fields including gravitation: asymptotic behaviour
cites work: Null strings and Bianchi identities
cites work: Complex relativity and real solutions. I: Introduction
cites work: Complex relativity and real solutions. II: Classification of complex bivectors and metric classes
cites work: On extended conformal transformations of spinors and spinor equations
full work available at URL: https://doi.org/10.1007/bf00763452
OpenAlex ID: W2081209266
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description: scientific article; zbMATH DE number 3986108