Kerr-Schild rides again
type: Item
instance of: scholarly article
title: Kerr-Schild rides again
zbMATH Open document ID: 0667.53055
DOI: 10.1007/BF00756184
author: S. H. Smith
published in: General Relativity and Gravitation
publication date: 1989-01-01T00:00:00Z
review text: The Kerr-Schild metric is known to be algebraically special and \textit{R. Debever} [Bull. Cl. Sci., V. Sér., Acad. R. Belg. 62, 662-677 (1976; Zbl 0354.53020)] gave necessary and sufficient conditions for the metric to be of that form. The form was generalized [\textit{A. H. Thompson}, Tensor, New Ser. 17, 92-95 (1966; Zbl 0151.436)] by introducing a scalar multiplier. It is not known whether the Thompson version is algebraically special. Here it is shown that, if a metric is, and has an expanding degenerate principal vector and a preferred Killing vector, then it must be of Thompson type and under certain further conditions may be used as seed-metric in a Kerr-Schild transformation to generate new metrics.
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 83C15
zbMATH DE Number: 4092302
zbMATH Keywords: algebraically special
zbMATH Keywords: Killing vector
zbMATH Keywords: Thompson type
zbMATH Keywords: Kerr-Schild transformation
reviewed by: C. W. Kilmister
MaRDI profile type: Publication
cites work: An Approach to Gravitational Radiation by a Method of Spin Coefficients
cites work: A space-time calculus based on pairs of null directions
cites work: Killing vectors in empty space algebraically special metrics. I
cites work: Type D Vacuum Metrics
cites work: Q3896182
full work available at URL: https://doi.org/10.1007/bf00756184
OpenAlex ID: W1975016665
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description: scientific article; zbMATH DE number 4092302