Kerr-Schild rides again
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.
scientific article; zbMATH DE number 4092302
scientific article