Determination of kerr congruences by algebraic methods in the theory of mapping of pseudo-Riemann into Riemann spaces

The spaces of general relativity theory are known to be pseudo-Riemannian. Sometimes, however, it is useful to transform to Riemann spaces of a definite signature (++++). The mapping of pseudo-Riemann spaces into Riemann spaces by means of a timelike congruence has been investigated by Mitskevich 1]. In the present article we elaborate certain aspects of the theory of such mappings; in particular, we introduce the concept of double mapping of a pseudo-Riemann space into Minkowski space and investigate methods for the determination of specific congruences in the example of the Kerr field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 50–53, January, 1982.