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

Abstract

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.