Fluid space–times including electromagnetic fields admitting symmetry mappings belonging to the family of contracted Ricci collineations

Abstract

This paper investigates certain symmetry mappings belonging to the family of contracted Ricci collineations (FCRC) (satisfying gijℒRij=0) admitted by the general fluid space–times, including electromagnetic fields, that were classified and studied earlier by Stewart and Ellis (1967). Many of the results obtained are applicable to the perfect fluid models treated by Wainwright (1970) and Krasiński (1974,1975). A major part of this paper represents an extension of previous investigations (1976) of the Robertson–Walker metrics and more general perfect fluid space–times that admit FCRC symmetry mappings and concomitant conservation expressions. More specifically, these results provide a number of theorems relating to the more general fluid space–times that admit FCRC symmetry mappings (including both timelike and spacelike symmetry vectors) that lead to conservation expressions and specific conditions on the metric tensors for the given particular cases of these space–times. Also the form of the symmetry mappings induced on the electromagnetic fields (when they are present) is investigated in the case where specific symmetry mappings on the metric tensor are admitted. In particular, the results of Wainwright and Yaremovicz (1976) relating to homothetic motions admitted by given space–times, corresponding to perfect fluids including electromagnetic fields, are largely embraced by the more general results obtained in this paper.