AbslracL An invariant characterization of warped spacetimes is given and a clauillcalion scheme for them is proposed. Some resuits on the cuvature StNCtUre (Petrov and Segre types of the Weyl and Ricci lensom) are given and a thomugh study of the hometry group that each class of warped spacetime may admit is carried out.
Matter collineations, as a symmetry property of the energy-momentum tensor Tab, are studied from the point of view of the Lie algebra of vector fields generating them. Most attention is given to space-times with a degenerate energy-momentum tensor. Some examples of matter collineations are found for dust fluids (including Szekeres's space-times), and null fluid space-times.
Although curvature collineations (curvature preserving transformations) have been studied within the context of general relativity for 20 years, there has been little attempt to study them systematically and there does not appear to have been a detailed mathematical investigation of their properties. This is the first of two papers that are intended as a contribution to this deficiency. This paper presents a discussion of the more general mathematical aspects of curvature collineations and suggests a program for studying them. The implementation of this program and the analysis of specific examples will be carried out in the second paper.
The existence of affine collineations in space-time is discussed and the types of space-time admitting proper affine collineations is displayed. The close connection between such space-times and their holonomy structure and local decomposability is established. Affine collineations with fixed points are also considered as is the problem of extending local affine collineations to the whole of space-time.
This paper is the second of a set of two papers on curvature collineations in general relativity. The first paper presented the mathematical basis of curvature collineations and a possible approach to their study. This paper continues from the first one by investigating in detail many of the cases where curvature collineations can occur in space-time. It is based on a classification of the curvature tensor which is discussed in the first paper and reviewed briefly here. This, together with the geometrical approach favored in this paper, leads to a rather general discussion of the problem which, it is hoped, does not obscure those physical aspects of the situation that are important in Einstein’s theory.
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