Ricci and matter collineations of locally rotationally symmetric space-times

Abstract

A new method is presented for the determination of Ricci Collineations (RC) and Matter Collineations (MC) of a given spacetime, in the cases where the Ricci tensor and the energy momentum tensor are non-degenerate and have a similar form with the metric. This method reduces the problem of finding the RCs and the MCs to that of determining the KVs whereas at the same time uses already known results on the motions of the metric. We employ this method to determine all hypersurface homogeneous locally rotationally symmetric spacetimes, which admit proper RCs and MCs. We also give the corresponding collineation vectors.

arXiv comment21 pages, Latex; to appear in General Relativity and Gravitation

References in corpus (4)

• Computation of the conformal algebra of 1+3 decomposable spacetimes
• Hypersurface homogeneous locally rotationally symmetric spacetimes admitting conformal symmetries
• Kinematic self-similar locally rotationally symmetric models
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Cited by in corpus (10)

• Symmetries of the Energy-Momentum Tensor of Cylindrically Symmetric Static Spacetimes
• Conformal Ricci collineations of static spherically symmetric spacetimes
• Generalized Self-similar Scalar-Tensor Theories
• Conformal symmetries of the energy-momentum tensor of spherically symmetric static spacetimes
• Symmetries of Locally Rotationally Symmetric Models
• Homothetic Motion in a Bianchi Type-I Model in Lyra Geometry
• Note on Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes
• Matter Inheritance Symmetries of Spherically Symmetric Static Spacetimes
• About Bianchi I with VSL
• Addendum: Symmetries of the energy-momentum tensor