Classification of Static Plane Symmetric Spacetimes according to their Matter Collineations

Abstract

In this paper we classify static plane symmetric spacetimes according to their matter collineations. These have been studied for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It turns out that the non-degenerate case yields either {\it four}, {\it five}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. There exists three interesting cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either {\it four}, {\it six} or {\it ten

arXiv comment15 pages, LaTex, no figures

References in corpus (3)

• Matter collineations of Spacetime Homogeneous Gödel-type Metrics
• Symmetries of Bianchi I space-times
• Symmetries of the Energy-Momentum Tensor of Spherically Symmetric Lorentzian Manifolds

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• Kinematic Self-Similar Plane Symmetric Solutions
• Symmetries of the Energy-Momentum Tensor: Some Basic Facts
• Matter Inheritance Symmetries of Spherically Symmetric Static Spacetimes
• Expanding, shearing and accelerating isotropic plane symmetric universe with conformal Kasner geometry
• Comments on matter collineations of plane symmetric, cylindrically symmetric and spherically symmetric spacetimes
• Addendum: Symmetries of the energy-momentum tensor