Ricci and matter collineations in space-time
type: Item
instance of: scholarly article
title: Ricci and matter collineations in space-time
zbMATH Open document ID: 0862.53057
DOI: 10.1007/BF02106969
published in: General Relativity and Gravitation
publication date: 1996-05-12T00:00:00Z
review text: Let \(M\) be a spacetime manifold with Lorentz metric \(g\). Various symmetries arise in the exact solutions of Einstein's field equations given by \(G_{ab} \equiv R_{ab} - {1\over 2} Rg_{ab} = \kappa T_{ab}\), where \(G_{ab}\), \(R_{ab}\), and \(T_{ab}\) are components of the Einstein tensor, the Ricci tensor, and the matter (or energy-momentum) tensor, respectively. A vector field \(X\) on \(M\) is called a matter collineation if \({\mathfrak L}_X T_{ab} = 0\) and a Ricci collineation if \({\mathfrak L}_X R_{ab} = 0\). In this paper, the authors study Ricci and matter collineations. They give a mathematical description of their dimensionality, differentiability, extendibility etc., and construct examples of Ricci collineations in decomposable spacetimes.
reviewed by: Andrew Bucki
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83C05
zbMATH DE Number: 877795
zbMATH Keywords: symmetries
zbMATH Keywords: matter collineation
zbMATH Keywords: Ricci collineation
zbMATH Keywords: decomposable spacetimes
author: G. S. Hall
author: I. M. Roy
author: E. G. L. R. Vaz
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02106969
OpenAlex ID: W2090321536
description: scientific article; zbMATH DE number 877795