Local and global algebraic structures in general relativity
type: Item
instance of: scholarly article
title: Local and global algebraic structures in general relativity
zbMATH Open document ID: 0682.53090
DOI: 10.1007/BF00670208
published in: International Journal of Theoretical Physics
publication date: 1989-01-01T00:00:00Z
review text: Two important questions are considered. First, to what extent is the Petrov classification and related canonical forms smooth over the manifold if the tensor is? No surprises here; everything is as one might have thought. Second, suppose a smooth, symmetric second-order tensor has the same algebraic type at all points and has all real eigenvalues. Then the first problem shows that these eigenvalues are global smooth functions. But are there global, smooth eigenvectors ? Roughly, yes, if the manifold is simply connected (and the same for the Weyl tensor) so the topology of a manifold supporting certain types of energy tensor/Weyl tensor is restricted.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83C40
zbMATH DE Number: 4117436
zbMATH Keywords: global field
zbMATH Keywords: Petrov classification
zbMATH Keywords: second-order tensor
zbMATH Keywords: algebraic type
author: G. S. Hall
author: Alan D. Rendall
reviewed by: C. W. Kilmister
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00670208
OpenAlex ID: W2056945176
description: scientific article; zbMATH DE number 4117436