Three-dimensional spacetimes of maximal order

We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is sharp by exhibiting a class of 3D Lorentzian manifolds which realize this bound. The analysis is based on a three-dimen...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 30; no. 9; pp. 95004 - 25
Main Authors Milson, R, Wylleman, L
Format Journal Article
LanguageEnglish
Published IOP Publishing 07.05.2013
Subjects
Derivatives
Equivalence
Formalism
invariant classification
Karlhede bound
Manifolds
Mathematical analysis
maximal order
Quantum gravity
Tensors
Three dimensional
three-dimensional spacetimes
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Summary:We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is sharp by exhibiting a class of 3D Lorentzian manifolds which realize this bound. The analysis is based on a three-dimensional analogue of the Newman-Penrose formalism, and spinorial classification of the three-dimensional Ricci tensor.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/30/9/095004