The generic condition is generic
type: Item
instance of: scholarly article
title: The generic condition is generic
zbMATH Open document ID: 0783.53015
DOI: 10.1007/BF00759194
author: John K. Beem
author: Steven (Stacey) G. Harris
published in: General Relativity and Gravitation
publication date: 1993-12-12T00:00:00Z
review text: The authors study the usual genericity condition in general relativity for vectors at a given point of a Lorentz manifold. A vector \(X \neq 0\) is called generic if \(X^ cX^ dX_{[a}R_{b]cd[e}X_{f]}\neq 0\). This condition holds in an open, dense set of vectors. Their main result is that in a 4-dimensional Lorentz manifold the Riemann tensor vanishes (at the given point) if there are 5 non-null vectors in general position which are all non-generic. In the case that the Ricci tensor satisfies \(\text{Ric} = \lambda g\) for some \(\lambda\in\mathbb{R}\) at this point 3 linearly independent, timelike vectors (or 5 distinct non-zero null vectors) which are non-generic are sufficient to conclude that the Riemann tensor vanishes at the given point. These (and related results) are proved with the methods of linear algebra.
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 83C75
Mathematics Subject Classification ID: 15A99
zbMATH DE Number: 465601
zbMATH Keywords: genericity condition
zbMATH Keywords: general relativity
zbMATH Keywords: Lorentz manifold
zbMATH Keywords: Riemann tensor
zbMATH Keywords: Ricci tensor
zbMATH Keywords: linear algebra
reviewed by: Marcus Kriele
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 465601