Bianchi and Weyl equations as sufficient equations for Einstein spaces
type: Item
instance of: scholarly article
title: Bianchi and Weyl equations as sufficient equations for Einstein spaces
zbMATH Open document ID: 0820.53027
DOI: 10.1007/BF02107960
author: S. Brian Edgar
published in: General Relativity and Gravitation
publication date: 1995-09-05T00:00:00Z
review text: The author assumes the Bianchi identities and the Weyl wave equations (in the form which they take for an Einstein space) for an arbitrary symmetric 4-spinor, with the background space being unspecified. It is then proven that -- in general -- the consistency of these equations demands that the background space be an Einstein space and that the arbitrary symmetric 4-spinor be the Weyl 4-spinor. In other words, the Bianchi identities and the Weyl wave equations are sufficient conditions for an Einstein space. The implications of this result for the Newman- Penrose and Geroch-Held-Penrose spin-coefficient formalisms are briefly discussed.
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 743928
zbMATH Keywords: Bianchi identity
zbMATH Keywords: spinor calculus
zbMATH Keywords: Weyl wave equations
zbMATH Keywords: Einstein space
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02107960
OpenAlex ID: W2090029379
description: scientific article; zbMATH DE number 743928