On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds

Graham Stanley Hall, D. P. Lonie

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper considers four-dimensional manifolds upon which there is a Lorentz metric It and a symmetric connection Gamma which are originally assumed unrelated. It then derives sufficient conditions on h and Gamma (expressed through the curvature tensor of Gamma) for Gamma to be the Levi-Civita connection of some (local) Lorentz metric g and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.

Original languageEnglish
Pages (from-to)2995-3010
Number of pages15
JournalJournal of Physics A: Mathematical and General
Volume39
DOIs
Publication statusPublished - 2006

Keywords

  • GENERAL-RELATIVITY
  • CURVATURE COLLINEATIONS
  • EINSTEIN SPACES
  • HOLONOMY GROUPS
  • TERMS
  • GIJ

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