Lorentzian Manifolds Close to Euclidean Space

V. N. Berestovskii

Research output: Contribution to journalArticlepeer-review

Abstract

We study the Lorentzian manifolds M 1 , M 2 , M 3 , and M 4 obtained by small changes of the standard Euclidean metric on ℝ 4 with the punctured origin O. The spaces M 1 and M 4 are closed isotropic space-time models. The manifolds M 3 and M 4 (respectively, M 1 and M 2 ) are geodesically (non)complete; M 1 are M 4 are globally hyperbolic, while M 2 and M 3 are not chronological. We found the Lie algebras of isometry and homothety groups for all manifolds; the curvature, Ricci, Einstein, Weyl, and energy-momentum tensors. It is proved that M 1 and M 4 are conformally flat, while M 2 and M 3 are not conformally flat and their Weyl tensor has the first Petrov type.

Original languageEnglish
Pages (from-to)235-248
Number of pages14
JournalSiberian Mathematical Journal
Volume60
Issue number2
DOIs
Publication statusPublished - 1 Mar 2019

Keywords

  • closed isotropic model
  • density
  • Einstein tensor
  • energy-momentum tensor
  • homothety group
  • isometry group
  • pressure
  • Weyl tensor

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