TY - JOUR

T1 - Lorentzian Manifolds Close to Euclidean Space

AU - Berestovskii, V. N.

N1 - Publisher Copyright: © 2019, Pleiades Publishing, Ltd.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

KW - closed isotropic model

KW - density

KW - Einstein tensor

KW - energy-momentum tensor

KW - homothety group

KW - isometry group

KW - pressure

KW - Weyl tensor

UR - http://www.scopus.com/inward/record.url?scp=85064807004&partnerID=8YFLogxK

U2 - 10.1134/S0037446619020058

DO - 10.1134/S0037446619020058

M3 - Article

AN - SCOPUS:85064807004

VL - 60

SP - 235

EP - 248

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -