TY - JOUR
T1 - Lorentzian Manifolds Close to Euclidean Space
AU - Berestovskii, V. N.
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 -