A Note on the Geometry of RW Space-Times

A conformally flat GRW space-time is a perfect fluid RW space-time. In this note, we investigated the influence of many differential curvature conditions, such as the existence of recurrent and semi-symmetric curvature tensors. In each case, the form of the Ricci curvature tensor, the energy–momentu...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-03, Vol.11 (6), p.1440
Main Authors: Shenawy, Sameh, De, Uday Chand, Bin Turki, Nasser
Format: Article
Language:English
Subjects:
Curvature
Dark matter
Eigenvalues
Eigenvectors
Energy
Equations of state
Geometry
Mathematical analysis
Mathematical research
projective curvature tensor
Ricci recurrent
Ricci semi-symmetric
RW space-times
Space and time
Spacetime
Tensors
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Summary:A conformally flat GRW space-time is a perfect fluid RW space-time. In this note, we investigated the influence of many differential curvature conditions, such as the existence of recurrent and semi-symmetric curvature tensors. In each case, the form of the Ricci curvature tensor, the energy–momentum tensor, the energy density, the pressure of the fluid, and the equation of state are determined and interpreted. For example, it is demonstrated that a Ricci semi-symmetric RW space-time reduces to Einstein space-time or a Ricci recurrent RW space-time, and the perfect fluid space-time is referred to as Yang pure space-time or dark matter era.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11061440