It is shown that a general relativistic space-time with covariant-constant energy-momentum tensor is Ricci symmetric. Two particular types of such general relativistic space-times are considered and the nature of each is determined.

M C CHAKI

S RAY

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Space-times with covariant-constant energy-momentum tensor

International Journal of Theoretical Physics

The object of the present paper is to study a spacetime admitting conharmonic curvature tensor and some geometric properties related to this spacetime. It is shown that in a conharmonically flat spacetime with cyclic parallel Ricci tensor, the energy-momentum tensor is cyclic parallel and conversely. Finally, we prove that for a radiative perfect fluid spacetime if the energy-momentum tensor satisfying the Einstein's equations without cosmological constant is generalized recurrent, then the fluid has vanishing vorticity and the integral curves of the vector field U are geodesics. © 2017 World Scientific Publishing Company.

International Journal of Geometric Methods in Modern Physics

On a type of spacetime

The object of the present paper is to study spacetimes admitting pseudo-projective curvature tensor. At first we prove that a pseudo-projectively flat spacetime is Einstein and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying Einstein's field equation with cosmological constant is covariant constant. Next, we prove that if the perfect fluid spacetime with vanishing pseudo-projective curvature tensor obeys Einstein's field equation without cosmological constant, then the spacetime has constant energy density and isotropic pressure, and the perfect fluid always behaves as a cosmological constant and also such a spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field U. Moreover, it is shown that a pseudo-projectively flat spacetime satisfying Einstein's equation without cosmological constant for a purely electromagnetic distribution is an Euclidean space. We also prove that under certain conditions a perfect fluid spacetime with divergence-free pseudo-projective curvature is a Robertson-Walker spacetime and the possible local cosmological structure of such a spacetime is of type I, D or O. We also study dust-like fluid spacetime with vanishing pseudo-projective curvature tensor. © 2016 Author(s).

Fulltext

Journal of Mathematical Physics

A spacetime with pseudo-projective curvature tensor

The object of the present paper is to study weakly cyclic Z symmetric spacetimes. At first we prove that a weakly cyclic Z symmetric spacetime is a quasi Einstein spacetime. Then we study (WCZS) 4 spacetimes satisfying the condition div C= 0. Next we consider conformally flat (WCZS) 4 spacetimes. Finally, we characterise dust fluid and viscous fluid (WCZS) 4 spacetimes. © 2016, Akadémiai Kiadó, Budapest, Hungary.

Acta Mathematica Hungarica

On weakly cyclic Z symmetric spacetimes

The object of this paper is to study spacetimes admitting W 2-curvature tensor. At first we prove that a W2-flat spacetime is conformally flat and hence it is of Petrov type O. Next, we prove that if the perfect fluid spacetime with vanishing W2-curvature tensor obeys Einstein's field equation without cosmological constant, then the spacetime has vanishing acceleration vector and expansion scalar and the perfect fluid always behaves as a cosmological constant. It is also shown that in a perfect fluid spacetime of constant scalar curvature with divergence-free W 2-curvature tensor, the energy-momentum tensor is of Codazzi type and the possible local cosmological structure of such a spacetime is of type I, D or O. © 2014 World Scientific Publishing Company.

Spacetimes admitting W2-curvature tensor

We consider a conformally flat almost pseudo-Ricci symmetric spacetime. At first we show that a conformally flat almost pseudo-Ricci symmetric spacetime can be taken as a model of the perfect fluid spacetime in general relativity and cosmology. Next we show that if in a conformally flat almost pseudo-Ricci symmetric spacetime the matter distribution is perfect fluid whose velocity vector is the vector field corresponding to 1-form B of the spacetime, the energy density and the isotropic pressure are not constants. We also show that a conformally flat almost pseudo-Ricci symmetric spacetime is the Robertson-Walker spacetime. Finally we give an example of a conformally flat almost pseudo-Ricci symmetric spacetime with non-zero non-constant scalar curvature admitting a concircular vector field. © 2012 Springer Science+Business Media, LLC.

Journal	International Journal of Theoretical Physics
Publisher	Kluwer Academic/Plenum Publishers
ISSN	0020-7748