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On a type of spacetime

Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata 700019, West Bengal, India

E-mail Address: uc_de@yahoo.com

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Ljubica Velimirović

Department of Mathematics and Informatics, Faculty of Science and Mathematics, University of Niś, Visegradska 33, P. O. Box 202, 18000 Niś, Serbia

E-mail Address: ljubicavelimirovic@yahoo.com

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Sahanous Mallick

Department of Mathematics, Chakdaha College, P. O.-Chakdaha, Dist-Nadia, West Bengal, 741222, India

E-mail Address: sahanousmallick@gmail.com

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https://doi.org/10.1142/S0219887817500037Cited by:4 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 53C15, 53C25, 53C50

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