# Spacetimes admitting quasi-conformal curvature tensor

Document Type : Research Paper

Authors

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

2 Department of Applied Mathematics‎, ‎Nanjing University of Science and Technology‎, ‎Nanjing 210094‎, ‎P‎. ‎R‎. ‎China.

3 Department of Pure Mathematics‎, ‎University of Calcutta‎, ‎35‎, ‎B‎. ‎C‎. ‎Road‎, ‎Kolkata 700019‎, ‎West Bengal‎, ‎India.

Abstract

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally 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 pacetime with‎ ‎vanishing quasi-conformal 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 behave‎ ‎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 in a purely electromagnetic distribution the spacetime with vanishing quasi-conformal curvature tensor is filled with‎ ‎radiation and extremely hot gases‎. ‎We also study dust-like fluid spacetime with vanishing quasi-conformal curvature tensor.

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### History

• Receive Date: 16 June 2015
• Revise Date: 09 September 2015
• Accept Date: 27 September 2015