Author/Authors :
-، - نويسنده Department of Mathematics, Chakdaha College, P. O. Chakdaha,
Dist-Nadia, West Bengal, India. Mallick, S. , -، - نويسنده Department of Applied Mathematics, Nanjing University of Science and Technology,
Nanjing 210094, P. R. China. Zhao, P. , -، - نويسنده Department of Pure Mathematics, University of Calcutta, 35, B. C. Road,
Kolkata 700019, West Bengal, India. De, U. C.
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 Einsteinʹs field equation with cosmological constant is covariant constant. Next, we prove that if the perfect fluid pacetime with vanishing quasi-conformal curvature tensor obeys Einsteinʹs 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.
