%0 Journal Article
%T Spacetimes admitting quasi-conformal curvature tensor
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Mallick, S.
%A Zhao, P.
%A De, U. C.
%D 2016
%\ 12/18/2016
%V 42
%N 6
%P 1535-1546
%! Spacetimes admitting quasi-conformal curvature tensor
%K Quasi-conformal curvature tensor
%K Einstein space
%K perfect fluid spacetime
%K Einstein's field equation
%K energy momentum tensor
%R
%X 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.
%U http://bims.iranjournals.ir/article_908_ca47683e2d4c028ece8b6d5e9a07b102.pdf