A spacetime admitting semiconformal curvature tensor.

In the present paper, our main objective is to study spacetimes which admit a semiconformal curvature tensor. First, we prove that the energy-momentum tensor with vanishing semiconformal curvature tensor, satisfying Einstein's field equations (with cosmological constant), is covariantly constant. Next, we prove that if in a perfect fluid spacetime with divergence-free semiconformal curvature tensor satisfying Einstein field equations without cosmological constant, has constant pressure and density. Finally, we prove that if the perfect fluid spacetime has vanishing semiconformal curvature tensor satisfying Einstein field equations without cosmological constant, then the spacetime has constant energy density and isotropic pressure, and the perfect fluid always behaves as having a cosmological constant. [ABSTRACT FROM AUTHOR]