Perfect Fluid Spacetimes and Gradient Solitons

Abstract In this article, we investigate perfect fluid spacetimes equipped with concircular vector field. At first, in a spacetime admitting field, prove that the velocity field annihilates conformal curvature tensor. addition, dimension 4, show is generalized Robertson–Walker Einstein fibre. It proved if furnished admits second order symmetric parallel tensor P , then either equation of state characterized by $$p=\frac{3-n}{n-1} \sigma $$ p = 3 - n 1 σ or constant multiple metric Finally, The whose Lorentzian metrics are Ricci soliton, gradient Yamabe solitons, and m -quasi characterized.