On harmonicity and Miao–Tam critical metrics in a perfect fluid spacetime

Abstract

The curvature properties of a perfect fluid spacetime have been studied when the Riemann curvature, the projective curvature, the concircular curvature, the conformal curvature and the conharmonic curvature tensors are, respectively, harmonic. In the flatness case, if the velocity vector of the fluid is torse-forming, we can completely characterize it. Also, we study the consequences of the existence of $$\eta $$ -Einstein, $$\eta $$ -Ricci and $$\eta $$ -Yamabe solitons in perfect fluid spacetime satisfying Miao–Tam critical metric condition.