Perfect fluid spacetimes and gradient solitons

Abstract

This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal curvature tensor and in dimension 4, a perfect fluid spacetime is a generalized Robertson-Walker spacetime with Einstein fibre. Moreover, we prove that if a perfect fluid spacetime equipped with concircular vector field admits a second order symmetric parallel tensor, then either the state equation of the perfect fluid spacetime is characterized by $p=\frac{3-n}{n-1}\sigma$ , or the tensor is a constant multiple of the metric tensor. We also characterize the perfect fluid spacetimes with concircular vector field whose Lorentzian metrics are Ricci soliton, gradient Ricci soliton, gradient Yamabe solitons and gradient $m$-quasi Einstein solitons, respectively.

More authors are added in the new version and many mistakes are considered and corrected

References in corpus (5)

• A simple characterization of generalized Robertson-Walker spacetimes
• Cosmology with a stiff matter era
• Generalized Robertson-Walker space times, a survey
• Solitons and geometrical structures in a perfect fluid spacetime
• A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time

Cited by in corpus (5)

• Perfect fluid spacetimes and $k$-almost yamabe solitons
• Almost co-Kähler manifolds and $(m,\rho )$-quasi-Einstein solitons
• Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons
• Characterizations of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons
• Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection