Perfect fluid spacetimes and gradient solitons

TL;DR

This paper explores perfect fluid spacetimes with concircular vector fields, revealing their geometric properties, characterizations, and conditions under which they admit various types of gradient solitons and symmetric tensors.

Contribution

It provides new characterizations of perfect fluid spacetimes with concircular vector fields, including their relation to generalized Robertson-Walker spacetimes and conditions for admitting gradient solitons.

Findings

Perfect fluid spacetimes with concircular vector fields are generalized Robertson-Walker spacetimes in 4D.

Certain symmetric tensors imply specific equations of state for the fluid.

Conditions under which these spacetimes admit Ricci and gradient solitons are established.

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.