Perfect fluid spacetimes and gradient solitons

• Main Authors: De, Krishnendu De Uday Chand, Syied, Abdallah Abdelhameed, Turki, Nasser Bin, Alsaeed, Suliman
• Format: Journal Article
• Language: English
• Published: 21-05-2022
• Subjects: Mathematics - Differential Geometry; Physics - General Relativity and Quantum Cosmology
• DOI: 10.48550/arxiv.2105.03149

Journal of Nonlinear Mathematical Physics, 29 (2022), 843-858 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.