Perfect Fluid Spacetimes and Gradient Solitons
Krishnendu De, Uday Chand De, Abdallah Abdelhameed Syied, Nasser Bin Turki, Suliman Alsaeed
Abstract
Abstract In this article, we investigate perfect fluid spacetimes equipped with concircular vector field. At first, in a perfect fluid spacetime admitting concircular vector field, we prove that the velocity vector field annihilates the conformal curvature tensor. In addition, in dimension 4, we show that a perfect fluid spacetime is a generalized Robertson–Walker spacetime with Einstein fibre. It is proved that if a perfect fluid spacetime furnished with concircular vector field admits a second order symmetric parallel tensor P , then either the equation of state of the perfect fluid spacetime is characterized by $$p=\frac{3-n}{n-1} \sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>-</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfrac> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> , or the tensor P is a constant multiple of the metric tensor. Finally, 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, are characterized.