Gradient Ricci Bourguignon solitons on perfect fluid space-times

Abstract

The main purpose of the present paper is about characterizing the properties of the perfect fluid space-time that admits the gradient Ricci-Bourguignon soliton. This gives some results about the stability of the energy-momentum tensor and also under some conditions pursues that a perfect fluid space-time is Ricci symmetric. As a special case, when a perfect fluid space-time is equipped with the Ricci-Bourguignon soliton which has Ricci biconformal vector field, we show that the metric of this space is Einstein.

Keywords

• perfect‏ ‎fluid space-time
• gradient ricci soliton
• gradient ricci bourguignon soliton
• grw space-time