Ricci‐Bourguignon Solitons With Certain Applications to Relativity

This article concerns with the investigation of Ricci‐Bourguignon solitons and gradient Ricci‐Bourguignon solitons in perfect fluid space‐times and generalised Robertson–Walker space‐times. First, we deduce the criterion for which the Ricci‐Bourguignon soliton in a perfect fluid space‐time is steady, expanding or shrinking. Then, we establish that if a perfect fluid space‐time of dimension four admits a gradient Ricci‐Bourguignon soliton with killing velocity vector, then either the space‐time represents phantom era or the gradient Ricci‐Bourguignon soliton is expanding or shrinking under some condition. Moreover, we illustrate that a generalised Robertson–Walker space‐time represents a perfect fluid space‐time if it admits the differential equations of Ricci‐Bourguignon solitons. Then, we establish that if a generalised Robertson–Walker space‐time allows a Ricci‐Bourguignon soliton of gradient type with constant scalar curvature, then it also represents a perfect fluid space‐time. Also, several interesting results are obtained as a corollary.