Geometric Classifications of Perfect Fluid Space-Time Admit Conformal Ricci-Bourguignon Solitons

This paper is dedicated to the study of the geometric composition of a perfect fluid space-time with a conformal Ricci-Bourguignon soliton, which is the extended version of the soliton to the Ricci-Bourguignon flow. Here, we have delineated the conditions for conformal Ricci-Bourguignon soliton to be expanding, steady, or shrinking. We have studied certain curvature conditions on the spacetime that admit conformal Ricci-Bourguignon soliton. We have also discussed conformal Ricci-Bourguignon soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid, and radiation era.