Geometrical Structure in a Perfect Fluid Spacetime with Conformal Ricci–Yamabe Soliton

Abstract

The present paper aims to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci–Yamabe metric and conformal η-Ricci–Yamabe metric. We delineate the conditions for conformal Ricci–Yamabe soliton to be expanding, steady or shrinking. We also discuss conformal Ricci–Yamabe soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid and radiation era. Furthermore, we design conformal η-Ricci–Yamabe soliton to find its characteristics in a perfect fluid spacetime and lastly acquired Laplace equation from conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type. Overall, the main novelty of the paper is to study the geometrical phenomena and characteristics of our newly introduced conformal Ricci–Yamabe and conformal η-Ricci–Yamabe solitons to apply their existence in a perfect fluid spacetime.