Geometrical structure in a perfect fluid spacetime with conformal Ricci-Yamabe soliton

TL;DR

This paper explores the geometric structure of perfect fluid spacetimes with conformal Ricci-Yamabe solitons, deriving conditions for their expansion behavior and linking to physical models like Robertson-Walker spacetime.

Contribution

It introduces conditions for conformal Ricci-Yamabe solitons in perfect fluid spacetimes and connects these geometric structures to physical models such as Robertson-Walker spacetime.

Findings

Conditions for solitons to be expanding, steady, or shrinking.

Laplace equation derived from the soliton equation with gradient potential.

Applications to physics and gravity in cosmological models.

Abstract

The present paper is to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field {\xi} in connection with conformal Ricci-Yamabe metric and conformal {\eta}-Ricci-Yamabe metric. Here we have delineated the conditions for conformal Ricci-Yamabe soliton to be expanding, steady, or shrinking. Later, we have acquired Laplace equation from conformal {\eta}-Ricci-Yamabe soliton equation when the potential vector field {\xi} of the soliton is of gradient type. Lastly, we have designated perfect fluid with Robertson-Walker spacetime and some applications of physics and gravity.