Abstract
The aim of this paper is to study certain types of metrics such as conformal [Formula: see text]-Ricci soliton and Yamabe soliton in general relativistic spacetime. Here, we have shown the nature of the soliton when the spacetime with semisymmetric energy–momentum tensor admits conformal [Formula: see text]-Ricci soliton, whose potential vector field is torse-forming. We have studied certain curvature conditions on the spacetime that admits conformal [Formula: see text]-Ricci soliton. Also, we have enriched the importance of the Laplace equation on the spacetime admitting conformal [Formula: see text]-Ricci soliton. Next, we have given some applications of physical connection of dust fluid, dark fluid and radiation era on general relativistic spacetime admitting conformal [Formula: see text]-Ricci soliton and Yamabe soliton.