Characterization of general relativistic spacetime equipped with different types of solitons.

The aim of this paper is to study certain types of metrics such as conformal η -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 η -Ricci soliton, whose potential vector field is torse-forming. We have studied certain curvature conditions on the spacetime that admits conformal η -Ricci soliton. Also, we have enriched the importance of the Laplace equation on the spacetime admitting conformal η -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 η -Ricci soliton and Yamabe soliton. [ABSTRACT FROM AUTHOR]