Abstract
The goal of the present study is to study the *-eta-Ricci soliton and gradient almost *-eta-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics. We demonstrate that a para-Kenmotsu metric as a *-eta-Ricci soliton is an Einstein metric if the soliton vector field is contact. Next, we discuss the nature of the soliton and discover the scalar curvature when the manifold admits a *-eta-Ricci soliton on a para-Kenmotsu manifold. After that, we expand the characterization of the vector field when the manifold satisfies the *-eta-Ricci soliton. Furthermore, we characterize the para-Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies the gradient almost *-eta-Ricci soliton.