$LP$-Kenmotsu manifolds admitting almost $\ast$-Ricci-Bourguignon solitons and gradient almost $\ast$-Ricci-Bourguignon solitons

In this work, a solitonic study of $LP$-Kenmotsu $n$-manifolds (in brief $(LPK{)}_n$) was performed. Key properties of almost $\ast$-RBSs are established, thus generalizing some of the known results. Additionally, we examine gradient almost $\ast$-RBSs, thereby deriving conditions for the realization of the soliton structure. These results provide new insights into the theory of Ricci-Bourguignon solitons and geometric flows in semi-Riemannian manifolds. It is proven that an $(LPK{)}_n$ that admits an almost $\ast$-RBSs or a gradient almost $\ast$-RBSs is a generalized $\omega$-Einstein spacetime. Moreover, under certain assumptions, an $(LPK{)}_n$ that admits an almost $\ast$-RBSs or a gradient almost $\ast$-RBSs is a perfect fluid spacetime.