Generalized \(\mathcal {Z}\)-Solitons on Magneto-Fluid Spacetimes in f(r)-Gravity

This research paper explores the characteristics of almost generalized \(\mathcal {Z}\)-solitons and almost gradient generalized \(\mathcal {Z}\)-solitons in the framework of magneto-fluid spacetime governed by f(r)-gravity. The investigation initiates with the derivation of the divergence of the almost generalized \(\mathcal {Z}\)-soliton vector field, articulated in relation to the scalar curvature pertinent to magneto-fluid spacetime in the context of f(r)-gravity. Following this, we employ the generalized \(\mathcal {Z}\)-soliton as a metric to delineate the essential conditions for the scalar curvature linked to this specific spacetime. Additionally, we determine the criteria under which the soliton can exhibit behaviors of shrinking, steady, or expanding.