h-Almost Conformal η-Ricci–Bourguignon Solitons and Spacetime Symmetry in Barotropic Fluids Within f(R,T) Gravity

We investigate the geometric and physical properties of the h-almost conformal η-Ricci–Bourguignon soliton and its gradient form by employing a barotropic equation of state within the framework of f(R,T) gravity. We derive this barotropic equation of state under the assumption that the matter content of f(R,T) gravity is modeled by a barotropic perfect fluid. We also examine the way in which these soliton structures both reveal and limit the underlying symmetries of the spacetime geometry. Furthermore, we obtain modified Poisson and Liouville equations associated with these solitons in such a gravitational setting. Additionally, we explore certain harmonic aspects of the h-almost conformal η-Ricci–Bourguignon soliton on a spacetime filled with a barotropic perfect fluid, considering a harmonic potential function Ψ. Finally, we present physical interpretations of the conformal pressure p˜ in the context of the h-almost conformal η-Ricci–Bourguignon soliton within f(R,T) gravity.