Geometry of almost conformal Ricci solitons on weakly Ricci symmetric spacetime

The aim of this paper is to study geometrical aspects of the almost conformal Ricci solitons on weakly Ricci symmetric perfect fluid spacetime obeying Einstein field equations. Among others, we first find the soliton constant and cosmological constant in weakly Ricci symmetric spacetime. Further, we find in weakly Ricci symmetric spacetime, the symmetry inheritance property of energy–momentum tensor and establish a relation between conformal and isotropic pressure for an almost conformal Ricci soliton. Next, we explain the equation of state for weakly Ricci symmetric spacetime, and we find the phase of universe for such spacetime under matter collineation condition and when there is dust matter, radiation era and dark matter of fluid is obtained with potential vector field as torse forming vector field. Also, we calculate the weakly Ricci symmetric spacetime admitting an almost conformal Ricci soliton is acceleration-free, vorticity free, shear-free when the potential vector field is torse forming vector field and we obtain some results for conformally flat weakly Ricci symmetric spacetime admitting an almost conformal Ricci soliton. Finally, the study of space-matter tensor and Einstein tensor on weakly Ricci symmetric spacetime admitting an almost conformal Ricci soliton with potential vector field as torse forming vector field is made.