Almost Ricci solitons on pseudo Ricci symmetric spacetime

The purpose of this paper is to examine the geometric properties of an almost Ricci soliton on a pseudo Ricci symmetric spacetime that satisfies the Einstein field equation. Among other results, we first determine the soliton constant and the cosmological constant in terms of the scalar curvature and the potential vector field of the spacetime, assuming the scalar curvature is constant. Next, we show that the soliton is shrinking when the spacetime is either dust or dark space, and we prove that the soliton can never be steady on a pseudo Ricci symmetric spacetime with constant scalar curvature whose potential vector field is solenoidal. Furthermore, we establish that the soliton is shrinking when the potential vector field is anti-torqued on a pseudo Ricci symmetric spacetime. We also investigate R-harmonic pseudo Ricci symmetric spacetimes, showing that the associated soliton is shrinking and determining the corresponding cosmological constant. An explicit example is provided to establish the existence of an almost Ricci soliton on a pseudo Ricci symmetric spacetime. Finally, we examine the structure of almost Ricci solitons on conformally flat pseudo Ricci symmetric spacetimes that satisfy the Einstein field equations. In this setting, we compute the soliton constant and scalar curvature when the potential vector field is taken to be an anti-torqued vector field, and we derive the equation of state. We also determine the soliton constant and establish the strong energy condition in the case, where the spacetime admits a Ricci collineation.