Characterizations of a space-time admitting a generalized $\varphi(Ric)$-vector

Abstract

This study focuses on a generalized $\varphi(Ric)$-vector in space-times. We illustrate that a conformally flat space-time, which possesses a generalized $\varphi(Ric)$-vector that is a unit time-like vector, behaves as a perfect fluid and exhibits quasi-constant curvature under a certain condition.  Additionally, we establish that this space-time can be classified as both a generalized Robertson-Walker space-time and a Robertson-Walker space-time. Furthermore, we demonstrate that this space-time represents the quintessence phase. Then, we adopt the flat Friedmann-Robertson-Walker metric to derive Hubble, jerk, deceleration and snap parameters and we observe that the null, dominant and weak energy conditions are fulfilled, but the strong energy condition has failed. Finally, we scrutinize the space-time with the generalized $\varphi(Ric)$-vector in cases it admits Ricci solitons and generalized Ricci solitons.