Self-Similar Vector Fields and Curvature Properties of Bianchi Type V Spacetime with Imperfect Fluid Sources

This paper explores self-similar vector fields (SSVFs) of Bianchi type V spacetime using the Rif tree approach. The symmetry equations governing the SSVFs are systematically solved to derive the explicit form of the metric coefficients and vector fields, classifying the SSVFs into various kinds. Unlike the conventional method of directly integrating the symmetry equations, the Rif tree approach ensures a comprehensive classification of the spacetime under consideration. Additionally, the curvature properties of the derived metrics are explored by finding their corresponding Kretschmann and Gauss-Bonnet invariants. These invariants provide insight into the total curvature and the geometric characteristics of spacetime, revealing the influence of temporal and spatial expansions. Moreover, the Einstein's field equations with an imperfect fluid source are applied to the obtained metrics, revealing specific physical properties such as energy density, pressure, and equation of state.