Self-Similar Symmetry in LRS Bianchi-V Spacetime: A Study in <i>f</i> ( <i>T</i> ) Gravity with Physical Implications and Stability Analysis

This study investigates self-similar vector fields (SSVFs) in locally rotationally symmetric (LRS) Bianchi type-V spacetimes within the context of f(T) gravity with a perfect fluid matter source. Our findings demonstrate that certain spacetimes admit SSVFs of infinite, first, zeroth, and second kinds. To address the problem, we employ the Rif tree approach to transform symmetry and field equations via Maple, which generates constraints on spacetime functions that are subsequently used to determine the exact form of the SSVFs. Furthermore, we compute the physical quantitiesenergy density 𝜌, pressure p, torsion scalar T, and the torsion function f(T) for each solution. A detailed physical analysis of the most viable branches (2a, 5, and 9) is presented, including the graphical behavior of energy conditions, equation of state parameters, and cosmological implications. Our analysis reveals that the obtained solutions exhibit transitions from deceleration to acceleration, satisfy weak and dominant energy conditions, and provide viable descriptions of late-time cosmic acceleration consistent with observational constraints. Furthermore, stability analysis for (2a, 5, and 9) are also computed.