Classification of LRS Bianchi-I spacetime in context of f(T) gravity via its self-similar symmetry.

This study investigates self-similar vector fields of locally rotationally symmetric Bianchi type-I spacetimes within the framework of f(T) gravity, incorporating a perfect fluid as the matter source. The analysis demonstrates that certain spacetimes with a perfect fluid admit self-similar vector fields of infinite, first, zeroth, and second kinds. To address this problem, the Rif tree approach has been employed. In this method, the symmetry and field equations are transformed using Maple, which generates a set of constraints on the spacetime functions. These constraints are then applied to solve the symmetry equations, ultimately yielding the exact form of the self-similar vector field. Furthermore, the physical quantities-energy density ρ, pressure p, torsion scalar T, and torsion-based function f(T)-are calculated for each solution, providing a comprehensive understanding of the physical and geometric properties of the spacetime. In addition, the kinematic variables associated with the derived metrics have also been calculated. The findings of this study have significant applications in cosmology, astrophysics, and modified gravity theories, particularly in modeling cosmic evolution, black hole formation, and anisotropic spacetime structures. The classified self-similar solutions in f(T) gravity contribute to understanding gravitational collapse, the dynamics of the early universe, and the stability of astrophysical objects.