Metrics admitting SSVFs.

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.

本研究在f(T)引力（f(T) gravity）的框架下，探讨了局域旋转对称Bianchi I型时空的自相似矢量场，并将理想流体作为物质源纳入研究范畴。分析表明，部分包含理想流体的时空可容许无穷阶、一阶、零阶及二阶自相似矢量场。为解决该研究问题，本研究采用了Rif树方法。在此方法中，借助Maple软件对对称性方程与场方程进行变换，生成了一组针对时空函数的约束条件；随后利用这些约束条件求解对称性方程，最终得到自相似矢量场的精确形式。此外，本研究针对每一组解计算了能量密度ρ、压强p、挠率标量T以及基于挠率的函数f(T)等物理量，以全面阐释该时空的物理与几何属性。同时，针对导出的度规所关联的运动学变量也开展了计算。本研究的结论在宇宙学、天体物理学以及修正引力理论中具备重要应用价值，尤其可用于宇宙演化、黑洞形成与各向异性时空结构的建模工作。本次研究所得到的f(T)引力下分类自相似解，有助于深化对引力坍缩、早期宇宙动力学以及天体物理天体稳定性问题的理解。