We obtained the solutions of Einstein’s Field Equations (EFEs) for locally rotationally symmetric (LRS) Bianchi type-I perfect fluid spacetimes through the concircular vector fields (CCVFs) in $f(T)$ gravity. It is shown that such metrics admit CCVFs of 4, 5, 6, 7, 8 and 15 dimensions. We also calculated the energy density, fluid pressure, torsion scalar $T$ and the form of the function $f(T)$. We did not specify the form of $f(T)$ for the solution of EFEs but found a particular form of $f(T)$ during the process of finding the CCVFs. It is observed that energy density and fluid pressure of some solutions are related as $p=-\rho$, which means that the universe represented by these spacetime metrics behaves like dark energy models. For other solutions, it is observed that the fluid pressure and energy density can remain positive for particular choices of the constants involved. Thus, in these cases the rate of expansion can slow down due to positive attractive effect. We also calculated the Hubble’s parameter ($H$), scalar expansion ($𝜃$), shear scalar (${\sigma }^2$), anisotropy parameter ($A_m$) and the deceleration parameter ($q$) associated with each of the obtained exact LRS Bianchi type-I solutions. It is observed that the physical behavior of the spacetime changes with the number of admitting CCVFs. A constant anisotropic behavior for 15-dimensional CCVFs is observed to change to isotropic nature for seven-dimensional CCVFs.

我们通过同圆矢量场 (CCVF) 获得了局部旋转对称 (LRS) Bianchi I 型完美流体时空的爱因斯坦场方程 (EFE) 的解$F（\mathrm{时间}）$重力。结果表明，此类指标允许 4、5、6、7、8 和 15 维的 CCVF。我们还计算了能量密度、流体压力、扭转标量$\mathrm{时间}$和函数的形式$F（\mathrm{时间}）$。我们没有指定具体的形式$F（\mathrm{时间}）$寻找 EFE 的解决方案，但发现了一种特殊形式$F（\mathrm{时间}）$在寻找 CCVF 的过程中。据观察，一些溶液的能量密度和流体压力之间的关系为$p=-\rho$，这意味着这些时空度量所代表的宇宙的行为类似于暗能量模型。对于其他解决方案，观察到流体压力和能量密度对于所涉及的常数的特定选择可以保持正值。因此，在这些情况下，由于积极的吸引力效应，扩张速度可能会减慢。我们还计算了哈勃参数（$H$), 标量展开 ($𝜃$), 剪切标量 (${\sigma }^2$), 各向异性参数 ($A_{米}$）和减速度参数（$q$）与每个获得的精确 LRS Bianchi I 型解相关。据观察，时空的物理行为随着接纳 CCVF 的数量而变化。观察到 15 维 CCVF 的恒定各向异性行为会变为 7 维 CCVF 的各向同性性质。