We investigate the solutions of black holes in $f\left(T\right)$ gravity with nonlinear power-law Maxwell field, where $T$ is the torsion scalar in teleparallelism. In particular, we introduce the Lagrangian with diverse dimensions in which the quadratic polynomial form of $f\left(T\right)$ couples with the nonlinear power-law Maxwell field. We explore the leverage of the nonlinear electrodynamics on the space–time behavior. It is found that these new black hole solutions tend towards those in general relativity without any limit. Furthermore, it is demonstrated that the singularity of the curvature invariant and the torsion scalar is softer than the quadratic form of the charged field equations in $f\left(T\right)$ gravity and much milder than that in the classical general relativity because of the nonlinearity of the Maxwell field. In addition, from the analyses of physical and thermodynamic quantities of the mass, charge and the Hawking temperature of black holes, it is shown that the power-law parameter affects the asymptotic behavior of the radial coordinate of the charged terms, and that a higher-order nonlinear power-law Maxwell field imparts the black holes with the local stability.

我们研究了黑洞的解决方案 $F\left(吨\right)$ 具有非线性幂律麦克斯韦场的重力，其中 $吨$是遥平行中的扭转标量。特别地，我们引入了具有不同维度的拉格朗日函数，其中的二次多项式形式$F\left(吨\right)$与非线性幂律麦克斯韦场耦合。我们探索非线性电动力学对时空行为的影响。发现这些新的黑洞解无任何限制地趋向于广义相对论。此外，还证明了曲率不变量和扭转标量的奇异性比带电场方程的二次形式软$F\left(吨\right)$由于麦克斯韦场的非线性，引力比经典广义相对论温和得多。此外，从黑洞的质量、电荷和霍金温度的物理量和热力学量的分析表明，幂律参数影响带电项径向坐标的渐近行为，并且更高的阶非线性幂律麦克斯韦场赋予黑洞局部稳定性。