In Bahamonde etal (2019 arXiv:1907.10858 [gr-qc]), a spherically symmetric black hole (BH) was derived from the quadratic form of f(T). Here we derive the associated energy, invariants of curvature, and torsion of this BH and demonstrate that the higher-order contribution of torsion renders the singularity weaker compared with the Schwarzschild BH of general relativity (GR). Moreover, we calculate the thermodynamic quantities and reveal the effect of the higher-order contribution on these quantities. Therefore, we derive a new spherically symmetric BH from the cubic form of , where ϵ ≪ 1, α, and β are constants. The new BH is characterized by the two constants α and β in addition to ϵ. At ϵ = 0 we return to GR. We study the physics of these new BH solutions via the same procedure that was applied for the quadratic BH. Moreover, we demonstrate that the contribution of the higher-order torsion, , may afford an interesting physics.

在 Bahamonde等人(2019 arXiv:1907.10858 [gr-qc]) 中，从f ( T )的二次形式导出了一个球对称黑洞 (BH )。在这里，我们推导出该 BH 的相关能量、曲率不变量和扭转，并证明与广义相对论 (GR) 的 Schwarzschild BH 相比，扭转的高阶贡献使奇点更弱。此外，我们计算了热力学量并揭示了高阶贡献对这些量的影响。因此，我们从 的三次形式推导出一个新的球对称 BH ，其中ϵ ≪ 1、α和β是常数。新 BH 的特点是两个常数除了ϵ之外，还有α和β。在ϵ = 0 时，我们回到 GR。我们通过应用于二次 BH 的相同程序研究这些新 BH 解的物理特性。此外，我们证明了高阶扭转的贡献，可以提供一个有趣的物理。