Recently, it was shown that the power-Maxwell (PM) theory could remove the singularity of the electric field (B. Eslam Panah, Europhys. Lett. 134, 20005 (2021)). Motivated by a great interest in three-dimensional black holes and a surge of success in studying massive gravity from both the cosmological and astrophysical points of view, we investigate three-dimensional black hole solutions in de Rham, Gabadadze, and Tolley massive theory of gravity in the presence of PM electrodynamics. First, we extract exact three-dimensional solutions in this theory of gravity. Then we study the geometrical properties of these solutions. Calculating conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics for these black holes. We also examine the stability of these black holes in the context of the canonical ensemble. We continue calculating this kind of black hole’s optical features, such as the photon orbit radius, the energy emission rate, and the deflection angle. Considering these optical quantities, finally, we analyze the effective role of the parameters of models on them.

最近，研究表明功率麦克斯韦（PM）理论可以消除电场的奇点（B. Eslam Panah, Europhys. Lett. 134, 20005 (2021)）。出于对三维黑洞的极大兴趣以及从宇宙学和天体物理学角度研究大质量引力的巨大成功，我们研究了德拉姆、加巴达泽和托利质量引力理论中的三维黑洞解决方案在存在 PM 电动力学的情况下。首先，我们在这个引力理论中提取精确的三维解。然后我们研究这些解的几何性质。通过计算守恒量和热力学量，我们检查了热力学第一定律对于这些黑洞的有效性。我们还在规范系综的背景下检查了这些黑洞的稳定性。我们继续计算这种黑洞的光学特征，如光子轨道半径、能量发射率、偏转角度等。考虑到这些光学量，最后我们分析了模型参数对其的有效作用。