The aim of the present article is to evaluate the motion of charged test particles in the vicinity of a near-extremal rotating black hole in the presence of magnetic fields. Euler-Lagrange motion equations and effective potential methods are used to characterize the motion out of the equatorial plane. Such approach is of peculiar significance if it is considered, e.g., accretion processes onto rotating black holes. In general investigations concerning accretion focus mostly on the simplest case of particles moving in the equatorial plane. Here it will be considered that particles initially moving around some particular orbit may be perturbed by a kick along the $\theta$ direction, giving rise to other possible orbits. We confirm the possibility that ultra high energy cosmic rays would be produced at the very center of AGNs, for a specific range of magnetic field magnitudes, since it is possible that ultra-high center-of-mass energies can be produced by particles colliding near the horizon of fastly rotating black holes.

中文翻译：

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来自嵌入磁场的近极值旋转黑洞的带电粒子加速

本文的目的是评估带电测试粒子在存在磁场的情况下在接近极值的旋转黑洞附近的运动。欧拉-拉格朗日运动方程和有效的潜在方法用于表征赤道平面外的运动。如果考虑到旋转黑洞的吸积过程，这种方法具有特殊的意义。一般来说，关于吸积的研究主要集中在最简单的粒子在赤道平面上移动的情况。这里将考虑到最初围绕某个特定轨道运动的粒子可能会受到沿 $\theta$ 方向的踢动的干扰，从而产生其他可能的轨道。我们确认了在 AGN 的正中心会产生超高能宇宙射线的可能性，