Abstract A massive particle orbiting around a regular black hole (e.g., a Bardeen one) provides a lot of information about the black hole, allowing one to investigate the problem of spacetime singularities and get an insight into quantum gravity. In the present work, the bound orbits of the particle around the Bardeen black hole have been established by using a taxonomy proposed by Levin and Perez-Giz. It clearly shows that, both in the innermost stable circular orbits (ISCO) and the marginally bound orbits (MBO), the particle’s angular momentum and its radial distance decrease with k ≡ g 2 , where g is a parameter of the Bardeen model and characterizes the monopole charge of a self-gravitating magnetic field described by a nonlinear electrodynamics. In the strong gravitational field, by using the numerical method, a rational number defined by the taxonomy increases with the particle’s energy, but the case of the angular momentum is opposite. The periodic motion in the Bardeen black hole has lower energy in comparison to the one in Schwarzschild black hole. It is expected that the Bardeen black hole could be identified by using the method of the taxonomy when more sophisticated observations for detecting black holes can be implemented in the future and it will give us an inspiring answer to the problems of spacetime singularities and quantum gravity.

中文翻译：

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巴丁黑洞周围的束缚轨道

摘要 围绕规则黑洞（例如巴丁黑洞）运行的大质量粒子提供了大量关于黑洞的信息，使人们能够研究时空奇点问题并深入了解量子引力。在目前的工作中，巴丁黑洞周围粒子的束缚轨道已通过使用莱文和佩雷斯-吉兹提出的分类法建立。它清楚地表明，在最内稳定圆轨道 (ISCO) 和边缘约束轨道 (MBO) 中，粒子的角动量及其径向距离都随着 k ≡ g 2 减小，其中 g 是 Bardeen 模型的参数并表征非线性电动力学描述的自引力磁场的单极电荷。在强引力场中，利用数值方法，分类法定义的有理数随着粒子能量的增加而增加，但角动量的情况相反。与史瓦西黑洞中的周期性运动相比，巴丁黑洞中的周期性运动具有较低的能量。预计当未来可以实现更复杂的黑洞探测观测时，可以使用分类学的方法识别巴丁黑洞，这将为我们解决时空奇点和量子引力问题提供一个鼓舞人心的答案。