The orbital dynamics in a black hole spacetime can give us a chance to get deep insight into quantum gravity and fundamental physics. In this paper, we mainly focus on a massive particle’s motion around a quantum-corrected Schwarzschild black hole. In order to reveal some signatures of the adiabatic inspiral stage for probing the gravitational wave, the geodesics and periodic orbits around the black hole are investigated. It is found that bound orbits around the quantum-corrected Schwarzschild black hole have larger angular momentum and radius compared to the classic (Schwarzschild) black hole. Furthermore, by taking a taxonomy into account, periodic orbits for the massive particle are studied by a rational number with a triplet of integers. It suggests that the rational number increases with the increased of the energy of the massive particle. Besides, in the adiabatic inspiral stage, the particle’s periodic orbits around the quantum-corrected Schwarzschild black hole have higher energy in comparison to the ones in the classic black hole. These results demonstrated that the dynamical approach for the taxonomy enables us to distinguish the quantum-corrected Schwarzschild black hole from the classic black hole only by a massive particle’s periodic orbits.

黑洞时空中的轨道动力学可以使我们有机会深入了解量子引力和基本物理学。在本文中，我们主要关注质量粒子在量子校正的Schwarzschild黑洞周围的运动。为了揭示绝热吸气阶段的一些特征以探测引力波，研究了黑洞周围的测地线和周期轨道。发现与经典（Schwarzschild）黑洞相比，量子校正Schwarzschild黑洞周围的束缚轨道具有更大的角动量和半径。此外，通过考虑分类法，通过三元整数的有理数研究了质点的周期性轨道。这表明有理数随质量粒子能量的增加而增加。此外，在绝热吸气阶段，与经典黑洞中的粒子相比，量子校正过的Schwarzschild黑洞周围粒子的周期性轨道具有更高的能量。这些结果表明，分类学的动力学方法使我们能够仅通过大质量粒子的周期性轨道将量子校正的Schwarzschild黑洞与经典黑洞区分开。