The orbital dynamics in the strong gravitational field might present unique features of quantum gravity and high-dimensional theory. In this paper, a timelike particle’s periodic orbits around the 4-dimensional Einstein–Lovelock (4$\mathcal{D}-$EL) black holes are investigated by employing a classification of the zoom–whirl structure with a rational number $q$. It is found that these rational (periodic) orbits around 4$\mathcal{D}-$EL black holes have a higher or lower energy than the ones around Schwarzschild black holes during the inspiral stage of detecting the gravitational waves. It depends strongly on the sign of a coupling constant in the theory. These results might provide hints for distinguishing 4$\mathcal{D}-$EL black holes from Schwarzschild ones by using the orbital dynamical approach in the strong gravitational field.

强引力场中的轨道动力学可能表现出量子引力和高维理论的独特特征。在本文中，一个类似时间的质点在4维爱因斯坦-洛夫洛克（4$\mathcal{d}-$EL）黑洞是通过使用具有合理数的zoom-whirl结构分类来研究的 $q$。发现这些有理（周期）轨道绕4$\mathcal{d}-$在探测重力波的吸气阶段，EL黑洞的能量比Schwarzschild黑洞周围的能量高或低。它在很大程度上取决于理论中耦合常数的符号。这些结果可能为区分4提供提示。$\mathcal{d}-$Schwarzschild的EL黑洞是通过在强引力场中使用轨道动力学方法进行的。