近日，烟台大学的刘岩与北京农学院的孙兵合作并取得一项新进展。经过不懈努力，他们获得克尔时空中赤道测地线运动的解析解。相关研究成果已于2024年4月15日在国际知名学术期刊《中国物理C》上发表。

因此，在本研究中，研究人员提供了克尔时空中赤道类时测地线的显式解析解，包括捕获轨道的解，这些解捕获了特殊测地线的特征，如圆轨道、束缚轨道和偏转轨道的位置和守恒量。具体而言，研究人员确定了由于旋转黑洞附近的强引力作用，逆行轨道从反向旋转到顺行运动转变的具体位置。尤为有趣的是，尽管这些轨道的角动量为负，但能量为负的轨道却仍呈现顺行状态。

此外，他们还探究了一个引人入胜的现象：当拐点逐渐接近捕获轨道的拐点时，偏转轨道在黑洞周围的旋转次数会相应增加。研究还发现，只有渐进式边缘偏转测地线能够穿越遍历区。综上所述，这项研究不仅为赤道类时测地线提供了明确的解析方案，还为理解旋转黑洞附近粒子运动的动力学机制提供了宝贵见解。

据悉，克尔测地线的研究历史悠久，特别是赤道平面内的测地线，其特性已被深入解析。然而，与[Phys.Rev. D 105, 024075(2022)]研究中的一位作者提出的分类相比，显然某些类型的测地线，例如捕获轨道，仍然缺乏解析解。

附：英文原文

Title: Analytical solutions of equatorial geodesic motion in Kerr spacetime

Author: Yan Liu, Bing Sun

Issue&Volume: 2024-04-15

Abstract: The study of Kerr geodesics has a long history, particularly for those occurring within the equatorial plane, which are generally well-understood. However, when compared with the classification introduced by one of the authors [Phys. Rev. D 105, 024075 (2022)], it becomes apparent that certain classes of geodesics, such as trapped orbits, still lack analytical solutions. Thus, in this study, we provide explicit analytical solutions for equatorial timelike geodesics in Kerr spacetime, including solutions of trapped orbits, which capture the characteristics of special geodesics, such as the positions and conserved quantities of circular, bound, and deflecting orbits. Specifically, we determine the precise location at which retrograde orbits undergo a transition from counter-rotating to prograde motion due to the strong gravitational effects near a rotating black hole. Interestingly, the trajectory remains prograde for orbits with negative energy despite the negative angular momentum. Furthermore, we investigate the intriguing phenomenon of deflecting orbits exhibiting an increased number of revolutions around the black hole as the turning point approaches the turning point of the trapped orbit. Additionally, we find that only prograde marginal deflecting geodesics are capable of traversing through the ergoregion. In summary, our findings present explicit solutions for equatorial timelike geodesics and offer insights into the dynamics of particle motion in the vicinity of a rotating black hole.

DOI: 10.1088/1674-1137/ad260a

Source: http://hepnp.ihep.ac.cn/article/doi/10.1088/1674-1137/ad260a