Analytical solutions of equatorial geodesic motion in Kerr spacetime  

作　　者：刘岩 孙兵 Yan Liu;Bing Sun(Department of Physics,Yantai University,Yantai 264005,China;Department of Basic Courses,Beijing University of Agriculture,Beijing 102206,China;CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]Department of Physics,Yantai University,Yantai 264005,China [2]Department of Basic Courses,Beijing University of Agriculture,Beijing 102206,China [3]CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Chinese Physics C》2024年第4期222-239,共18页中国物理C（英文版）

基　　金：the Natural Science Foundation of Shandong Province(ZR2023QA133);Yantai University(WL22B218);B.S.is Supported by the National Natural Science Foundation of China(12375046);Beijing University of Agriculture(QJKC-2023032).

摘　　要：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.

关 键 词：geodesic motion analytical solutions equatorial plane Kerr spacetime 

分 类 号：P145.8[天文地球—天体物理]