Analytical solutions of equatorial geodesic motion in Kerr spacetime* * Y. L. is financially supported by the Natural Science Foundation of Shandong Province (ZR2023QA133) and Yantai University (WL22B218). B.S. is Supported by the National Natural Science Foundation of China (12375046) and Beijing University of Agriculture (QJKC-2023032).

IF 3.6 2区 物理与天体物理 Q1 PHYSICS, NUCLEAR
Yan Liu, Bing Sun
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引用次数: 0

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.
克尔时空中赤道大地运动的解析解* * Y. L. 得到山东省自然科学基金(ZR2023QA133)和烟台大学(WL22B218)的资助。B.S. 受国家自然科学基金(12375046)和北京农业大学(QJKC-2023032)资助。
对克尔大地线的研究由来已久,尤其是对发生在赤道面内的大地线的研究,一般都能很好地理解。然而,与其中一位作者提出的分类[Phys. Rev. D 105, 024075 (2022)]相比,某些类别的大地线,如受困轨道,显然仍然缺乏解析解。因此,在本研究中,我们提供了克尔时空中赤道时间似大地线的显式解析解,包括受困轨道的解,这些解捕捉到了特殊大地线的特征,如圆轨道、束缚轨道和偏转轨道的位置和守恒量。具体来说,我们确定了逆行轨道在旋转黑洞附近的强引力作用下从逆转运动过渡到顺行运动的精确位置。有趣的是,对于具有负能量的轨道,尽管角动量为负,但其轨迹仍然是顺行的。此外,我们还研究了一个有趣的现象:当转折点接近被困轨道的转折点时,偏转轨道绕黑洞旋转的圈数增加。此外,我们还发现,只有顺行边缘偏转大地线能够穿越厄尔戈里区。总之,我们的研究结果提出了赤道时间似大地线的显式解,并提供了对旋转黑洞附近粒子运动动力学的见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
中国物理C
中国物理C 物理-物理:核物理
CiteScore
6.50
自引率
8.30%
发文量
8976
审稿时长
1.3 months
期刊介绍: Chinese Physics C covers the latest developments and achievements in the theory, experiment and applications of: Particle physics; Nuclear physics; Particle and nuclear astrophysics; Cosmology; Accelerator physics. The journal publishes original research papers, letters and reviews. The Letters section covers short reports on the latest important scientific results, published as quickly as possible. Such breakthrough research articles are a high priority for publication. The Editorial Board is composed of about fifty distinguished physicists, who are responsible for the review of submitted papers and who ensure the scientific quality of the journal. The journal has been awarded the Chinese Academy of Sciences ‘Excellent Journal’ award multiple times, and is recognized as one of China''s top one hundred key scientific periodicals by the General Administration of News and Publications.
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