Motion of spinning test bodies in Kerr spacetime
Motion of spinning test bodies in Kerr spacetime
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DOI：
10.1103/physrevd.90.064035
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发表时间：
2014-08
影响因子：
5
通讯作者：
E. Hackmann;C. Lammerzahl;Y. Obukhov;D. Puetzfeld;Isabell Schaffer
中科院分区：
文献类型：
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作者：
E. Hackmann;C. Lammerzahl;Y. Obukhov;D. Puetzfeld;Isabell Schaffer
在天体物理情况下，例如在银河系中心发现的极端质量比，允许在某些参数制度下对运动进行近似的解析描述。银河系中心观测情况的稳步改善[1-3]可能很快使我们能够测试不同的相互竞争的理论方法来模拟广义相对论中天体物理物体的运动。本文研究了克尔背景下扩展自旋试验体的运动。我们的出发点是基于极-偶极子测试体的多极描述[4-8]的显式速度公式，利用该公式我们对克尔黑洞赤道平面内对准和反对准测试体自旋的轨道运动进行了分类。给出了近视点位移的精确表达式，并与相应的后牛顿计算结果进行了比较。我们提供了银河系中心黑洞周围轨道的测试体自旋修正的估计。本文的结构如下。在第二节中，我们给出了旋转试验体的运动方程，并推导出了试验体动量和速度的一般公式。然后在第三节中在克尔背景下研究旋转试验体的运动。这些运动方程具有一个数学结构，它允许解析解[9,10]，并在第四节中对不同的轨道类型进行系统分类。在第五节中，给出了近日点位移的一般公式，并与相应的后牛顿结果进行了比较。我们的结论载于第六节。在附录A和B中，我们提出
Extreme mass ratios in astrophysical situations, for example as found in the galactic center, allow for an approximate analytic description of the motion in certain parameter regimes. The steadily improving observational situation of the galactic center [1–3] may soon enable us to test different competing theoretical approaches to model the motion of astrophysical objects in the theory of General Relativity. In this work we study the motion of extended spinning test bodies in a Kerr background. Our starting point is an explicit velocity formula based on the multipolar description [4–8] of pole-dipole test bodies, with the help of which we classify the orbital motion in the equatorial plane of a Kerr black hole for aligned and anti-aligned test body spin. An exact expression for the periastron shift is given and compared with corresponding post-Newtonian results. We provide an estimate of the test body spin corrections for orbits around the black hole in the galactic center. The structure of the paper is as follows. In section II we provide the equations of motion for spinning test bodies and derive a general formula which relates the momentum and the velocity of the test body. The motion of spinning test bodies is then studied in a Kerr background in section III. These equations of motion are of a mathematical structure which allows for an analytic solution [9, 10] and a systematic classification of different orbit types in section IV. In section V a general formula for the periastron shift is given and compared to corresponding post-Newtonian results. Our conclusions are drawn in section VI. In the appendices A and B we pro