General relativistic effects on Hill stability of multibody systems: Stability of three-body systems containing a massive black hole
General relativistic effects on Hill stability of multibody systems: Stability of three-body systems containing a massive black hole
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DOI：
10.1103/physrevd.102.124063
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发表时间：
2020-09
影响因子：
5
通讯作者：
Haruka Suzuki;Y. Nakamura;S. Yamada
中科院分区：
文献类型：
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作者：
Haruka Suzuki;Y. Nakamura;S. Yamada
我们研究广义相对论引力对希尔稳定性的影响，即多体系统在一个轨道接近另一个轨道时的稳定性，迄今为止主要在牛顿力学中研究并应用于行星系统。我们在本文中重点关注三体问题，并将牛顿分析扩展到后牛顿近似中的广义相对论体系。解析推导了三体系统相对论希尔稳定性的近似充分条件，并通过数值验证了其有效性和实用性。事实上，正如我们的理论预测所预期的，在希尔稳定性的意义上，相对论使系统比牛顿力学更不稳定。该准则将有助于分析密集环境的大规模 N 体模拟的结果，其中三体子系统的稳定性非常重要。
We study the effects of general relativistic gravity on the Hill stability, that is, the stability of a multi-body system against a close approach of one orbit to another, which has been hitherto studied mainly in Newtonian mechanics and applied to planetary systems. We focus in this paper on the three-body problem and extend the Newtonian analyses to the general relativistic regime in the post-Newtonian approximation. The approximate sufficient condition for the relativistic Hill stability of three-body systems is derived analytically and its validity and usefulness are confirmed numerically. In fact, relativity makes the system more unstable than Newtonian mechanics in the sense of the Hill stability as expected by our theoretical prediction. The criterion will be useful to analyze the results of large-scale N-body simulations of dense environments, in which the stability of three-body sub-systems is important.