论文标题
对多体系统的山丘稳定性的一般相对论影响I：包含大型黑洞的三体系统的稳定性
General Relativistic Effects on Hill Stability of Multi-Body Systems I: Stability of Three-Body Systems Containing a Massive Black Hole
论文作者
论文摘要
我们研究了一般相对论重力对山丘稳定性的影响，即多体系统与一个轨道对另一个轨道的紧密方法的稳定性，迄今主要是在牛顿力学中研究的，并应用于行星系统。我们将重点放在三体问题上，并将牛顿分析扩展到牛顿后近似中的一般相对论制度。三体系统的相对论山稳定性的近似条件是分析得出的，其有效性和有用性被数值确认。实际上，相对论使系统在山坡稳定意义上比我们的理论预测所期望的那样更加不稳定。该标准对于分析密集环境的大规模N体模拟的结果将很有用，其中三体子系统的稳定性很重要。
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.
