The Sitnikov problem is a classical problem broadly studied in physics which can represent an illustrative example of chaotic scattering. The relativistic version of this problem can be attacked by using the post-Newtonian formalism. Previous work focused on the role of the gravitational radius $\lambda$ on the phase space portrait. Here, we add two new and relevant issues on the influence of the gravitational radius in the context of chaotic scattering phenomena. First of all, we uncovered a metamorphosis of the KAM islands for which the escape regions change insofar $\lambda$ increases. Second, there are two inflection points in the unpredictability of the final state of the system when $\lambda \simeq 0.02$ and $\lambda \simeq 0.028$. We analyze these inflection points in a quantitative manner by using the basin entropy. This work can be useful for a better understanding of the Sitnikov problem in the context of relativistic chaotic scattering. In addition, the described techniques can be applied to similar real systems, such as binary stellar systems, among others.

中文翻译：

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引力半径对相对论Sitnikov问题的渐近行为的影响

锡尼科夫问题是物理学中广泛研究的经典问题，可以代表混沌散射的一个示例。此问题的相对论形式可以通过使用后牛顿形式主义来加以攻击。先前的工作着重于重力半径的作用$\lambda$在相空间肖像上。在这里，我们在混沌散射现象的背景下，增加了两个有关重力半径的新问题。首先，我们发现了KAM岛的变态，其逃逸区域在此范围内发生了变化$\lambda$增加。其次，当系统最终状态不可预测时，存在两个拐点$\lambda \simeq 0.02$ 和 $\lambda \simeq 0.028$。我们利用盆地熵定量分析了这些拐点。这项工作对于在相对论混沌散射的背景下更好地理解Sitnikov问题可能是有用的。此外，所描述的技术可以应用于类似的真实系统，例如二进制恒星系统。