标题： 关于“Chazy-Curzon时空的测地线动力学”的评论 显示英文标题

标题： Comment on "Geodesic dynamics on Chazy-Curzon spacetimes"

摘要： 杜贝贝等人 [arXiv:1812.08663] 最近的数值结果被解读为暗示了在 Chazy-Curzon 时空的测地线可能存在第四个运动常数（卡特常数）。然而，我们在此表明，与此相反，单粒子 Chazy-Curzon 时空的测地线动力学表现出非可积系统的特征：子午面内的混沌轨道以及截面中的伯克霍夫链。因此，对于该系统不应期望刘维尔可积性，也不应期望存在第四个运动常数。 显示英文摘要

摘要： The recent numerical results of Dubeibe et al. [arXiv:1812.08663] were interpreted as hinting at the existence of a fourth constant of motion (Carter's constant) for geodesics on Chazy-Curzon spacetimes. Here we show that, to the contrary, the geodesic dynamics of the single-particle Chazy-Curzon spacetime exhibit features of a non-integrable system: chaotic orbits in the meridian plane, and Birkhoff chains in the surface of section. Thus, one should not expect Liouville-integrability, nor a fourth constant, for this system.