标题： 如何观测非克尔时空 显示英文标题

标题： How to observe a non-Kerr spacetime

摘要： 我们提出了一种通用准则，可用于引力波数据分析，以区分进入Kerr背景时空的极端质量比旋进与进入非Kerr背景时空的极端质量比旋进。 该准则利用了一个事实，即当一个可积系统（如描述Kerr时空中的测地线轨道的系统）受到扰动时，最初对应于共振的相空间中的环面会根据Poincaré-Birkhoff定理分解，形成所谓的Birkhoff链在截面上。 这些链中岛屿的KAM曲线具有相同的频率比，尽管频率本身在岛屿内的不同KAM曲线上会有所变化。 另一方面，不在Birkhoff链中的KAM曲线不具有这一特性。 在引力波信号演化过程中频率比的这种时间恒定性将表明一个非Kerr时空，然后可以进一步探索。 显示英文摘要

摘要： We present a generic criterion which can be used in gravitational-wave data analysis to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr background spacetime. The criterion exploits the fact that when an integrable system, such as the system that describes geodesic orbits in a Kerr spacetime, is perturbed, the tori in phase space which initially corresponded to resonances disintegrate so as to form the so called Birkhoff chains on a surface of section, according to the Poincar\'{e}-Birkhoff theorem. The KAM curves of these islands in such a chain share the same ratio of frequencies, even though the frequencies themselves vary from one KAM curve to another inside an island. On the other hand, the KAM curves, which do not lie in a Birkhoff chain, do not share this characteristic property. Such a temporal constancy of the ratio of frequencies during the evolution of the gravitational-wave signal will signal a non-Kerr spacetime which could then be further explored.