发表机构
Department of Mathematics, University at Buffalo; The State University of New York, Buffalo（布法罗大学数学系; 纽约州立大学布法罗分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究一阶微分可观测量对黑洞波动方程零频行为的影响，给出移除格林函数领头阈值项的简单条件，并发现史瓦西Regge-Wheeler模的晚期尾部多获得一个时间逆幂。
AI 中文摘要
我们研究一阶微分可观测量如何影响黑洞波动方程的零频行为。准正则模和晚期尾部并不总是以相同方式变化。我们给出了一个简单条件，用于判断可观测量何时移除格林函数的领头阈值项。对于史瓦西Regge-Wheeler模，相关算符由正则静态解确定。该变换在非零频率下是非退化的，但在零频率下变为全局退化的。因此，非零准正则模问题保持不变，而领头固定半径晚期尾部则多获得一个额外的时间逆幂。
英文摘要
We study how first-order differential observables affect the zero-frequency behavior of black-hole wave equations. Quasinormal modes and late-time tails do not always change in the same way. We give a simple condition for when an observable removes the leading threshold term of a Green function. For Schwarzschild Regge-Wheeler modes, the relevant operator is determined by the regular static solution. The transformation is nondegenerate at nonzero frequency but becomes globally degenerate at zero frequency. As a result, the nonzero quasinormal-mode problem is unchanged, while the leading fixed-radius late-time tail gains one extra inverse power of time.
Comments13 pages
