发表机构
Nankai University; Yantai University（南开大学; 烟台大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明高斯或Pöschl-Teller凸起加性方案与达布变换不相容，提出两种一致方案，并确认缺乏一致性会导致虚假的轴向-极向分裂。
AI 中文摘要
局域高斯或Pöschl-Teller凸起被广泛用于探测Schwarzschild准正规模式的敏感性，通常将其同时添加到Regge-Wheeler和Zerilli势中。我们证明，这种加性方案通常与连接两个宇称扇区的达布变换不相容。原因是该变换将宇称盲凸起限制为具有不可避免的$r^{-2}$尾部的固定凸起族，排除了加性方案中具有任意振幅、中心或宽度的任何高斯或Pöschl-Teller轮廓。我们给出了达布允许的轴向和极向凸起对的完整分类，并提出了两种一致的情景：达布生成子方案，其中高斯或Pöschl-Teller轮廓被保留为凸起对的生成子而非凸起本身；以及Riccati完备化方案，其中高斯或Pöschl-Teller轮廓被视为凸起对之一，其伙伴将从Riccati方程中求解。我们的频域计算证实，如果缺乏达布一致的情景，将产生有限且虚假的轴向-极向准正规模式分裂，而基模的质心位移几乎不变。
英文摘要
A localized Gaussian or Pöschl-Teller bump is widely used to probe the sensitivity of Schwarzschild quasinormal modes, where it is typically added to both the Regge-Wheeler and Zerilli potentials. We show that such an additive prescription is generically incompatible with the Darboux transformation connecting the two parity sectors. The reason is that such a transformation restricts a parity-blind bump to a fixed family of bumps with an unavoidable $r^{-2}$ tail, excluding any Gaussian or Pöschl-Teller profile with arbitrary amplitude, center, or width in the additive prescription. We give the complete classification of Darboux-admissible axial and polar pairs of bumps and propose two consistent scenarios: Darboux generator prescription in which a Gaussian or Pöschl-Teller profile is retained as a generator of the bump pair rather than as the bump itself, and Riccati completion prescription in which a Gaussian or Pöschl-Teller profile is regarded as one of the bump pair and its partner will be solved from the Riccati equation. Our frequency-domain calculations confirm that a finite and spurious axial-polar splitting of quasinormal modes will be produced if the Darboux-consistent scenarios are absent, while the centroid shift of the fundamental mode is nearly unchanged.
Comments34 pages, 10 figures
