AI 中文总结
本研究针对奇异致密天体引力回波，利用Riccati方程与宏观阻抗映射的解析框架，发现光子球波色散引发双曲型光谱致密化，可分离外部时空结构色散，为视界尺度物理提供新探针。
AI 中文摘要
奇异致密天体（ECOs）的引力波回波为视界尺度物理提供了可观测探针，这类信号的标准唯象模型通常依赖几何光学近似，假设自由光谱范围为常数。本研究表明，光子球处的波色散会引发与该假设的系统性偏差，表现为双曲型光谱致密化。利用基于Riccati方程与宏观阻抗映射的解析框架，无需半经典近似即可提取这些高精细度共振的光谱。我们表征了从程函几何渐近（ℓ≫1）到隧穿主导的四极模（ℓ=2）的结构转变，在该波主导区域（ℓ∈[2,10]），与半经典极限的宏观偏差由唯象ℓ⁻³/²逆幂律支配。最终证明，若膜相位移与频率无关，这种宏观致密化可分离外部时空的结构色散，使其与边界微观物理解耦。
英文摘要
Gravitational-wave echoes from Exotic Compact Objects (ECOs) provide an observable probe for horizon-scale physics. Standard phenomenological models for these signals typically assume a constant Free Spectral Range, relying on the geometric optics approximation. In this work, we demonstrate that wave dispersion at the photon sphere induces a systematic deviation from this assumption, manifesting instead as a hyperbolic spectral densification. By employing an analytical framework based on the Riccati equation and macroscopic impedance mapping, we extract the spectrum of these high-finesse resonances without semi-classical approximations. We characterize the structural transition from the eikonal geometric asymptote ($\ell \gg 1$) down to the wave-tunneling dominated quadrupolar mode ($\ell=2$). In this wave-dominated regime ($\ell \in [2, 10]$), the macroscopic deviation from the semi-classical limit is governed by a phenomenological $\mathcal{L}^{-3/2}$ inverse power law. Finally, we show that this macroscopic densification isolates the structural dispersion of the external spacetime, decoupled from the boundary microphysics, provided the membrane phase shift is frequency-independent.
Journal refThe European Physical Journal Plus, 2026, 141 (7), pp.883
