对称达莫-索洛杜金虫洞的非对称情况下的反射less和回声模式
Reflectionless and echo modes in asymmetric Damour-Solodukhin wormholes
AI总结：
本文通过扩展准反射less模式定义并推广对称达莫-索洛杜金虫洞至非对称情况，研究反射less和回声模式谱在复频域的相似性，发现两者在复频平面中具有近似均匀分布特性，且反射less模式更接近实频轴。
摘要：
已知超致密天体中的回声波形主要由渐近高频准正常模式（称为回声模式）组成，这些模式主要平行于实频轴。然而，Rosato等人最近提出高频率准反射less散射模式主要负责回声现象。本文通过将准反射less模式定义扩展为反射less模式，并将对称达莫-索洛杜金虫洞推广到非对称情况，研究反射less和回声模式谱在复频平面中的相似性。通过主要的解析处理，证明这两种谱的渐近性质具有强相似性，特征为近似均匀分布平行于实频轴，且相邻模式之间的间距相同。具体而言，在极限$|\mathrm{Re}ω| \gg |\mathrm{Im}ω|$下，回声模式的实部与反射less模式的实部相同。虽然回声模式通常具有非零虚部，但对称达莫-索洛杜金虫洞的反射less模式精确位于实频轴上，任何偏差均作为虫洞不对称程度的度量。对于给定的相同源，利用格林函数计算波形。发现与反射less模式相关的波形幅度比回声模式更显著，因为反射less模式通常更接近实频轴。认为两种观点都为描述回声现象提供了有效工具。
英文摘要：
It is understood that the echo waveforms in ultracompact objects can be regarded as composed mainly of the asymptotic high-overtone quasinormal modes, dubbed echo modes, which predominantly lie parallel to the real frequency axis. Alternatively, Rosato {\it et al.} recently suggested that high-frequency quasi-reflectionless scattering modes are primarily responsible for the echo phenomenon. In this work, by extending the definition of quasi-reflectionless modes to reflectionless ones and generalizing symmetric Damour-Solodukhin wormholes to asymmetric cases, we examine the underlying similarity between the reflectionless and echo mode spectra in the complex frequency plane. Through a primarily analytical treatment, we demonstrate that the asymptotic properties of these two spectra exhibit a strong resemblance, featuring an approximately uniform distribution parallel to the real frequency axis with the same spacing between successive modes. Specifically, the real parts of echo modes coincide with those of reflectionless modes at the limit $|\mathrm{Re}ω| \gg |\mathrm{Im}ω|$. While echo modes typically possess non-vanishing imaginary parts, the reflectionless modes of symmetric Damour-Solodukhin wormholes lie precisely on the real frequency axis, with any deviation serving as a measure of the degree of asymmetry of the wormhole. For a given identical source, the waveforms are calculated numerically using the Green's functions. The amplitudes of the waveforms associated with reflectionless modes are found to be more pronounced than those of the echo modes, because reflectionless modes typically lie closer to the real frequency axis than the latter. It is argued that both perspectives provide effective tools for describing the echo phenomenon.
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