AI 中文总结
本文将黑洞建模为频率依赖滤波器，定量分析其对稳态随机引力波的散射与吸收，证明视界吸收是唯一光谱畸变来源，并指出可观测效应更可能来自罕见邻近系统而非宇宙学累积传播。
AI 中文摘要
黑洞在受到扰动时会发出“振铃”信号，而它们对稳态引力波背景的响应则是一个实频率散射问题，并非额外准正则模谱线的来源。我们通过将黑洞视为一个依赖于频率、角度和极化的滤波器，使这一标准区分变得定量化。对于史瓦西黑洞周围的各向同性稳态背景，弹性散射不会产生净单极信号，因此视界吸收是唯一的人口级光谱畸变来源。我们详细计算了史瓦西黑洞的传递函数，识别了其吸收和相位延迟特征，并将稳态响应与有限波包激发的因果振铃联系起来。随后，我们将单黑洞结果推广为宇宙学人口群体的角向和极化输运核。对于现实的黑洞群体，包括构成全部暗物质的小行星质量原初黑洞，所得光学深度可忽略不计。接着，我们将分析扩展到克尔黑洞，其中超辐射允许在选定的共转模式中实现真正的放大，但各向同性入射和随机自旋取向会强烈稀释弥散信号。因此，可观测效应更可能出现在罕见、邻近、对齐、快速旋转或瞬态照明的系统中，而非通过累积的宇宙学传播产生。
英文摘要
Black holes ring when perturbed, whereas their response to a stationary gravitational-wave background is a real-frequency scattering problem, not a source of additional quasi-normal-mode lines. We make this standard distinction quantitative by treating a black hole as a frequency-, angle-, and polarization-dependent filter. For an isotropic stationary background around Schwarzschild holes, elastic scattering produces no net monopole signal, so horizon absorption is the only population-level spectral distortion. We calculate this transfer function for Schwarzschild holes in detail, identify its absorptive and phase-delay signatures, and connect the stationary response to the causal ringdown excited by a finite wave packet. We then promote the single-hole result to an angular and polarization transport kernel for a cosmological population. The resulting optical depth is negligible for realistic black-hole populations, including asteroid-mass primordial black holes comprising all dark matter. We then extend the analysis to Kerr holes, for which superradiance allows genuine amplification in selected co-rotating modes, but isotropic incidence and random spin orientations strongly dilute the diffuse signal. Observable effects are therefore more likely in rare, nearby, aligned, rapidly spinning, or transiently illuminated systems than through cumulative cosmological propagation.
Comments38 pages, 18 figures
