AI 中文总结
利用施瓦茨-皮克定理推导动力学爱数的边界，中子星的该边界由静态爱数和f-模频率确定，黑洞的边界可用于获取耗散潮汐加热系数信息。
AI 中文摘要
致密天体的潮汐形变能力由一个单一的频率相关函数编码，即关联诱导多极矩与外加潮汐的推迟格林函数。因果性、实域性、被动性以及正测度色散表示所需的高频条件，使该响应可被重标度为复频率上半平面的全纯自映射。利用已用于推导黑洞物理中量子混沌边界的施瓦茨-皮克定理，我们给出了潮汐响应对频率的变化率的一个边界。对于中子星，动力学爱数由静态爱数和第一内部模式（f-模）的频率界定，且单模（f-模）模型可达到该边界；对于黑洞，该边界提供了耗散潮汐加热系数的相关信息。
英文摘要
The tidal deformability of a compact object is encoded in a single function of frequency, the retarded Green's function relating the induced multipole to the applied tide. Causality, reality, passivity, and the high-frequency conditions required for a positive-measure dispersion representation allow this response to be rescaled into a holomorphic self-map of the upper complex frequency half-plane. Using the Schwarz--Pick theorem, already employed to derive the quantum chaos bound in black hole physics, we provide a bound on the rate of the tidal response with respect to the frequency. For a neutron star the dynamical Love number is bounded in terms of the static one and of the frequency of the first internal mode, with the single-mode ($f$-mode) model saturating the bound. For a black hole, the bound gives information on the dissipative tidal-heating coefficient.
Comments24 pages, 1 figure
