A Bound on the Dynamical Love Number
arXiv:2607.26686
The paper derives a theoretical bound on the frequency dependence of the tidal deformability (Love number) of compact objects such as neutron stars and black holes, using the Schwarz‑Pick theorem and dispersion relations.
Abstract
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 (-mode) model saturating the bound. For a black hole, the bound gives information on the dissipative tidal-heating coefficient.
24 pages, 1 figure