A Bound on the Dynamical Love Number
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 with a positive tidal spectral threshold, the dynamical Love number is bounded in terms of the static response and the lowest frequency carrying nonzero tidal spectral weight, with the ideal single-mode model saturating the bound. For a black hole, whose tidal spectrum is gapless, the dynamical Love number is a finite-part moment of the horizon absorption spectrum. Under a growth hypothesis on the complete response the theorem constrains the full Euclidean response, but it does not bound the dynamical Love number.
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BibTeX
@misc{kehagias2026bound,
title = {{A Bound on the Dynamical Love Number}},
author = {Alex Kehagias and Antonio Riotto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.26686},
eprint = {2607.26686},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26686},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bound on the Dynamical Love Number
AU - Alex Kehagias
AU - Antonio Riotto
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2607.26686
UR - https://arxiv.org/abs/2607.26686
AB - 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 with a positive tidal spectral threshold, the dynamical Love number is bounded in terms of the static response and the lowest frequency carrying nonzero tidal spectral weight, with the ideal single-mode model saturating the bound. For a black hole, whose tidal spectrum is gapless, the dynamical Love number is a finite-part moment of the horizon absorption spectrum. Under a growth hypothesis on the complete response the theorem constrains the full Euclidean response, but it does not bound the dynamical Love number.
ER -