The Good, the Bad, and the Subtle: Relativistic mode sums for neutron-star tidal response

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Main Authors: R., Abhishek Hegade K., Kwon, K. J., Venumadhav, Tejaswi, Yu, Hang, Yunes, Nicolas
Format: Preprint
Published: 2026
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author R., Abhishek Hegade K.
Kwon, K. J.
Venumadhav, Tejaswi
Yu, Hang
Yunes, Nicolas
author_facet R., Abhishek Hegade K.
Kwon, K. J.
Venumadhav, Tejaswi
Yu, Hang
Yunes, Nicolas
contents Time-dependent tidal interactions during the late inspiral of binary neutron stars encode valuable information about neutron-star structure, but systematically extending the familiar Newtonian mode-sum picture into full general relativity is nontrivial. In this paper, we develop a practical relativistic implementation of mode-sum tidal response for non-rotating neutron stars in Regge-Wheeler gauge. Using near-zone boundary conditions, we systematically define the interior tidal field, the relativistic overlap integrals, and the corresponding mode amplitudes. The good is that the dominant f-mode contribution is remarkably robust, reproducing the direct matching calculation to within $\sim 3$\% across the equations of state we consider. The bad is that the operator governing mode inner product is not positive definite on the full Regge-Wheeler-gauge function space, so the relativistic mode sum truncated at ${\cal{O}}(ω^2)$ is not expected to strictly converge to the direct matching solution. The subtle is that the tidal field inside the star is not unique, although this ambiguity has only a limited impact on the dominant f-mode response for the classes of extensions studied here. Our results establish the practical utility of relativistic mode-sum approximations, while making clear that their predictive power comes from a controlled low-mode description, rather than from a formally convergent strong-field expansion.
format Preprint
id arxiv_https___arxiv_org_abs_2605_08569
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The Good, the Bad, and the Subtle: Relativistic mode sums for neutron-star tidal response
R., Abhishek Hegade K.
Kwon, K. J.
Venumadhav, Tejaswi
Yu, Hang
Yunes, Nicolas
General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
Nuclear Theory
Time-dependent tidal interactions during the late inspiral of binary neutron stars encode valuable information about neutron-star structure, but systematically extending the familiar Newtonian mode-sum picture into full general relativity is nontrivial. In this paper, we develop a practical relativistic implementation of mode-sum tidal response for non-rotating neutron stars in Regge-Wheeler gauge. Using near-zone boundary conditions, we systematically define the interior tidal field, the relativistic overlap integrals, and the corresponding mode amplitudes. The good is that the dominant f-mode contribution is remarkably robust, reproducing the direct matching calculation to within $\sim 3$\% across the equations of state we consider. The bad is that the operator governing mode inner product is not positive definite on the full Regge-Wheeler-gauge function space, so the relativistic mode sum truncated at ${\cal{O}}(ω^2)$ is not expected to strictly converge to the direct matching solution. The subtle is that the tidal field inside the star is not unique, although this ambiguity has only a limited impact on the dominant f-mode response for the classes of extensions studied here. Our results establish the practical utility of relativistic mode-sum approximations, while making clear that their predictive power comes from a controlled low-mode description, rather than from a formally convergent strong-field expansion.
title The Good, the Bad, and the Subtle: Relativistic mode sums for neutron-star tidal response
topic General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
Nuclear Theory
url https://arxiv.org/abs/2605.08569