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