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arXiv · 2605.08569

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

Abhishek Hegade K. R.·K. J. Kwon·Tejaswi Venumadhav·Hang Yu·Nicolas Yunes
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Abstract

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 ${\cal{O}}(\omega^2)$ 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.

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Abhishek Hegade K. R., K. J. Kwon, Tejaswi Venumadhav, Hang Yu, Nicolas Yunes. 2026-05-09. The Good, the Bad, and the Subtle: Relativistic mode sums for neutron-star tidal response. https://arxiv.org/abs/2605.08569

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