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Relativistic mode sums for neutron-star tidal response

Abhishek Hegade K. R.1,*, K. J. Kwon2,†, Tejaswi Venumadhav2,3,‡, Hang Yu4,§, and Nicolas Yunes5,∥

  • *Contact author: ah4278@princeton.edu
  • †Contact author: jameskwon@ucsb.edu
  • ‡Contact author: teja@ucsb.edu
  • §Contact author: hang.yu2@montana.edu
  • ∥Contact author: nyunes@illinois.edu
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Phys. Rev. D 114, 064048 – Published 9 September, 2026

DOI: https://doi.org/10.1103/4jv6-twnk

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 nonrotating 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 ∼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 O(ω2) 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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Phys. Rev. D 114, 064048– Published 9 September, 2026
  • Received 16 May 2026
  • Accepted 26 August 2026
Article part of CHORUS
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