Nonlinear Perturbations of Relativistic Stars
Abstract
We extend the general relativistic Lagrangian perturbation formalism of Friedman and Schutz [Astrophys. J. 200, 204 (1975)] beyond linear order, retaining full time dependence of the perturbations. We provide general formulae to relate the Lagrangian and Eulerian perturbations to any general perturbative order. As a proof of principle, we apply the framework to tidally perturbed relativistic stars in Regge-Wheeler gauge and reduce the second-order field and conservation equations to master equations with a nonlinear source. Projecting the source onto the star's eigenmodes, we obtain a nonlinear equation of motion for the mode amplitudes and the coupling coefficients, which describe the interactions among the eigenmodes and with the external tidal field. Approximating the tidal field and the coupling coefficients, we compute the static quadratic Love number from the quadrupolar fundamental mode alone and find that it reproduces the direct metric-matching value to a reasonable accuracy of 4%, up to a further correction arising from the Hamiltonian and momentum constraints of the second-order tidal field.
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BibTeX
@misc{kwon2026nonlinear,
title = {{Nonlinear Perturbations of Relativistic Stars}},
author = {K. J. Kwon and Abhishek Hegade K. R. and Tejaswi Venumadhav and Hang Yu and Nicolás Yunes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18952},
eprint = {2610.18952},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18952},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonlinear Perturbations of Relativistic Stars
AU - K. J. Kwon
AU - Abhishek Hegade K. R.
AU - Tejaswi Venumadhav
AU - Hang Yu
AU - Nicolás Yunes
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18952
UR - https://arxiv.org/abs/2610.18952
AB - We extend the general relativistic Lagrangian perturbation formalism of Friedman and Schutz [Astrophys. J. 200, 204 (1975)] beyond linear order, retaining full time dependence of the perturbations. We provide general formulae to relate the Lagrangian and Eulerian perturbations to any general perturbative order. As a proof of principle, we apply the framework to tidally perturbed relativistic stars in Regge-Wheeler gauge and reduce the second-order field and conservation equations to master equations with a nonlinear source. Projecting the source onto the star's eigenmodes, we obtain a nonlinear equation of motion for the mode amplitudes and the coupling coefficients, which describe the interactions among the eigenmodes and with the external tidal field. Approximating the tidal field and the coupling coefficients, we compute the static quadratic Love number from the quadrupolar fundamental mode alone and find that it reproduces the direct metric-matching value to a reasonable accuracy of 4%, up to a further correction arising from the Hamiltonian and momentum constraints of the second-order tidal field.
ER -