Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1150263659, Linear and Nonlinear Tides in Coalescing Binary Neutron Stars, G3806454686, G4274203451, WoU-MMA: Targeted Search for Binary Mergers with Multiple Harmonics in Gravitational Wave Data, G7089268233, WoU-MMA: Expanding the Horizons of Gravitational Wave Searches and Parameter Estimation, G8696814194
OpenAlex ID: W7222348717