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Gravitational wave and electromagnetic observations can provide new insightsinto the nature of matter at supra-nuclear densities inside neutron stars.Improvements in electromagnetic and gravitational wave sensing instrumentscontinue to enhance the accuracy with which they can measure the masses, radii,and tidal deformability of neutron stars. These better measurements placetighter constraints on the equation of state of cold matter above nucleardensity. In this article, we discuss a complementary approach to get insightsinto the structure of neutron stars by providing a model prediction fornon-linear fundamental eigenmodes (f-modes) and their decay over time, whichare thought to be induced by time-dependent tides in neutron star binaries.Building on pioneering studies that relate the properties of f-modes to thestructure of neutron stars, we systematically study this link in thenon-perturbative regime using models that utilize numerical relativity. Using asuite of fully relativistic numerical relativity simulations of oscillating TOVstars, we establish blueprints for the numerical accuracy needed to accuratelycompute the frequency and damping times of f-mode oscillations, which we expectto be a good guide for the requirements in the binary case. We show that theresulting f-mode frequencies match established results from linear perturbationtheory, but the damping times within numerical errors depart from linearpredictions. This work lays the foundation for upcoming studies aimed at acomparison of theoretical models of f-mode signatures in gravitational waves,and their uncertainties with actual gravitational wave data, searching forneutron star binaries on highly eccentric orbits, and probing neutron starstructure at high densities.

Probing neutron star structure via f-mode oscillations and damping in dynamical spacetime models