General Relativistic Triplet Interaction of Oscillation Eigenmodes in Deformed Neutron Stars

Tidal deformation of neutron stars in binary systems modifies the phasing of their gravitational-wave signals. This phasing effect is typically modeled using the linear response of the stars' oscillation eigenmodes. However, in principle, the eigenmodes experience nonlinear forcing arising from coupling across themselves as well as the nonlinear coupling between the modes and the tidal potential. These nonlinear tidal effects are of great significance, as they introduce rich phenomenology in tidal interactions, including enhanced tidal responses of neutron stars and resonance locking of low-frequency oscillation modes. We present a fully general relativistic calculation of mode coupling and demonstrate that it reproduces the nonlinear Love numbers in the static limit. Our calculation enables studies of truly dynamical tides, where the star's tidal response depends on the history of the tidal forcing, in general relativistic regime on the mode basis.