Gravitational waves emitted in the late inspiral of binary neutron stars are affected by their tidal deformation. We study the tidal dynamics in full general relativity through matched-asymptotic expansions and show that the dynamical tidal response can be expanded in a set of modes. We further show that the mode amplitudes satisfy an effective, forced harmonic oscillator equation, which generalizes the overlap-integral formulation of Newtonian gravity. Our relativistic treatment of dynamical tides will avoid systematic biases in future gravitational-wave parameter estimation and can be generalized to model nonlinear tidal interactions and include the presence of elastic, electromagnetic, or dark matter field interactions with nuclear matter.

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• Gravitation
• Neutron stars & pulsars