Relativistic and Dynamical Love Numbers

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.