We develop a fully relativistic approach for determining the response of a compact star to a time/frequency dependent (tidal) environment. The strategy involves matching the solution for the linearized fluid dynamics in the star’s interior to the spacetime perturbations in the near-zone surrounding the body, along with an identification of the tidal driving and the star’s response. Notably, this identification is exact in Newtonian gravity and we provide strong evidence that it remains robust also in the relativistic case. The argument does not involve a sum over the star’s quasinormal modes and hence circumvents one of the obstacles that have held up the development of models for relativistic tides. Numerical results are provided, at the proof-of-principle level, for a realistic matter equation of state from the Brussels-Skyrme models of the Equation of State family, including composition stratification leading to the presence of low-frequency gravity modes. We also sketch the connection with the field-theory inspired approach to the problem, in which the tidal response is expressed in terms of asymptotic scattering amplitudes. We argue that progress in this direction is essential in order to complete the description of tides in relativistic stars.

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• General relativity
• Gravitational waves
• Neutron stars & pulsars