Relativistic dynamical tides: Subtleties and calibration

The response of astrophysical compact objects to external tidal fields carries valuable information on the nature of these objects, on the equation of state of matter, and on the underlying gravitational theory. In this work, we highlight subtleties in describing relativistic dynamical tidal responses that arise from ambiguities in the decomposition of a perturbed metric into external tidal and induced response pieces. Observables are unambiguous. However, in practice, differences arising from implicit assumptions in the definition of tidal deformabilities may lead to a bias in constraining nuclear physics or gravitational theories, if not properly tied to observational data. We propose calibration of a tidal response function for any compact objects in vacuum general relativity. Within this framework, the dynamical tidal Love numbers of a Schwarzschild black hole (BH) in both even and odd sectors vanish at any multipole order. The calibration allows one to define dynamical tidal deformabilities of relativistic stars, such as neutron stars, as the difference from the BH values (zero) under the unified definition in a simple manner. As a straightforward extension of our framework, we compute the next-to-leading dissipative tidal response of Schwarzschild black holes for the first time to our knowledge.