Tidal Response of a Rotating Neutron Star in General Relativity
Internal-structure-dependent tidal deformations in inspiralling neutron star binaries alter the phase of the gravitational waves generated by these systems' orbital motion. Measurement of the tidal phase shift could serve as a probe of the neutron star equation of state, which is poorly constrained above nuclear density. Motivated by this prospect, we extend the general-relativistic theory of tidal deformations to the astrophysically relevant case of spinning bodies. Working in a perturbative framework of weak, slowly varying tides and slow rotation, we find that the familiar gravitational Love numbers K₂ᵉˡ and K₂ᵐᵃᵍ, which fully describe the external geometry of a deformed nonrotating body, must be supplemented by rotational-tidal Love numbers to account for couplings between the body's spin and the applied tidal field. By integrating the Einstein field equations inside the body, we compute the rotational-tidal Love numbers explicitly for polytropes, and we find that they vanish identically for black holes. The field equations also reveal that the tidal field generically induces time-dependent fluid motions within the rotating body; these tidal currents are dynamical even if the tidal field is stationary. We calculate the amplitude of the currents for a typical neutron star in an equal-mass binary system, and find that it is on the order of kilometers per second.