Correction to the two-fluid description of superfluid isolated rotating neutron stars and the corresponding tidal problem in perturbation theory

The analytical study of rotating stars in General Relativity is usually addressed within the Hartle-Thorne model, a formalism that describes rotating stars composed of a perfect fluid with a barotropic equation of state in perturbation theory. This formalism has been widely employed in Astrophysics, and has laid the groundwork for numerous works on compact objects, such as neutron stars. Nevertheless, throughout the construction of this model it was implicitly assumed that the functions describing the perturbations were continuous everywhere. However, Reina and Vera (2015) demonstrated, using the modern theory of perturbed matchings, that one of the functions presented a jump at the boundary of the star, proportional to the value of the energy density there. Consequently, all works based on the original Hartle-Thorne model needed to be revisited. Moreover, due to the purely geometrical nature of the correction, it needs to be taken into consideration irrespective of the matter content of the star, that can be more general than a perfect fluid. In this regard, we correct the adaptation of the original Hartle-Thorne model to a two-fluid formalism to describe superfluid neutron stars. In addition, we address the study of the tidal problem in binary systems, where the asymptotically flat vacuum exterior is replaced by a quadrupolar tidal field. This problem requires a matching of spacetimes in which the corrections apply. The corrections are found to be needed for the inclusion of quark stars in the so-called universal I-Love-Q relations.