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Slowly rotating homogeneous masses revisited

Hartle's model for slowly rotating stars has been extensively used to compute equilibrium configurations of slowly rotating stars to second order in perturbation theory in General Relativity, given a barotropic equation of state (EOS). A recent study based on the modern theory of perturbed matchings show that the model must be amended to accommodate EOS's in which the energy density does not vanish at the surface of the non rotating star. In particular, the expression for the change in mass given in the original model, i.e. a contribution to the mass that arises when the perturbations are chosen so that the pressure of the rotating and non rotating configurations agree, must be modified with an additional term. In this paper, the amended change in mass is calculated for the case of constant density stars.