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I-Love irrotationally

In this short note, we investigate the existence of universal relations between the gravimagnetic Love number of irrotational stars and the dimensionless moment of inertia. These Love numbers take into account the internal motion of the fluid, while the star is globally irrotational. The goal is to extend the so-called I-Love-Q relations - providing a strong correlation between the gravitoelectric Love number, the dimensionless moment of inertia and the dimensionless rotation-induced quadrupole - to the gravitomagnetic sector, where internal motion is taken into account. As a byproduct, we present for the first time this new gravitomagnetic Love number for realistic equations of state.