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A considerable effort has been dedicated recently to the construction ofgeneric equations of state (EOSs) for matter in neutron stars. The advantage ofthese approaches is that they can provide model-independent information on theinterior structure and global properties of neutron stars. Making use of morethan $10^6$ generic EOSs, we asses the validity of quasi-universal relations ofneutron star properties for a broad range of rotation rates, from slow-rotationup to the mass-shedding limit. In this way, we are able to determine withunprecedented accuracy the quasi-universal maximum-mass ratio between rotatingand nonrotating stars and reveal the existence of a new relation for thesurface oblateness, i.e., the ratio between the polar and equatorial properradii. We discuss the impact that our findings have on the imminent detectionof new binary neutron-star mergers and how they can be used to set new and morestringent limits on the maximum mass of nonrotating neutron stars, as well asto improve the modelling of the X-ray emission from the surface of rotatingstars.

On the maximum mass and oblateness of rotating neutron stars with generic equations of state