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Recently it was shown that slowly rotating neutron stars exhibit aninteresting correlation between their moment of inertia $I$, their quadrupolemoment $Q$, and their tidal deformation Love number $\lambda$ (the I-Love-Qrelations), independently of the equation of state of the compact object. Inthe present work a similar, more general, universality is shown to hold truefor all rotating neutron stars within General Relativity; the first fourmultipole moments of the neutron star are related in a way independent of thenuclear matter equation of state we assume. By exploiting this relation, we candescribe quite accurately the geometry around a neutron star with fewerparameters, even if we don't know precisely the equation of state. Furthermore,this universal behavior displayed by neutron stars, could promote them to amore promising class of candidates (next to black holes) for testing theoriesof gravity.

Effectively universal behavior of rotating neutron stars in general relativity makes them even simpler than their Newtonian counterparts