  Recently it was shown that slowly rotating neutron stars exhibit an
interesting correlation between their moment of inertia $I$, their quadrupole
moment $Q$, and their tidal deformation Love number $\lambda$ (the I-Love-Q
relations), independently of the equation of state of the compact object. In
the present work a similar, more general, universality is shown to hold true
for all rotating neutron stars within General Relativity; the first four
multipole moments of the neutron star are related in a way independent of the
nuclear matter equation of state we assume. By exploiting this relation, we can
describe quite accurately the geometry around a neutron star with fewer
parameters, even if we don't know precisely the equation of state. Furthermore,
this universal behavior displayed by neutron stars, could promote them to a
more promising class of candidates (next to black holes) for testing theories
of gravity.
