Multipole Love Relationship

We found universal relations among the moment of inertia, tidal Love number and quadrupole moment (I-Love-Q relations) of neutron stars and quark stars that do not depend sensitively on the equation of state. We recently found similar relations between higher order electric, magnetic and shape Love numbers. Such relations have following interesting applications. On the astrophysics front, they allow us to distinguish neutron stars and quark stars. Also, by measuring one of the quantities, one automatically obtains information of all the other quantities. On the gravitational wave front, the relations allow us to break degeneracies between binary parameters and to increase the measurement accuracy of spins and tidal Love numbers. On the fundamental physics front, one can perform model-independent and equation of state independent tests of general relativity.