I-Q relation of neutron star affected by massive graviton

Recently, it has been found that there is a relationship between the moment of inertia I and gravitational quadrupole moment Q of a neutron star, which is well-known as the I-Q relation of a neutron star. Specifically, the I-Q relation is found to be independent of the state equation of matter inside a neutron star and is only related to gravitational theories. Therefore, this I-Q relation can be used to test gravitational theories. The dRGT massive gravity is a well-defined modified gravity with massive graviton, which has attracted considerable attention. In this study, we mainly investigate the I-Q relation of a neutron star affected by massive graviton in the dRGT massive gravity. By focusing on a slow rotational neutron star, and using the state equation of matter inside the star with n =0 case in the polytropic process, we analytically obtain the I-Q relation under the Newtonian limit of neutron stars in the dRGT massive gravity. We compare our results with those in Einstein gravity, and obtain that the I-Q relation still holds in the presence of massive graviton. However, the proportional coefficient of the I-Q relation is dependent on the graviton mass parameter m .