Mass-radius and I-Q relationships of neutron stars in Bumblebee gravity

Bumblebee gravity theory has garnered considerable interest in recent years owing to its potential to induce Lorentz symmetry breaking. This paper presents our calculations regarding the interior Tolman-Oppenheimer-Volkoff (TOV) equation of neutron stars under static conditions, using this modified gravity for spherically symmetric ideal fluids. To obtain analytical quantitative results, we applied a simple polytropic model with n =0. Within this model, we analytically derived the mass-radius relationship of neutron stars under the influence of Bumblebee gravity. We found that the Lorentz breaking parameter l can enhance the upper limit of a neutron star's mass. Moreover, we computed the specific relationship between the rotational inertia I and the quadrupole moment Q of neutron stars under the Newtonian limit and the slow-rotation approximation. Our findings indicate that while the Lorentz breaking parameter l does not change the square proportionality relationship of the dimensionless I and Q , it does indeed modify their proportionality coefficient. Our analytical results provide potential theoretical support for testing the breaking of Lorentz symmetry.