Stars and quark stars in bumblebee gravity

In this work, the interior spacetime of stars is built in a Lorentz symmetry breaking model called bumblebee gravity. Firstly, we calculated the modified Tolman-Oppenheimer-Volkoff equation in this context of modified gravity. Then we show that the bumblebee field, responsible for the symmetry breaking, increases the star mass-radius relation when it assumes its vacuum expectation value. When compared to the general relativity mass-radius relation, a Lorentz symmetry breaking context, like the bumblebee gravity, could provide more massive stars, surpassing the $2.5M_{\odot }$ limit as the interior of the star is described by quark matter with the MIT bag model. Also, we investigate the stability of the solution with the MIT bag equation of state in this context of modified gravity.