Strange Quark Stars and Condensate Dark Stars in Bumblebee Gravity

In this paper, we investigate the properties of relativistic stars made of isotropic matter within the framework of the minimal Standard Model Extension, where a Bumblebee field (BF) coupled to spacetime induces spontaneous Lorentz symmetry breaking. We adopt analytic equations-of-state describing either condensate dark stars or strange quark stars. We solve the structure equations numerically, and we compute the mass-to-radius relationships. The influence of the Bumblebee parameter $\mathbf{l}$ is examined in detail, and an upper bound is obtained using the massive pulsar (PSR) J0740+6620 and the strangely light High Energy Stereoscopic System (HESS) J1731-347 compact object.