Lorentz violation alleviates gravitationally induced entanglement degradation

Lorentz violation is a significant phenomenon in the framework of quantum physics, with implications for fundamental symmetries. In this paper, we explore the effects of Lorentz violation on quantum entanglement through a black hole spacetime that is coupled with a Lorentz-violating field. We establish the relationship between the Hartle-Hawking vacuum state and the Boulware number states for this case, and employ the near horizon approximation in an appropriate form to rewrite the black hole metric into a Rindler-like form. Subsequently, using this revised metric, the analytical forms of logarithmic negativity and mutual information are derived and plotted as functions of Rob's distance from the $ r=0 $ point. Based on the results, we find that the coupling between spacetime and the Lorentz-violating vector field alleviates gravity-induced entanglement degradation. At high mode frequencies, the effects of Lorentz violation are negligible, but they become significant at low frequencies. This suggests that investigating Lorentz violation at astrophysical scales requires low-frequency detectors, as the low energy of these fields enhances the significance of the Lorentz-violating field's non-zero vacuum expectation value.