Entanglement, equivalence principle, and HBAR entropy, in a new bumblebee black hole

Abstract: We investigate quantum information and thermodynamic properties of a new bumblebee black hole arising from spontaneous Lorentz symmetry breaking by analyzing near-horizon physics through complementary quantum probes. We study the degradation of quantum entanglement for field modes shared by inertial and accelerated observers in spacelike and lightlike Lorentz-violating vacua that generate identical spacetime metrics. Using the near-horizon Rindler correspondence, we derive analytic expressions for the logarithmic negativity and mutual information and examine their dependence on detector position, frequency, and Lorentz-violation parameters. Despite sharing the same metric, the two Lorentz-violating vacua become distinguishable near the horizon, particularly at low frequencies. We analyze the excitation of a freely falling two-level atom coupled to quantum fields near the horizon. The associated acceleration-radiation transition probabilities are computed explicitly. The resulting atomic response is locally indistinguishable from that in flat spacetime, confirming the validity of the equivalence principle even in the presence of Lorentz-violating corrections. Finally, we extend the notion of horizon-brightened acceleration radiation (HBAR) entropy to the bumblebee black hole and derive the corresponding entropy production rate induced by infalling atoms.