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

TL;DR

The authors study quantum information and thermodynamics near the horizon of a new Lorentz-violating bumblebee black hole, using near-horizon Rindler methods to derive entanglement measures and detector responses. They demonstrate that spacelike and lightlike LV vacua, though sharing the same metric, are operationally distinguishable near the horizon via entanglement and information measures, especially at low frequencies. An excited freely falling atom exhibits a locally flat-spacetime-like response, supporting the equivalence principle despite LV corrections. The work extends horizon-brightened acceleration radiation (HBAR) entropy to the bumblebee geometry, showing LV-modified entropy production yet preserving the underlying framework.

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.

Figures (5)

• Figure 1: Alice and Bob are initially prepared in a maximally entangled Bell state near the Earth and then transported toward the black hole, where entanglement degrades as Alice falls across the horizon while Bob remains static at radius $r_0$.
• Figure 2: The entanglement and mutual information of the Alice-Bob system is analyzed as a function of Bob's position $r_0/r_h$, the effective bumblebee parameters $\alpha\ell$, and the mode frequency $\omega_i$.
• Figure 3: Relative deviation of entanglement and mutual information between the spacelike and lightlike Lorentz--violating branches as functions of Bob's position $r_0/M$, the Bumblebee parameter $\ell$, and the vacuum-orientation parameter $\beta$, showing that the two branches become maximally distinguishable in the near--horizon and low--frequency regimes.
• Figure 4: $\Gamma_{\text{exc}}$ is shown as a function of $\omega$ for different values of $\chi$.
• Figure 5: $\Gamma_{\text{abs}}$ is shown as a function of $\omega$ for different values of $\chi$.