Observational signature of Lorentz violation in acceleration radiation

In recent years, Lorentz violation (LV) has emerged as a vibrant area of research in fundamental physics. Despite predictions from quantum gravity theories that Lorentz symmetry may break down at Planck-scale energies, which are currently beyond experimental reach, its low-energy signatures could still be detectable through alternative methods. In this paper, we propose a quantum optical approach to investigate potential LV effects on the acceleration radiation of a freely falling atom within a black hole spacetime coupled to a Lorentz-violating vector field. Our proposed experimental setup employs a Casimir-type apparatus, wherein a two-level atom serves as a dipole detector, enabling its interaction with the field to be modeled using principles from quantum optics. We demonstrate that LV can introduce distinct quantum signatures into the radiation flux, thereby significantly modulating particle emission rates. It is found that while LV effects are negligible at high mode frequencies, they become increasingly pronounced at lower frequencies. This suggests that detecting LV at low-energy scales may depend on advancements in low-frequency observational techniques or detectors.

💡 Research Summary

The paper investigates whether Lorentz‑violating (LV) physics can be probed through the acceleration radiation emitted by a freely falling two‑level atom in a black‑hole spacetime that is coupled to a Lorentz‑violating vector (bumblebee) field. The authors adopt the Einstein‑bumblebee model, in which a vector field Bμ acquires a non‑zero vacuum expectation value bμ, thereby spontaneously breaking Lorentz symmetry. The non‑minimal coupling constant ϱ and the magnitude of the VEV combine into a dimensionless LV parameter ℓ = ϱ b². In the resulting Schwarzschild‑like metric, the lapse function F(r)=1−2M/r is modified by the factor (1+ℓ) in the radial component, shifting the effective geometry of the horizon while leaving the horizon radius r_g = 2M unchanged.

The trajectory of a freely falling atom is obtained from the geodesic equations. With conserved energy per unit mass e, the radial velocity and the relation between proper time τ, coordinate time t and the radial coordinate r are derived (Eqs. 9‑10). Plots (Fig. 1) show that positive ℓ pushes the proper‑time curve outward, whereas negative ℓ pulls it inward, illustrating how LV deforms the near‑horizon kinematics.

In the near‑horizon region (r≈r_g) the massless Klein‑Gordon equation for the field reduces to a conformal quantum‑mechanics (CQM) problem with an effective inverse‑square potential V_D(x)=λ_eff x⁻², where x = r−r_g and λ_eff = ¼+Θ² with Θ = ν √(1+ℓ)/F′_g. The CQM solutions are power‑law modes u(x)∝x^{iΘ}, which translate into outgoing field modes φ(r,t)≈x^{iΘ} e^{-iν