Acceleration Radiation from Derivative-Coupled Atoms Falling in Modified Gravity Black Holes

TL;DR

The paper develops a general framework to study acceleration radiation from a derivatively coupled Unruh–DeWitt detector on radial infall into static, spherically symmetric black holes. It derives a universal integral expression for the excitation probability that encodes the background metric and applies it to two modified gravity spacetimes: an Extended Uncertainty Principle black hole and a Ricci‑coupled Kalb–Ramond Bumblebee gravity black hole with a global monopole. The results show a perfect thermal spectrum at the Hawking temperature for the EUP case and a thermally modified spectrum in the Bumblebee case, with the effective temperature controlled by Lorentz‑violating parameters; moreover, derivative coupling enhances the associated entropy flux relative to minimal coupling. These findings establish acceleration radiation as a sensitive probe of near‑horizon physics and a potential observational signature to distinguish GR from alternative gravity theories in the strong‑field regime.

Abstract

The interaction of quantum detector models with fields in curved spacetimes provides fundamental insights into phenomena such as Hawking and Unruh radiation. While standard models typically assume a minimal coupling between the detector and the field, physically motivated derivative couplings, which are sensitive to field gradients, have been less explored, particularly in the context of modified gravity theories. In this paper, we develop a general framework to analyze the acceleration radiation from a two-level atomic detector with a derivative coupling undergoing a radial geodesic infall into a generic static, spherically symmetric black hole. We derive a general integral expression for the excitation probability and apply it to two distinct spacetimes. For an extended uncertainty principle (EUP) black hole, we demonstrate that the detector radiates with a perfect thermal spectrum at the precise Hawking temperature, reinforcing the universality of this phenomenon. For a black hole solution in a Ricci-coupled Bumblebee gravity model, the radiation is also thermal. Still, its temperature is modified in direct correspondence with the theory's Lorentz-violating parameters, consistent with the modified Hawking temperature. Furthermore, we demonstrate that derivative coupling results in a significantly enhanced entropy flux compared to minimal coupling models. Our results establish acceleration radiation as a sensitive probe of near-horizon physics and demonstrate that this phenomenon can provide distinct observational signatures to test General Relativity (GR) and alternative theories of gravity in the strong-field regime.

Figures (3)

• Figure 1: Conceptual illustration of acceleration radiation from an atom near a black hole. A reflective boundary, or "mirror," is held at a fixed position outside the event horizon. This boundary establishes a defined Boulware-like vacuum state for the infalling atom, effectively shielding it from pre-existing Hawking radiation. As the atom plunges through this vacuum, the immense proper acceleration it experiences relative to the quantum field modes induces the emission of a photon, a phenomenon known as acceleration radiation.
• Figure 2: The excitation probability $P_{\text{exc}}^{\text{(der)}}$ for a derivatively coupled atom undergoing radial free-fall into a dimensionless EUP-corrected black hole ($M=1$, $\alpha=1$). The thermal radiation spectrum is plotted as a function of dimensionless frequency $\nu$ for several values of the EUP fundamental length scale, $L_*$, relative to the black hole mass. The plot shows that as $L_*$ increases, the EUP-corrected spectrum (solid lines) systematically converges to the standard GR case (dashed line), which represents the limit $\alpha = 0$. Here, $g = 0.001$.
• Figure 3: The excitation probability $P_{\text{exc}}^{\text{(der)}}$ for a derivatively coupled atom in radial free-fall, plotted as a function of dimensionless frequency $\nu$ for a black hole in a Ricci-coupled Bumblebee gravity model. The thermal spectrum is shown for several values of the Lorentz-violating parameter $a$. The results are compared to the standard GR case, which corresponds to $a = 0$. The plot demonstrates that as the parameter $a$ increases, the radiation is enhanced, and the effective temperature of the spectrum increases, shifting the thermal cutoff to higher frequencies. Here, $g = 0.001$.