HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle

TL;DR

The paper analyzes acceleration radiation for a two-level atom freely falling into a GUP-corrected Schwarzschild black hole. It derives closed-form excitation probabilities and shows the near-horizon physics remains equivalent to a uniformly accelerating mirror, with the local temperature given by $T_H^{(GUP)} = \kappa_{\rm GUP}/(2\pi)$. Treating field modes as open quantum systems driven by infalling atoms, the authors compute the GUP-corrected HBAR entropy and show it reproduces the Bekenstein-Hawking area law with a leading logarithmic correction, $S_{\rm GUP} = A_p/4 + (\beta \pi /4) \ln A_p + \text{const}$, alongside a modified specific heat $C^{(GUP)} \approx -8\pi M^2 (1 + 3β/(16M^2))$. The results support the robustness of thermal horizon processes under Planck-scale deformations and reveal a universal structure of entropy corrections that could inform black hole evaporation and information-thermodynamics, including potential remnants in the quantum gravity regime. Overall, the work provides a concrete, microscopic bridge between quantum optics in curved spacetime and quantum-gravity-inspired corrections to black hole thermodynamics, with implications for analogue systems and primordial black hole phenomenology.

Abstract

In this work, we have investigated the phenomenon of acceleration radiation exhibited by a two-level atom freely falling into a Generalized Uncertainty Principle (GUP)-corrected Schwarzschild black hole. We derive analytic expressions for the atom's excitation probability with simultaneous emission of a scalar quantum and observe that it satisfies the Einstein equivalence principle when compared to the excitation probability induced by a uniformly accelerating mirror, motivated by studies [10.1103/PhysRevLett.121.071301] and [10.1073/pnas.1807703115]. Adopting an open-quantum-system framework, we then compute the horizon-brightened acceleration radiation (HBAR) entropy for the GUP-corrected spacetime and find that it reproduces the Bekenstein-Hawking entropy law, with corrections characteristic of GUP effects. These results underline the robustness of thermal radiation processes near horizons and the universality of entropy corrections in quantum-improved black hole spacetimes.