Atom falling into a quantum corrected charged black hole and HBAR entropy

Abstract: In an earlier analysis \href{https://link.aps.org/doi/10.1103/PhysRevD.105.085007}{Phys. Rev. D 105 (2022) 085007}, we have explored the event of acceleration radiation for an atom freely falling into the event horizon of a quantum-corrected Schwarzschild black hole. We want to explore the acceleration-radiation when the atom is freely falling into the event horizon of a charged quantum-corrected black hole. We consider the quantum effects of the electromagnetic field along with the gravitational field in an asymptotic safety regime. Introducing the quantum improved Reisner-Nordstr\"{o}m metric, we have calculated the excitation probability of a two-level atom freely falling into the event horizon of quantum improved charged black hole. Recently, in the case of the braneworld black hole (where the tidal charge has the same dimension as the square of the charge of a Reissner-Nordstr\"{o}m black hole in natural units), we have observed from the form of the transition probability that the temperature will have no contribution in the first order of the tidal charge. We observe that for a quantum corrected Reissner-Nordstr\"{o}m black hole, there is a second-order contribution in the charge parameter in the temperature that can be read off from the transition probability. Next, we calculate the HBAR entropy in this thought experiment and show that this entropy has a leading order Bekenstein-Hawking entropy term along with some higher order correction terms involving logarithmic as well as fractional terms of the black hole area due to infalling photons. We have finally investigated the validity of Wien's displacement law and compared the critical value of the field wavelength with the general Schwarzschild black hole and its corresponding quantum-corrected case.