Inverse logarithmic correction in the HBAR entropy of an atom falling into a renormalization group improved charged black hole

Abstract: In this work, we have considered a spherically symmetric non-rotating charged black hole geometry where both the Newton's gravitational constant and the charge of the black hole flows with the energy scale. We have used the Kretschmann scale identification to write down the finite cutoff for the momentum scale in terms of the proper distance. Introducing the flow of running couplings, the event horizon radius of the black hole using quantum improved Reissner-Nordstrom metric was found in \href{https://doi.org/10.1103/PhysRevD.104.066016}{Phys. Rev. D 104 (2021) 066016}. We have, in this work, explored the thought experiment of a two-level atom freely falling into the event horizon of a quantum improved charged black hole and have computed the transition probability of the atom for going from its ground state to the excited state via emission of a virtual photon. We find that the probability deviates slightly from the pure Planckian spectrum. We have showed that this deviation is due to the presence of incomplete lower gamma function in the distribution function. We have then computed the horizon brightened acceleration radiation entropy and found that it is identical to the Bekenstein-Hawking entropy followed by the renormalization group correction terms including an inverse logarithmic and a square root of the area term due to emitting photons.