Impact of Lorentz violation on Radiative transition of an atom falling into spherically symmetric black hole and related BHAR entropy

Abstract: In this work, we explore the intriguing phenomenon of acceleration radiation exhibited by an atom falling into a black hole. Our investigation focuses on examining the impact of Lorentz violation within the framework of the bumblebee gravity model on this phenomenon. We observe that the excitation probability although acquires Planck-like factor the exponential part of it acquires the Lorentz violation factor that shows a clear indication of violation of equivalence principle and it is rooted to Lorentz violation conformal symmetry has nothing to do with it. Then we calculate the horizon brightened acceleration radiation (HBAR) entropy for this black hole geometry. We observed that the HBAR entropy has the form similar to that of Bekenstein-Hawking black hole entropy however it has been observed that it is also influenced by Lorentz violation aspect of Bumblebee theory. We also study the prospect of equivalence principle in this Lorentz violation background. by investigating the transition probabilities of a two-level atomic detector. Transition probabilities depend both on conformal symmetry and Lorentz violation effect.