Decoherence of quantum superpositions in near-extremal Reissner-Nordstr\"om black holes with quantum gravity corrections

We study the quantum gravity corrected decoherence of quantum superpositions in the near-extremal Reissner-Nordstr\"om black holes. By employing the effective field theory approach, we model the black hole as a quantum system coupled to an external source via a scalar field, and derive the relation between the decoherence rate and the two-point correlation function of the operators acting on the black quantum system. By utilizing the low-energy Schwarzian effective theory, which captures the boundary dynamics of the $AdS_2$ near-horizon geometry of the near-extremal Reissner-Nordstr\"om black holes, we compute the decoherence rate both in the microcanonical and canonical ensembles. We find that in the microcanonical ensemble, where the black hole energy is fixed, quantum gravity corrections do not modify the decoherence rate compared to the semiclassical prediction. However, in the canonical ensemble, where the black hole is in a thermal equilibrium state, quantum gravitational effects significantly enhance the decoherence rate at low temperatures. Our results demonstrate that even in the near-extremal limit where Hawking radiation is suppressed, quantum gravitational fluctuations can strongly influence the coherence of nearby quantum systems.