Entanglement degradation of static black holes in effective quantum gravity

Abstract

Quantum information science has been broadly explored in Einstein gravity and in various modified gravity theories; however, its extension to quantum gravity settings remains largely unexplored. Motivated by this gap, in this paper we investigate the degradation of quantum entanglement of scalar and Dirac fields in the third-type black hole geometry arising from effective quantum gravity, which incorporates generic quantum gravitational corrections beyond classical general relativity. This quantum corrected spacetime is free of a Cauchy horizon and can be cast into a Rindler form in the near-horizon regime, allowing a direct identification of vacuum modes and a clear correspondence with the framework developed for uniformly accelerated observers. Within this framework, we compute the quantum entanglement and mutual information of uniformly entangled detector pairs in terms of the quantum parameter $\tildeζ$, the mode frequency $\tildeω$, and Bob's radial position $R_0$. The quantum parameter $\tildeζ$ consistently weakens the horizon-induced loss of correlations. For scalar fields this effect is pronounced, producing clear departures from the classical behavior, whereas for Dirac fields the familiar correlation pattern remains intact but its degradation is noticeably reduced. Overall, $\tildeζ$ acts as a universal protective factor against gravitational suppression of quantum correlations. The third-type effective quantum black hole therefore provides a controlled and physically transparent arena for probing how quantum-gravity corrections influence relativistic quantum information.