Entanglement degradation of static black holes in effective quantum gravity

TL;DR

This paper investigates how quantum-gravity corrections in a covariant, effective framework modify entanglement degradation near black holes. By focusing on the third-type effective quantum black hole, which admits a near-horizon Rindler limit and lacks a Cauchy horizon, the authors derive closed-form expressions for entanglement measures (logarithmic negativity) and mutual information for scalar and Dirac fields in terms of dimensionless parameters $\tilde{\omega}$, $\tilde{\zeta}$, and $R_0$. They find that the quantum parameter $\tilde{\zeta}$ acts as a universal protective factor against gravitational suppression of quantum correlations, with scalar entanglement more sensitive to these corrections than fermionic entanglement. A notable result for Dirac fields is the conservation of total correlations, $I_{AB}+I_{A\bar{B}}=2$, independent of $\tilde{\zeta}$, and a finite residual entanglement of $\mathcal{N}\approx 0.58$ as Bob nears the horizon. Overall, the work shows that quantum-gravity corrections can stabilize relativistic quantum information near horizons and establishes the third-type EQG black hole as a transparent platform for exploring quantum gravity effects on entanglement dynamics.

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.

Figures (7)

• Figure 1: The relationship between the quantum parameter and the black hole event horizon is analyzed in the effective quantum black holes, with $n = 0$.
• Figure 2: The comparison between the fitted horizon expression $r_h^{(5)}$ and the purely numerical result $r_h$, with the inset displaying the percentage difference between them.
• Figure 3: Two observers (field modes), Alice and Bob, are maximally entangled in the flat region and then transported toward the near-horizon region. As Alice freely falls into the black hole and Bob hovers outside the event horizon, their entanglement degrades due to gravitational effects.
• Figure 4: Scalar field: The entanglement of the Alice-Bob system is analyzed as a function of Bob’s position $R_0 = r_0/r_h$ and the quantum parameter $\tilde{\zeta}=\zeta/M$ for different values of $\tilde{\omega}=\omega_i M$. The entanglement vanishes as Bob approaches the horizon $r_h$, and no entanglement is created between Alice and antiBob.
• Figure 5: Scalar field: The mutual information of the Alice–Bob system is analyzed as a function of Bob’s position $R_0 = r_0/r_h$ and the quantum parameter $\tilde{\zeta}=\zeta/M$ for different values of $\tilde{\omega}=\omega_i M$.