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arxiv: 2605.05143 · v1 · submitted 2026-05-06 · ✦ hep-th

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Quantum Entanglement in the Dirac Field Quantization around Charged Black Holes

Abdessamie Chhieb , Chaimae Banouni , Saliha Abdessamie , Mohamed Ouchrif
Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:39 UTC · model grok-4.3

classification ✦ hep-th
keywords Dirac fieldReissner-Nordström black holequantum entanglementHawking radiationconcurrenceBures distancecurved spacetimefermionic modes
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0 comments X

The pith

The electric charge of a Reissner-Nordström black hole enhances decoherence inside the event horizon while temporarily increasing accessible entanglement outside for the Dirac field.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the evolution of quantum entanglement in the Dirac field near a charged black hole when Hawking radiation is incorporated through quantum field theory in curved spacetime. It finds that increasing the black hole charge Q strengthens the loss of coherence inside the horizon yet produces a temporary rise in the entanglement detectable by an external observer. This pattern arises because the Hawking effect shifts correlations into regions behind the horizon, creating an apparent reduction for anyone outside. High-frequency modes maintain their correlations more effectively near the horizon than lower-frequency ones, and the initial entanglement angle influences the overall behavior.

Core claim

The authors show that the electric charge Q enhances decoherence inside the event horizon while, counterintuitively, temporarily increasing accessible entanglement outside. The Hawking effect induces an apparent loss of entanglement for an external observer due to correlation transfer to inaccessible regions. High-frequency modes ω exhibit greater resilience to gravitational effects, maintaining robust correlations near the horizon, with the measures of concurrence and Bures distance revealing the dependence on frequency and the initial entanglement angle θ.

What carries the argument

Concurrence C and Bures distance B applied to the quantized Dirac field modes in the Reissner-Nordström geometry, used to track how entanglement evolves with black hole charge Q, mode frequency ω, and initial angle θ under Hawking radiation.

If this is right

  • External observers register reduced entanglement because correlations are transferred to regions inside the horizon.
  • Higher black hole charge Q accelerates the loss of quantum correlations inside the horizon.
  • A temporary window of increased accessible entanglement appears outside the horizon as charge rises before other effects take over.
  • High-frequency fermionic modes preserve correlations better against gravitational decoherence than low-frequency modes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The reported redistribution of entanglement between accessible and inaccessible regions may link to questions of information flow during black hole processes, though the paper restricts itself to the static background.
  • The greater resilience of high-frequency modes offers a possible starting point for examining whether similar frequency dependence appears in other curved spacetimes or with different field types.
  • These charge-dependent trends suggest that entanglement measures could be used to probe horizon effects in analog systems that simulate charged horizons.

Load-bearing premise

Standard quantum field theory in curved spacetime is assumed to correctly quantize the Dirac field around the Reissner-Nordström geometry, and concurrence together with Bures distance are assumed to capture the relevant entanglement evolution under the chosen parameters.

What would settle it

An explicit computation of concurrence or Bures distance for fixed values of Q, ω, and θ that shows either no temporary rise in outside entanglement with increasing Q or no enhancement of inside decoherence would contradict the reported dependence on charge.

Figures

Figures reproduced from arXiv: 2605.05143 by Abdessamie Chhieb, Chaimae Banouni, Mohamed Ouchrif, Saliha Abdessamie.

Figure 1
Figure 1. Figure 1: Dynamics of C (1a-1b) and B (1c-1d) as functions the event horizon radius r+ , in two scenarios: with and without charge, for observables 1 and 2 with ω = 1, θ = π/4, view at source ↗
Figure 2
Figure 2. Figure 2: Plots illustrating C (2a-2b), B (2c-2d), as functions of the event horizon radius r+ for various values of the black hole charge Q, with θ = π/4 and ω = 1 , view at source ↗
Figure 3
Figure 3. Figure 3: Plots illustrating C (3a-3b), B (3c-3d), as functions of the event horizon radius r+ for various values of the frequency ω, with θ = π/4 and Q = 2, In the interior region, the entanglement behavior exhibits a strong dependence on the mode fre￾quency. For low-frequency modes (ω = 0), both the concurrence C1 and the Bures distance B1 remain nearly constant around moderate values (approximately 0.6), despite … view at source ↗
Figure 4
Figure 4. Figure 4: Plots illustrating C (4a-4b), B (4c-4d), as functions of the event horizon radius r+ for various values of the angle θ, with ω = 1 and Q = 2, view at source ↗
Figure 5
Figure 5. Figure 5: Plots illustrating C (5a-5b), B (5c-5d), as functions of the event horizon radius r+ and θ, with ω = 1, Q = 2, In this work, we have analyzed the quantum entanglement of the Dirac field in the vicinity of Reiss￾ner–Nordström black hole, taking into account the effects of Hawking radiation within the framework of quantum field theory in curved spacetime [23, 22]. Using concurrence and Bures distance as en￾t… view at source ↗
read the original abstract

We investigate the quantum entanglement properties of the Dirac field near a charged Reissner--Nordstr\"om black hole, incorporating the effects of Hawking radiation within the framework of quantum field theory in curved spacetime. Using concurrence \( C \) and Bures distance \( B \) as measures of entanglement, we analyze how quantum correlations evolve with respect to the electric charge \( Q \) of the black hole, the frequency \( \omega \) of fermionic modes, and the initial entanglement angle \( \theta \). Our results show that the electric charge \( Q \) enhances decoherence inside the event horizon while, counterintuitively, temporarily increasing accessible entanglement outside. The Hawking effect induces an apparent loss of entanglement for an external observer, due to correlation transfer to inaccessible regions. High-frequency modes \( \omega \) exhibit greater resilience to gravitational effects, maintaining robust correlations near the horizon. These findings highlight the redistribution of entanglement in a multipartite system in curved spacetime, with significant implications for quantum information in relativistic and gravitational contexts.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript studies quantum entanglement of Dirac fields in Reissner-Nordström spacetime within quantum field theory in curved spacetime. Using Bogoliubov transformations to incorporate Hawking radiation, it computes concurrence C and Bures distance B for two-mode fermionic states and examines their dependence on black-hole charge Q, mode frequency ω, and initial-state angle θ. The central claims are that increasing Q enhances decoherence inside the horizon while temporarily boosting accessible entanglement outside, that the Hawking effect produces apparent entanglement loss for external observers via correlation transfer to inaccessible regions, and that high-ω modes remain more robust near the horizon.

Significance. If the derivations hold, the work extends prior entanglement analyses from Schwarzschild to charged black holes and supplies concrete Q-dependence for fermionic modes. This adds to the literature on information redistribution in gravitational backgrounds and may inform models of decoherence and multipartite correlations near horizons.

minor comments (3)
  1. [Abstract] Abstract: the statement that Q 'temporarily increasing accessible entanglement outside' would be clearer if accompanied by a brief indication of the parameter range or functional form in which the increase occurs.
  2. [Formalism] The manuscript should explicitly state the normalization and cutoff procedure used for the Dirac modes when constructing the reduced density matrices for the concurrence and Bures-distance calculations.
  3. [Results] Figure captions (or the text near the plots of C and B versus Q) should indicate the fixed values of ω and θ employed so that the displayed trends can be reproduced.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our work on Dirac entanglement in Reissner-Nordström spacetime and for recommending minor revision. The assessment correctly identifies the key findings on Q-dependence, Hawking-induced correlation transfer, and mode robustness. Since no specific major comments or criticisms were raised in the report, we interpret the minor revision request as an opportunity for editorial polishing.

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper's central results follow from standard Bogoliubov transformations applied to Dirac modes in Reissner-Nordström geometry, followed by direct computation of concurrence and Bures distance on the resulting reduced density matrices. These operations are independent of any fitted parameters presented as predictions, self-definitional loops, or load-bearing self-citations. The Q-dependence of Hawking temperature enters via the standard surface-gravity formula, and the reported enhancement of decoherence inside the horizon and temporary increase in accessible entanglement outside are direct consequences of the mode mixing, not reductions to the input assumptions. The framework is self-contained against external benchmarks in quantum field theory in curved spacetime.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of quantum field theory in curved spacetime to the Dirac field in RN geometry and on the suitability of concurrence and Bures distance; no free parameters, new axioms, or invented entities are visible in the abstract.

axioms (1)
  • domain assumption Quantum field theory in curved spacetime applies to Dirac field quantization around Reissner-Nordström black holes including Hawking radiation
    Framework invoked for the entire analysis of entanglement evolution.

pith-pipeline@v0.9.0 · 5482 in / 1227 out tokens · 39666 ms · 2026-05-08T17:39:00.459156+00:00 · methodology

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Reference graph

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