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arxiv: 2606.26372 · v1 · pith:EWQU7XZYnew · submitted 2026-06-24 · 🌀 gr-qc · hep-th

Effect of the magnetic monopole charge on Dirac entanglement and Bell non-locality in Hayward spacetime

Abdessamie Chhieb , Mohamed Ouchrif This is my paper

Pith reviewed 2026-06-26 01:09 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Hawking radiationDirac fieldsquantum entanglementBell nonlocalityHayward black holeregular black holesfermionic correlationsPauli exclusion
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The pith

Dirac field entanglement in Hayward spacetime stays nonzero at infinite Hawking temperature due to the Pauli principle.

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

The paper studies how Hawking radiation degrades an entangled Dirac state shared by an inertial observer and one near the horizon of a Hayward regular black hole. It finds that fermionic correlations never reach zero even as temperature becomes infinite, because the exclusion principle blocks complete degradation, while some entanglement shifts to inaccessible interior modes. Accessible modes continue to violate Bell inequalities at any finite temperature, but interior modes never do. The regularity parameter g enters the results only by lowering the Hawking temperature, which in turn slows the loss of quantum information. This establishes a direct link between the resolution of the central singularity and the survival of fermionic quantum correlations.

Core claim

Using the Wootters concurrence and the CHSH Bell parameter on the entangled Dirac state, the calculation shows that accessible modes exhibit Bell nonlocality for every finite Hawking temperature while interior modes never violate the inequality. Fermionic correlations remain nonzero in the infinite-temperature limit owing to the Pauli exclusion principle, with part of the entanglement redistributed to inaccessible modes inside the horizon. The Hayward regularity parameter g affects the correlations only through the Hawking temperature, whose decrease with increasing g enhances preservation of quantum information.

What carries the argument

Wootters concurrence and CHSH Bell parameter applied to the Dirac entangled state, with the Hayward regularity parameter g entering exclusively through its effect on the Hawking temperature.

If this is right

  • Accessible modes violate Bell's inequality at all finite Hawking temperatures.
  • Interior modes never violate Bell's inequality.
  • Fermionic correlations remain nonzero at infinite temperature, unlike the bosonic case.
  • Increasing the Hayward parameter g lowers the Hawking temperature and thereby slows the loss of quantum correlations.
  • Singularity resolution in regular black holes is tied to greater robustness of fermionic quantum information.

Where Pith is reading between the lines

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

  • The temperature-only dependence may hold for other regular black-hole metrics whose surface gravity depends on a similar regularity parameter.
  • Analog condensed-matter systems with tunable effective temperatures could test whether fermionic entanglement persists at high temperature.
  • Quantum communication protocols near black holes could exploit regularity parameters to maintain correlations longer than in singular spacetimes.

Load-bearing premise

The standard Hawking temperature formula for the Hayward metric fully captures the effect on the chosen entangled Dirac state, with no additional back-reaction or mode-mixing terms required.

What would settle it

An explicit calculation of the concurrence or CHSH value that shows dependence on the Hayward parameter g at fixed Hawking temperature would falsify the claim that g acts only through temperature.

Figures

Figures reproduced from arXiv: 2606.26372 by Abdessamie Chhieb, Mohamed Ouchrif.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic representation of the physical setup. Alice, with qubit [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Concurrences [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Same quantities as in Fig [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Concurrences and CHSH parameters as functions of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Concurrences and CHSH parameters as functions of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Comparison of fermionic (Dirac, solid black) and bosonic (scalar, dashed red) concurrences. (a) Accessible [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original abstract

We investigate bipartite quantum correlations of Dirac fields in the spacetime of a Hayward regular black hole. Using the Wootters concurrence and the CHSH Bell parameter, we analyze the influence of Hawking radiation on an entangled state shared by an inertial observer and a near-horizon observer. We show that, unlike the bosonic case, fermionic correlations remain nonzero even in the infinite-temperature limit owing to the Pauli exclusion principle, while part of the entanglement is redistributed to inaccessible modes inside the horizon. The accessible modes exhibit Bell nonlocality for all finite Hawking temperatures, whereas the interior modes never violate Bell's inequality. The Hayward regularity parameter $g$ affects the correlations only through the Hawking temperature, whose decrease with increasing $g$ enhances the preservation of quantum information. These results suggest a close connection between singularity resolution and the robustness of fermionic quantum correlations in regular black-hole spacetimes.

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 investigates bipartite quantum correlations of Dirac fields in the Hayward regular black hole spacetime. It considers an initially entangled Dirac state shared between an inertial observer and a near-horizon observer, applies the Wootters concurrence and CHSH Bell parameter after tracing over inaccessible modes, and examines the effects of Hawking radiation. The central claims are that fermionic correlations remain nonzero in the infinite-temperature limit due to the Pauli exclusion principle (with part of the entanglement redistributed to interior modes), that accessible exterior modes exhibit Bell nonlocality for all finite Hawking temperatures while interior modes never violate the CHSH inequality, and that the regularity parameter g influences all results exclusively through the Hawking temperature (whose decrease with increasing g improves correlation preservation).

Significance. If the results hold, the work establishes a concrete connection between singularity resolution in regular black holes and the robustness of fermionic quantum information against Hawking radiation. It shows explicitly how the Pauli principle protects fermionic correlations at high temperatures in a manner absent for bosons, and demonstrates that the Hayward parameter g enters the final expressions only via the surface gravity at the outer horizon. The calculation follows the standard Bogoliubov transformation between Boulware and Hartle-Hawking modes for Dirac fields in a static spherically symmetric metric, yielding parameter-free predictions once the metric is fixed.

minor comments (3)
  1. [§3] §3 (or the section presenting the mode expansion): the explicit form of the Bogoliubov coefficients for the Dirac field in the Hayward metric should be written out, even if they reduce to the standard Fermi-Dirac factor; this would make the claim that g enters solely through T fully transparent.
  2. [Figures in §4/5] Figure captions (likely in §4 or §5): the range of g values and corresponding Hawking temperatures used in the plots should be stated explicitly, together with the precise definition of the initial entangled state (including any normalization constants).
  3. [Abstract and §5] The abstract states that interior modes 'never violate Bell's inequality'; the corresponding CHSH value should be shown to remain below 2 for all T, perhaps with a short analytic argument in addition to numerics.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive recommendation of minor revision. The provided summary accurately captures the scope, methods, and central claims of the manuscript.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained standard QFT calculation

full rationale

The paper computes Dirac field correlations via standard Bogoliubov transformations between Boulware and Hartle-Hawking modes in the Hayward metric. The Hawking temperature T = κ/2π is obtained directly from the surface gravity at the outer horizon (with g entering the metric and thus κ in the usual way), and all reported quantities (concurrence, CHSH) are explicit functions of this T and the fermionic mode structure. No parameters are fitted to data and then relabeled as predictions; no uniqueness theorems or ansatzes are imported via self-citation; the Pauli-exclusion and interior/exterior redistribution results follow algebraically from the two-mode fermionic vacuum without reducing to the input state by construction. The central claims are therefore independent of the paper's own fitted values or prior self-referential results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only; standard assumptions of quantum field theory in curved spacetime are used but not enumerated.

axioms (2)
  • domain assumption Hawking temperature is obtained from the surface gravity of the Hayward metric in the usual semiclassical way.
    Abstract states that g affects correlations only through this temperature.
  • domain assumption The initial state is a standard entangled Dirac pair with one observer inertial and one near the horizon.
    Central to the bipartite correlation calculation described.

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discussion (0)

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