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arxiv: 2605.10424 · v2 · pith:F6VAWXEAnew · submitted 2026-05-11 · 🌀 gr-qc · quant-ph

Quantum Correlations of Neutrinos in the Kerr-Newman Space-time

Ze-Wen Li , Shu-Jun Rong This is my paper

Pith reviewed 2026-06-30 22:35 UTC · model grok-4.3

classification 🌀 gr-qc quant-ph
keywords neutrinosquantum correlationsKerr-Newman spacetimeoscillation probabilitiesentanglementSchwarzschild metricweak-field approximationblack hole parameters
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The pith

In Kerr-Newman spacetime, neutrino oscillation probabilities and quantum correlations for inward paths differ from the Schwarzschild metric, with spin lengthening and charge shortening outward periods.

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

The paper establishes that the mass, angular momentum, and charge parameters of the Kerr-Newman metric alter neutrino survival probabilities and quantum correlations such as entanglement and coherence, with effects that depend on propagation direction. Under the weak-field approximation, inward radial propagations produce results that deviate from the Schwarzschild case, while outward radial paths show increased oscillation periods from larger angular momentum and decreased periods from larger charge. Non-radial paths exhibit amplitude modulation by mass and angular momentum that does not appear in radial cases. Entanglement and coherence maintain consistent oscillation patterns across both radial and non-radial scenarios despite differing variation ranges. A sympathetic reader would care because these differences link spacetime geometry directly to measurable quantum information quantities carried by neutrinos.

Core claim

The central claim is that in the Kerr-Newman spacetime, for inward propagations the oscillation probabilities and quantum correlations differ significantly from those in the Schwarzschild metric. For radial outward propagation, larger angular momentum a increases the oscillation period of the survival probability P_ee, entanglement, and monogamy of nonlocality, whereas larger charge Q decreases the corresponding periods. For non-radial propagations, M and a noticeably modulate the amplitudes of the considered quantum correlations. Entanglement and coherence exhibit highly consistent oscillation behaviors in both radial and non-radial cases despite differences in their variation ranges.

What carries the argument

The weak-field approximation in the Kerr-Newman metric applied to neutrino oscillation phases to derive quantum correlations including entanglement, coherence, and monogamy of nonlocality.

If this is right

  • Inward neutrino paths near rotating charged black holes produce quantum correlation signatures distinct from non-rotating uncharged cases.
  • Increasing black hole angular momentum lengthens the periods of P_ee, entanglement, and monogamy measures for outward radial neutrino propagation.
  • Increasing black hole charge shortens those same oscillation periods for outward radial paths.
  • Mass and angular momentum parameters modulate quantum correlation amplitudes only in non-radial neutrino paths.

Where Pith is reading between the lines

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

  • Astrophysical neutrinos could serve as probes of black hole spin and charge through quantum correlation measurements if the weak-field regime holds.
  • The consistent oscillation patterns between entanglement and coherence suggest they may be interchangeable observables for spacetime effects in this setting.
  • Similar calculations could extend to other fermions or to strong-field regimes to test the limits of the current approximation.

Load-bearing premise

The weak-field approximation remains valid for the radial and non-radial neutrino propagations considered in the Kerr-Newman metric, allowing standard quantum correlation calculations without additional curvature-induced corrections.

What would settle it

Measure the electron neutrino survival probability oscillation period for neutrinos traveling outward radially near a known Kerr-Newman black hole and check whether the period lengthens with measured spin and shortens with measured charge compared to Schwarzschild predictions.

Figures

Figures reproduced from arXiv: 2605.10424 by Shu-Jun Rong, Ze-Wen Li.

Figure 1
Figure 1. Figure 1: Neutrino oscillation probability Pνe→νe in different space-times. The left panel: radially outward propagations, the right panel: radially in￾ward propagations [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Neutrino oscillation probability Pνe→νe in the Kerr-Newman metric. The left column: a = 1×107 km, Q = 1×107 km; the middle : Q = 1×108 km, M = 1 × 103 km; the right: M = 1 × 107 km, a = 1 × 107 km. The top and bottom row correspond respectively to the radially outward and inward propagations. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Tripartite entanglement of neutrinos in different kinds of curved [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Tripartite entanglement of neutrinos for different metric parame [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Monogamy of non-locality for neutrinos in different kinds of [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Monogamy of non-locality for neutrinos in the Kerr-Newman space [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Monogamy of non-locality for neutrinos in the Kerr-Newman space [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Monogamy of non-locality for neutrinos in the Kerr-Newman space [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Schematic diagram for weak lensing of neutrinos in the Kerr [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: As shown in [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 10
Figure 10. Figure 10: Non-radial oscillation probability Pνe→νe in the Kerr-Newman metric. The left column: a = 1 × 103 m, Q = 1 × 103 m; the middle : Q = 1 × 104 m, M = 1 × 105 m; the right: M = 1 × 105 m, a = 1 × 107 m. 4.2 Entanglement of neutrinos for non-radial propaga￾tion in the Kerr-Newman metric Here we employ the same quantification method and initial neutrino state as those used in the radial case, as given in Eq. 4… view at source ↗
Figure 11
Figure 11. Figure 11: Tripartite entanglement of neutrinos for non-radial propagation [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Monogamy of neutrino non-locality for non-radial propagation [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Quantum coherence of neutrinos in different kinds of curved space [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Quantum coherence of neutrinos for different metric parameters. [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Quantum coherence of neutrinos for non-radial propagation under [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
read the original abstract

Quantum phases provide a connection between gravitation and quantum information, which proposes a novel avenue to explore the properties of space-time. In this paper, we investigate the quantum correlations (QCs) of neutrinos in the Kerr--Newman space-time. Both radial and non-radial propagations are considered under the weak-field approximation. The results show that, for inward propagations, the oscillation probabilities and QCs differ significantly from those obtained in the Schwarzschild metric. In the case of radial outward propagation, the larger angular momentum $a$ increases the oscillation period of the survival probability $P_{ee}$, entanglement, and monogamy of nonlocality, whereas the larger charge $Q$ decreases the corresponding periods. For non-radial propagations, $M$ and $a$ can noticeably modulate the amplitudes of the considered QCs, which is not observed in the case of radial propagations. Furthermore, we find that, despite differences in their variation ranges, entanglement and coherence exhibit highly consistent oscillation behaviors in both radial and non-radial propagation cases. These findings provide a comprehensive understanding for the neutrinos-based relativistic quantum information.

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

2 major / 2 minor

Summary. The paper studies quantum correlations (entanglement, coherence, monogamy of nonlocality) of neutrinos propagating in Kerr-Newman spacetime under the weak-field approximation. It considers both radial (inward/outward) and non-radial trajectories, reporting that inward paths yield oscillation probabilities and QCs that differ markedly from Schwarzschild results; outward radial propagation shows a increasing and Q decreasing the periods of P_ee, entanglement, and monogamy; non-radial cases exhibit amplitude modulation by M and a; and entanglement/coherence display consistent oscillation patterns despite differing ranges.

Significance. If the weak-field approximation holds along the trajectories, the results would extend prior Schwarzschild analyses to include charge and spin, demonstrating directional dependence and parameter modulation of neutrino QCs. This could offer a concrete link between spacetime parameters and relativistic quantum information measures, with potential implications for neutrino-based probes of strong gravity. The work supplies explicit trends (e.g., period shifts with a and Q) that are falsifiable in principle once the approximation is validated.

major comments (2)
  1. [Inward propagation results (abstract and corresponding section)] The central claims for inward propagations (significant differences from Schwarzschild in P_ee and QCs) rest on inserting the first-order weak-field Kerr-Newman line element into the standard neutrino phase integral and then applying flat-space QC formulas. No explicit check or error bound is supplied showing that the neglected O((M/r)^2, (a/r)^2, (Q/r)^2) terms remain ≪1 along the actual inward geodesics, which approach smaller r where the approximation is most vulnerable.
  2. [Radial outward and non-radial propagation analyses] The reported modulation of oscillation periods by a and Q (outward radial) and amplitudes by M and a (non-radial) likewise follow from the first-order metric insertion. Without a quantitative assessment of curvature-induced corrections to the phase or to the QC measures themselves, it is unclear whether these trends survive in the full Kerr-Newman geometry.
minor comments (2)
  1. [Methods] Notation for the neutrino flavor states and the precise definition of the quantum correlation measures (e.g., concurrence or negativity) should be stated explicitly with references to the flat-space formulas being used.
  2. [Abstract] The abstract states results for 'inward propagations' without specifying the range of r or impact parameter; a brief statement of the validity domain assumed for the weak-field limit would improve clarity.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments on the weak-field approximation. We address each major comment below and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [Inward propagation results (abstract and corresponding section)] The central claims for inward propagations (significant differences from Schwarzschild in P_ee and QCs) rest on inserting the first-order weak-field Kerr-Newman line element into the standard neutrino phase integral and then applying flat-space QC formulas. No explicit check or error bound is supplied showing that the neglected O((M/r)^2, (a/r)^2, (Q/r)^2) terms remain ≪1 along the actual inward geodesics, which approach smaller r where the approximation is most vulnerable.

    Authors: We agree that the absence of an explicit error bound is a limitation. Our analysis follows the standard first-order weak-field approach used in prior Schwarzschild studies, with trajectories restricted to regions satisfying r ≫ M, a, Q. We will revise the manuscript to add an explicit discussion of the validity range of the approximation and note that the reported differences from the Schwarzschild case arise at leading order. A full quantitative error analysis along the entire inward path would require higher-order metric terms and is beyond the present scope. revision: partial

  2. Referee: [Radial outward and non-radial propagation analyses] The reported modulation of oscillation periods by a and Q (outward radial) and amplitudes by M and a (non-radial) likewise follow from the first-order metric insertion. Without a quantitative assessment of curvature-induced corrections to the phase or to the QC measures themselves, it is unclear whether these trends survive in the full Kerr-Newman geometry.

    Authors: The observed modulations originate from the linear contributions of a and Q in the Kerr-Newman metric. While we acknowledge that higher-order curvature corrections are not quantified, the leading-order trends are expected to remain robust because they are directly tied to the included metric components. In the revised version we will insert a paragraph clarifying this limitation and the anticipated persistence of the directional and parameter-dependent behaviors within the weak-field regime. revision: partial

standing simulated objections not resolved
  • A complete quantitative assessment of O((M/r)^2, (a/r)^2, (Q/r)^2) corrections to the neutrino phase and quantum correlation measures along the full trajectories in the exact Kerr-Newman geometry.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation proceeds by substituting the first-order weak-field Kerr-Newman line element into the standard neutrino phase integral along geodesics, then feeding the resulting phases into conventional flat-space quantum-correlation measures (concurrence, coherence, monogamy). None of these steps is self-definitional, a fitted input renamed as prediction, or dependent on a load-bearing self-citation; the metric components, phase formula, and QC definitions are taken from independent literature and applied without circular reduction. The reported differences for inward paths and the modulation trends with a, Q, and M are therefore direct algebraic consequences of the inserted metric rather than tautological restatements of the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on validity of weak-field approximation for neutrino propagation and standard application of quantum correlation measures in curved spacetime; no free parameters, invented entities, or additional axioms are extractable from the abstract.

axioms (1)
  • domain assumption Weak-field approximation is sufficient for the propagations considered
    Explicitly stated in the abstract for both radial and non-radial cases.

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