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arxiv: 2606.12698 · v1 · pith:4YKKZ7AXnew · submitted 2026-06-10 · 🌀 gr-qc · hep-ph· hep-th

Higher Dimensional Loop Quantum Black hole in de Sitter Spacetime: Quasinormal Modes and Shadow Signatures

Kourosh Nozari , Sara Saghafi , Ali Mohammadpour This is my paper

Pith reviewed 2026-06-27 08:42 UTC · model grok-4.3

classification 🌀 gr-qc hep-phhep-th
keywords quasinormal modesblack hole shadowloop quantum gravityhigher dimensionsde Sitter spacetimedynamical stabilityEvent Horizon Telescope
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The pith

Higher-dimensional loop-quantum-corrected de Sitter black holes are stable to scalar perturbations and their shadow sizes yield bounds on the model parameters from M87* data.

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

The paper examines the stability and optical appearance of a black hole that incorporates loop quantum gravity corrections, extra spacetime dimensions, and a positive cosmological constant. Computations of quasinormal modes for massless scalar fields using three independent numerical techniques all yield negative imaginary parts, showing that perturbations damp rather than grow. The radius of the black hole shadow varies with the strength of the loop quantum correction, the cosmological constant value, and the number of dimensions, with extra dimensions generally producing smaller shadows. Matching the calculated shadow radius to Event Horizon Telescope measurements of M87* produces limits on the allowed values of these parameters.

Core claim

The central claim is that loop quantum corrections produce only moderate changes to the quasinormal spectrum of massless scalar perturbations while the number of spacetime dimensions exerts a stronger influence on both oscillation frequencies and damping rates; all modes display negative imaginary parts, establishing dynamical stability within the explored parameter range; the shadow radius depends sensitively on the loop quantum parameter, the cosmological constant, and dimensionality, and comparison with Event Horizon Telescope constraints for M87* supplies concrete bounds on the model parameters.

What carries the argument

The higher-dimensional loop-quantum-corrected de Sitter black hole metric, employed as the fixed background for deriving the wave equation solved by three numerical methods and for integrating null geodesics that determine the shadow radius.

If this is right

  • All quasinormal modes damp with time, confirming dynamical stability against massless scalar perturbations in the studied parameter range.
  • Increasing the number of spacetime dimensions raises both the real frequencies and the damping rates of the modes.
  • Extra dimensions reduce the size of the black hole shadow.
  • The loop quantum parameter and cosmological constant can be bounded by requiring the theoretical shadow radius to agree with Event Horizon Telescope data for M87*.

Where Pith is reading between the lines

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

  • Tighter future measurements of black hole shadows could narrow the allowed range for loop quantum corrections in strong-gravity regimes.
  • The stability result may extend to other field types if the same metric and numerical methods are applied.
  • The sensitivity of the shadow to dimensionality offers a potential observational route to test extra-dimension scenarios.

Load-bearing premise

The analysis takes the given higher-dimensional loop-quantum-corrected de Sitter black hole metric as the accurate spacetime geometry for all perturbation and geodesic calculations.

What would settle it

Detection of a positive imaginary part in any quasinormal mode of a massless scalar field on this metric, or measurement of an M87* shadow radius lying outside the range permitted by the derived parameter bounds.

Figures

Figures reproduced from arXiv: 2606.12698 by Ali Mohammadpour, Kourosh Nozari, Sara Saghafi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: displays the dependence of the same mode on the loop quantum parameter γ for D = 4 and D = 5. While the effect of γ is relatively mild in four dimensions, higher dimensions exhibit a more noticeable response, particularly in the damping rate. These plots provide a clear visual confirmation of the trends inferred from the numerical tables and demonstrate that loop quantum corrections introduce controlled qu… view at source ↗
Figure 3
Figure 3. Figure 3: displays the shadow of the four-dimensional loop quantum de Sitter black hole for different values of the loop quantum parameter γ. The shadow remains perfectly circular due to the spherical symmetry of the spacetime, while its radius exhibits a clear dependence on the strength of the quantum correction. As γ increases, the shadow boundary progressively contracts, indicating a reduction in the critical imp… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original abstract

We investigate the dynamical and optical properties of a higher-dimensional loop-quantum-corrected black hole in a de Sitter background. The quasinormal modes of massless scalar perturbations are computed using time-domain evolution with Prony extraction, the matrix method, and the WKB approximation, showing good agreement among the three approaches. We find that loop quantum corrections induce moderate shifts in the quasinormal spectrum, whereas the spacetime dimensionality has a much stronger impact, leading to higher oscillation frequencies and damping rates. The negative imaginary parts of all modes indicate dynamical stability against massless scalar perturbations within the explored parameter range. We also analyze null geodesics and construct the corresponding black hole shadow. The shadow radius depends sensitively on the loop quantum parameter, the cosmological constant, and the number of spacetime dimensions, with extra dimensions generally reducing the shadow size. By comparing the theoretical shadow radius with the Event Horizon Telescope constraints for M87$^{\ast}$, we obtain bounds on the parameter space of the model. These results suggest that quasinormal modes and black hole shadow observables can provide complementary probes of loop quantum gravity effects and higher-dimensional spacetime structure in the strong-gravity regime.

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 the quasinormal modes (QNMs) of massless scalar perturbations and the shadow of a higher-dimensional loop-quantum-corrected black hole in de Sitter spacetime. It computes the QNMs using time-domain evolution with Prony extraction, the matrix method, and the WKB approximation, reporting good agreement among the three approaches; finds that loop quantum corrections induce moderate shifts while dimensionality has a stronger effect; concludes dynamical stability from negative imaginary parts of all modes within the explored parameter range; and derives bounds on the model parameters by comparing the theoretical shadow radius to Event Horizon Telescope constraints for M87*.

Significance. If the underlying metric derivation and numerical convergence hold, the work supplies concrete observational constraints on loop quantum gravity parameters in higher-dimensional de Sitter backgrounds using two independent strong-gravity observables. The explicit cross-validation of three distinct QNM extraction techniques is a methodological strength that supports the stability conclusion.

minor comments (3)
  1. [§3] §3 (or equivalent section on metric): the explicit form of the higher-dimensional loop-quantum-corrected de Sitter metric should be stated with all constants and the loop parameter clearly identified before the perturbation analysis begins.
  2. [Figure 4] Figure 4 (shadow radius plots): the curves for different spacetime dimensions should include error bands or tabulated values at the EHT-constrained shadow radius to make the derived parameter bounds visually quantitative.
  3. [Table 1] Table 1 (QNM frequencies): the reported real and imaginary parts for the fundamental mode should be accompanied by the grid resolution or truncation order used in each of the three methods to allow direct assessment of numerical convergence.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on the quasinormal modes and shadows of the higher-dimensional loop-quantum-corrected black hole in de Sitter spacetime. The recommendation for minor revision is appreciated, and we will make the necessary adjustments in the revised manuscript. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper adopts a higher-dimensional loop-quantum-corrected de Sitter metric as background and performs direct numerical computations of quasinormal modes for massless scalar perturbations via three independent methods (time-domain Prony, matrix, WKB) plus null-geodesic shadow construction, then compares the resulting shadow radius to external EHT constraints on M87*. These steps are standard numerical extractions and observational comparisons; they do not reduce by the paper's own equations to self-defined quantities, fitted inputs renamed as predictions, or load-bearing self-citation chains. The stability conclusion follows immediately from the sign of computed imaginary parts within the explored range, with no self-definitional or ansatz-smuggling patterns in the central claims.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the assumed form of the loop-quantum-corrected metric and standard linear perturbation theory; the loop quantum parameter is the main adjustable quantity constrained by data.

free parameters (1)
  • loop quantum parameter
    Controls the strength of quantum corrections and is bounded using shadow radius comparisons to observations.
axioms (1)
  • domain assumption The background spacetime is described by the higher-dimensional loop-quantum-corrected de Sitter black hole metric.
    This metric is adopted without re-derivation as the starting point for all quasinormal mode and geodesic calculations.

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