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arxiv: 2604.11357 · v1 · submitted 2026-04-13 · 🌀 gr-qc · hep-th

Recognition: unknown

Charged Black Holes in KR-gravity Surrounded by Perfect Fluid Dark Matter

Faizuddin Ahmed , Mohsen Fathi , Edilberto O. Silva
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:18 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords black holesKalb-Ramond gravityperfect fluid dark matterphoton sphereblack hole shadowISCOepicyclic frequenciesHawking radiation
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The pith

Charged black holes in KR-gravity with perfect fluid dark matter have their photon spheres, shadows, orbits, and thermodynamics modified by Lorentz violation.

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

This paper examines null geodesics and neutral test particle motion around charged black holes in a Kalb-Ramond gravity model that incorporates Lorentz violation from a background field and is surrounded by perfect fluid dark matter. It calculates the photon sphere radius, black hole shadow size, photon trajectories, innermost stable circular orbit, epicyclic frequencies, and quasi-periodic oscillations. The analysis extends to thermodynamic quantities and the sparsity of Hawking radiation. A sympathetic reader would care because these quantities connect directly to observable black hole images, accretion disk dynamics, and radiation signatures that could distinguish this framework from standard general relativity.

Core claim

The paper establishes that the spacetime metric for charged black holes in KR-gravity surrounded by perfect fluid dark matter yields explicit dependencies of the photon sphere radius, shadow radius, ISCO location, epicyclic frequencies, QPO frequencies, thermodynamic temperature and heat capacity, and Hawking radiation sparsity on the electric charge, the Kalb-Ramond parameter inducing Lorentz violation, and the dark matter density parameter.

What carries the argument

The charged black hole metric ansatz that incorporates the Kalb-Ramond field for Lorentz violation together with the perfect fluid dark matter distribution, which provides the geometry for all geodesic and thermodynamic calculations.

If this is right

  • Photon sphere and shadow sizes increase or decrease with the Kalb-Ramond and dark matter parameters relative to the Reissner-Nordström case.
  • The ISCO radius shifts outward or inward, altering the inner edge of accretion disks and orbital stability.
  • Epicyclic frequencies determine characteristic QPO peaks that depend on charge and the two additional parameters.
  • Thermodynamic quantities such as temperature and specific heat exhibit modified stability regions.
  • Hawking radiation sparsity changes with the model parameters, affecting the evaporation timescale.

Where Pith is reading between the lines

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

  • Shadow observations could place joint bounds on the Lorentz violation parameter and dark matter density once mass and charge are fixed.
  • Predicted QPO frequencies offer a testable signature for X-ray timing data around candidate black holes.
  • The thermodynamic and sparsity results may connect to how information is preserved during evaporation in Lorentz-violating spacetimes.

Load-bearing premise

The specific metric form for the charged black hole in KR-gravity with the chosen Kalb-Ramond field and perfect fluid dark matter distribution is assumed to be the correct spacetime solution.

What would settle it

A measured black hole shadow diameter for a known mass that deviates from the model's prediction after fixing charge and dark matter parameters would falsify the central results.

Figures

Figures reproduced from arXiv: 2604.11357 by Edilberto O. Silva, Faizuddin Ahmed, Mohsen Fathi.

Figure 1
Figure 1. Figure 1: FIG. 1. Behavior of the lapse function [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Behavior of the effective potential governing the photon dynamics by varying the charge [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Three-dimensional visualization of the photon sphere radius [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Three-dimensional visualization of the shadow radius [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Behavior of the effective force experienced by photon particles by varying the charge [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Photon trajectories in the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Photon trajectories in the [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Contour maps of the ISCO radius [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The radial profiles of [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Relations between the upper and lower frequencies of twin-peaked QPOs in the RP, ER2–ER4, and WD models [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Constraints on the parameters of the charged KR black hole in PFDM derived from the five-dimensional MCMC [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Overlay between the RP-model theoretical curves and the observed twin-peak QPO data for XTE J1550–564, GRO [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Contour maps of the event-horizon radius [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: illustrates the behavior of the mass function as the parameters are varied. The main message of this plot is that, for a given horizon radius, the required black hole mass is not fixed solely by the horizon scale, but also by the way in which the charge, the PFDM environment, and the Lorentz-violating KR background distribute the effective [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Hawking temperature [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Entropy diagnostics for the charged KR+PFDM black hole. The left panel shows the ratio [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Specific heat capacity [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Gibbs free energy [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Contour maps of the sparsity ratio [PITH_FULL_IMAGE:figures/full_fig_p030_19.png] view at source ↗
read the original abstract

In this work, we systematically investigate the null geodesics of electrically charged black holes in a gravitational framework that incorporates Lorentz violation induced by a background Kalb-Ramond (KR) field, in the presence of perfect-fluid dark matter. The properties of the photon sphere, black hole shadow, and photon trajectories are analyzed in detail. Furthermore, to explore the combined effects of Lorentz violation and dark matter on the motion of neutral test particles, we examine the innermost stable circular orbit (ISCO) in this spacetime. In addition, the epicyclic frequencies of test particles are studied to gain further insight into the dynamical behavior of particle motion around these black holes. The main analytical results are complemented by a phenomenological QPO analysis, a thermodynamic investigation, and a discussion of the sparsity of Hawking radiation, allowing us to connect optical, dynamical, and thermodynamic signatures within a single framework.

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

1 major / 2 minor

Summary. The paper investigates the null geodesics, photon sphere, black hole shadow, photon trajectories, innermost stable circular orbit (ISCO), epicyclic frequencies, quasi-periodic oscillations (QPOs), thermodynamics, and Hawking radiation sparsity for charged black holes in Kalb-Ramond (KR) gravity surrounded by perfect fluid dark matter (PFDM). It adopts a static spherically symmetric metric ansatz incorporating the KR coupling parameter, electric charge Q, and PFDM density, then computes observable quantities analytically and numerically from this line element.

Significance. If the metric ansatz is consistent with the KR-gravity field equations plus PFDM stress-energy, the work offers a unified phenomenological framework linking Lorentz violation and dark matter effects across optical, dynamical, and thermodynamic black hole signatures. The breadth of analyses (geodesics through QPOs and radiation sparsity) could aid in connecting modified-gravity predictions to observations, provided the underlying spacetime is rigorously justified.

major comments (1)
  1. [Section 2] Section 2 (Metric and field equations): The line element ds² = −f(r)dt² + dr²/f(r) + r²dΩ² with f(r) encoding the KR parameter, charge Q, and PFDM density is introduced as an ansatz without explicit derivation from the KR-gravity action or verification that it solves the modified Einstein equations for the chosen Kalb-Ramond field strength and perfect-fluid equation of state. All reported results (photon-sphere radius, shadow size, ISCO, epicyclic frequencies, thermodynamic quantities, and Hawking sparsity) are computed directly from this f(r); if the ansatz is not a solution, the entire analysis applies to a spacetime outside the claimed theory.
minor comments (2)
  1. [Abstract] The abstract and introduction could more explicitly state the range of free parameters (KR coupling, Q, DM density) and their physical bounds to clarify the scope of the parameter scans.
  2. [Figures] Figure captions for shadow and photon trajectories should specify the exact parameter values used for each curve to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for identifying this important point about the metric derivation. We respond to the major comment below and will incorporate the requested clarification in the revised version.

read point-by-point responses

  1. Referee: [Section 2] Section 2 (Metric and field equations): The line element ds² = −f(r)dt² + dr²/f(r) + r²dΩ² with f(r) encoding the KR parameter, charge Q, and PFDM density is introduced as an ansatz without explicit derivation from the KR-gravity action or verification that it solves the modified Einstein equations for the chosen Kalb-Ramond field strength and perfect-fluid equation of state. All reported results (photon-sphere radius, shadow size, ISCO, epicyclic frequencies, thermodynamic quantities, and Hawking sparsity) are computed directly from this f(r); if the ansatz is not a solution, the entire analysis applies to a spacetime outside the claimed theory.

    Authors: We agree that the original manuscript introduced the metric as an ansatz without a complete, self-contained derivation from the KR-gravity action. To address this, the revised version will include an explicit verification in Section 2: we will solve the modified Einstein equations with the Kalb-Ramond field strength and the perfect-fluid dark matter stress-energy tensor, showing step-by-step that the given f(r) satisfies the field equations under the stated assumptions. This addition will confirm that the spacetime is a solution within the theory and will not alter any of the subsequent calculations, which depend only on the metric coefficients. We thank the referee for this suggestion, which improves the rigor of the presentation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; analyses derive from assumed metric without reduction to inputs

full rationale

The paper takes a static spherically symmetric metric ansatz incorporating KR parameter, charge, and PFDM density as its starting point, then computes standard GR observables (photon sphere radius, shadow, ISCO, epicyclic frequencies, QPOs, thermodynamics, Hawking sparsity) via geodesic equations, effective potentials, and thermodynamic identities. These steps are direct applications of the line element and do not loop back to redefine or refit the input parameters or ansatz itself. No self-citations are invoked as load-bearing uniqueness theorems, no fitted subsets are relabeled as predictions, and no ansatz is smuggled via prior work by the same authors. The derivation chain remains self-contained against external benchmarks once the metric form is granted.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central results rest on an assumed metric form for the spacetime, plus free parameters for the KR field strength, black hole charge, and dark matter density; no new entities are postulated beyond the standard KR field and perfect fluid.

free parameters (3)
  • Kalb-Ramond coupling parameter
    Strength of Lorentz violation, introduced as a free parameter in the model.
  • Electric charge Q
    Black hole charge, a standard free parameter.
  • Dark matter density parameter
    Parameter controlling the perfect fluid dark matter distribution around the black hole.
axioms (1)
  • domain assumption The line element for charged black holes in KR-gravity with perfect fluid dark matter
    The specific metric ansatz is taken as the starting point without re-derivation.

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Forward citations

Cited by 3 Pith papers

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  3. Shadow, Quasinormal Modes, Sparsity, and Energy Emission Rate of Euler-Heisenberg Black Hole Surrounded by Perfect Fluid Dark Matter

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