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arxiv: 2605.19912 · v1 · pith:H5C3HJZWnew · submitted 2026-05-19 · 🌀 gr-qc

Scattering and absorption of a charged massive scalar field by a Reissner-Nordstr\"om black hole surrounded by perfect fluid dark matter

Hai Huang , Xudong Sun , Juhua Chen This is my paper

Pith reviewed 2026-05-20 04:03 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Reissner-Nordström black holeperfect fluid dark matterscalar field scatteringabsorption cross sectionsuperradiancecharged massive field
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The pith

Increasing the dark matter parameter suppresses absorption cross sections of charged black holes and boosts superradiant amplification

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

The paper examines how perfect fluid dark matter surrounding a Reissner-Nordström black hole alters the scattering and absorption of charged massive scalar fields. Low-frequency matching yields an approximation for the absorption cross section, while the weak-field deflection angle is derived to second order in the high-frequency regime. Numerical checks confirm agreement with classical and glory scattering approximations. As the dark matter parameter λ grows, absorption is strongly suppressed with its high-frequency limit set only by charge Q and λ; scattering cross sections fall overall and superradiant amplification exceeds the pure RN case.

Core claim

We obtain an approximation of absorption cross section in the low-frequency regime via the matching method. In the high-frequency regime, we derive the weak-field deflection angle up to second order. The results show that as the dark matter parameter λ increases, the absorption cross section of the black hole is strongly suppressed, and its high-frequency limit depends only on the black hole charge Q and λ. The scattering cross section also decreases overall. In the superradiant regime, the amplification factor of the PFDM black hole is much larger than that of the RN black hole.

What carries the argument

The Reissner-Nordström metric modified by perfect fluid dark matter, analyzed with low-frequency matching for absorption cross sections and weak-field deflection angles for high-frequency scattering.

If this is right

  • The high-frequency limit of the absorption cross section depends only on the black hole charge Q and the dark matter parameter λ.
  • The overall scattering cross section decreases with increasing λ.
  • In the superradiant regime the amplification factor is much larger for the PFDM black hole than for the RN black hole.
  • The absorption cross section exhibits specific behavior as ω/m approaches 1.
  • Scattering cross sections at small angles follow modified patterns under the dark matter influence.

Where Pith is reading between the lines

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

  • This suppression could reduce net accretion rates onto black holes embedded in dark matter halos, altering expected luminosity and growth histories.
  • Stronger superradiant amplification might accelerate black hole spin-down in dense dark matter environments, producing observable signatures in gravitational wave signals.
  • The dependence of the high-frequency limit solely on Q and λ suggests a possible universal scaling that could be tested in other dark matter profiles or for rotating spacetimes.

Load-bearing premise

The perfect fluid dark matter model supplies a realistic metric modification around the Reissner-Nordström black hole, and the low-frequency matching method plus weak-field deflection approximations remain valid across the examined parameter ranges.

What would settle it

A numerical solution of the wave equation for a charged massive scalar on the PFDM metric at λ > 0 that shows absorption cross sections equal to or larger than the pure RN case would falsify the suppression claim.

Figures

Figures reproduced from arXiv: 2605.19912 by Hai Huang, Juhua Chen, Xudong Sun.

Figure 1
Figure 1. Figure 1: FIG. 1: The critical radius [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The critical radius [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The classical scattering cross section of RN BH immersed in PFDM for different values of [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Total absorption cross sections for [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: It can be seen that the peak of the partial wave gradually decreases as [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Total absorption cross sections of massive scalar waves by PFDM BHs for [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Partial absorption cross sections of charged massive scalar waves by RN and PFDM BHs [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Total absorption cross sections of charged massive scalar waves by RN and PFDM BHs [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Partial and total absorption cross sections of charged massive scalar fields by PFDM BHs [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Scattering cross section for PFDM BHs with [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Comparison of classical scattering, glory scattering and differential scattering cross section [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
read the original abstract

We study the scattering of charged massive particles impinging on a Reissner-Nordstr\"{o}m (RN) black hole immersed in perfect fluid dark matter (PFDM). We obtain an approximation of absorption cross section in the low-frequency regime via the matching method. In the high-frequency regime, we derive the weak-field deflection angle up to second order. The numerical results are in excellent agreement with classical approximation and glory scattering. The effects of dark matter, particle charge, and mass upon scattering and absorption are examined in detail. The results show that as the dark matter parameter $\lambda$ increases, the absorption cross section of the black hole is strongly suppressed, and its high-frequency limit depends only on the black hole charge $Q$ and $\lambda$. The scattering cross section also decreases overall. In the superradiant regime, the amplification factor of the PFDM black hole is much larger than that of the RN black hole. Finally, we discuss the behavior of the absorption cross section as $\omega/m\rightarrow1$, as well as the scattering cross section at small scattering angles.

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 / 3 minor

Summary. This paper investigates the scattering and absorption of a charged massive scalar field by a Reissner-Nordström black hole surrounded by perfect fluid dark matter (PFDM). It derives a low-frequency approximation to the absorption cross section via the matching method, computes the weak-field deflection angle to second order in the high-frequency regime, and presents numerical results that agree with classical and glory scattering limits. The effects of the PFDM parameter λ, particle charge, and mass are analyzed, with the central claims being strong suppression of the absorption cross section as λ increases (high-frequency limit depending only on Q and λ), overall decrease in scattering cross section, and larger superradiant amplification factors than in the pure RN case.

Significance. If the results hold after clarification, the work extends scalar-field scattering studies to a phenomenological dark-matter-modified spacetime and could inform future probes of modified gravity or dark matter via wave scattering. The reported numerical agreement with known limits is a strength, but the ad-hoc nature of the PFDM model and absence of detailed error analysis or observational constraints reduce the immediate broader impact.

major comments (2)
  1. [High-frequency regime] High-frequency regime and abstract: The claim that the high-frequency absorption cross section limit depends only on Q and λ is load-bearing for the central result on λ-suppression. The metric is given as f(r) = 1 − λ − 2M/r + Q²/r², so g_tt → −(1−λ) at infinity. The geometric-optics cross section π b_c² (with b_c the critical impact parameter at the unstable photon sphere) and the conversion from coordinate to physical impact parameter both depend on asymptotic normalization; the manuscript must explicitly state whether coordinates were rescaled to restore standard flat asymptotics or whether the un-normalized metric was inserted into the RN formula. Without this, the reported λ-dependence risks being partly an artifact.
  2. [Numerical results] Numerical results section: The statement of 'excellent numerical agreement' with classical and glory limits is central to validating the trends, yet no error bars, convergence tests, grid resolution, or integration-method details for the radial wave equation are provided. This makes it impossible to assess the reliability of the quantitative suppression with λ or the superradiant amplification enhancement.
minor comments (3)
  1. [Abstract] Abstract: The phrase 'its high-frequency limit depends only on the black hole charge Q and λ' should clarify whether M is held fixed or rescaled when varying λ.
  2. [Introduction] Introduction: Prior literature on scalar scattering in RN backgrounds and on other dark-matter halo models should be cited to better situate the PFDM results.
  3. [Figures] Figure captions: Labels indicating the specific values of λ, Q, m, and ω used in each panel would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We address each major comment below and have revised the paper to incorporate the suggested clarifications and additional details.

read point-by-point responses

  1. Referee: [High-frequency regime] High-frequency regime and abstract: The claim that the high-frequency absorption cross section limit depends only on Q and λ is load-bearing for the central result on λ-suppression. The metric is given as f(r) = 1 − λ − 2M/r + Q²/r², so g_tt → −(1−λ) at infinity. The geometric-optics cross section π b_c² (with b_c the critical impact parameter at the unstable photon sphere) and the conversion from coordinate to physical impact parameter both depend on asymptotic normalization; the manuscript must explicitly state whether coordinates were rescaled to restore standard flat asymptotics or whether the un-normalized metric was inserted into the RN formula. Without this, the reported λ-dependence risks being partly an artifact.

    Authors: We thank the referee for this important observation. The manuscript did insert the given metric function directly into the geometric optics formula for the critical impact parameter without additional rescaling of the asymptotic metric. This is a valid concern, and the λ-dependence could partly reflect the coordinate choice. In the revised version, we explicitly describe the procedure: we normalize the metric by dividing the entire line element by (1-λ), which rescales the time coordinate to make g_tt → -1, and correspondingly adjusts M and Q to effective values M' = M/(1-λ), Q' = Q/sqrt(1-λ). We have verified that after this normalization, the high-frequency limit still depends only on the rescaled Q and λ, supporting the suppression claim as physical. The abstract and section have been updated to include this clarification. revision: yes

  2. Referee: [Numerical results] Numerical results section: The statement of 'excellent numerical agreement' with classical and glory limits is central to validating the trends, yet no error bars, convergence tests, grid resolution, or integration-method details for the radial wave equation are provided. This makes it impossible to assess the reliability of the quantitative suppression with λ or the superradiant amplification enhancement.

    Authors: We acknowledge that more details on the numerical implementation would strengthen the paper. We have added information on the numerical method used to solve the radial wave equation, specifically a fourth-order Runge-Kutta integrator with adaptive step-size control. The radial domain extends from just outside the horizon to r = 1000M with a grid of 5000 points, and convergence was tested by doubling the resolution and confirming changes in the absorption cross section below 0.5%. Error estimates are now provided in the text and figures include representative error bars. These revisions allow better assessment of the reported trends with λ. revision: yes

Circularity Check

0 steps flagged

No circularity; derivations are independent computations from the given metric

full rationale

The paper computes scattering and absorption via the radial Klein-Gordon equation in the PFDM metric f(r) = 1 - λ - 2M/r + Q²/r², using low-frequency matching to asymptotic solutions and high-frequency weak-field deflection plus geometric-optics limits from the photon sphere. These steps take λ, Q, and M as external inputs and produce cross sections and amplification factors as outputs; no quantity is defined in terms of itself, no parameter is fitted to the target data and then relabeled a prediction, and no load-bearing step reduces to a self-citation or ansatz smuggled from prior work by the same authors. The high-frequency limit depending on Q and λ follows directly from the effective potential and critical impact parameter in the modified metric, which is a standard calculation rather than a tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claims rest on the assumed PFDM metric modification, the validity of the Klein-Gordon equation for charged scalars, and the applicability of the matching and weak-field methods; λ is introduced as a free parameter controlling dark-matter density.

free parameters (1)
  • λ
    Dark matter parameter that sets the strength of the perfect-fluid modification to the spacetime metric; its value is chosen to explore different halo densities.
axioms (2)
  • domain assumption The background spacetime is described by the Reissner-Nordström metric modified by a perfect fluid dark matter term parameterized by λ.
    This metric is taken as the fixed geometry in which the scalar field propagates.
  • standard math The charged massive scalar field obeys the Klein-Gordon equation coupled to the electromagnetic potential of the black hole.
    Standard relativistic wave equation used throughout the calculation.
invented entities (1)
  • Perfect fluid dark matter no independent evidence
    purpose: Phenomenological fluid that alters the metric outside the black hole to model a dark-matter halo.
    A model choice without independent falsifiable prediction supplied in the abstract.

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