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arxiv: 2606.20931 · v1 · pith:RZEDAIBVnew · submitted 2026-06-18 · 🌀 gr-qc · hep-th

Scattering, Hawking Radiation and Neutrino Energy Deposition in Euler-Heisenberg Black Holes Surrounded by Perfect Fluid Dark Matter

Ramon Becar , P. A. Gonzalez , Ali Ovgun , Joel Saavedra , Yerko Vasquez This is my paper

Pith reviewed 2026-06-26 16:04 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords black holesquasinormal modesHawking radiationperfect fluid dark matterEuler-Heisenberg electrodynamicsgreybody factorsneutrino annihilationscattering
0
0 comments X

The pith

The PFDM parameter contracts the optical structure of Euler-Heisenberg black holes, raising oscillation frequencies and damping rates while suppressing transmission.

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

The paper examines scattering, quasinormal modes, greybody factors, and Hawking radiation for black holes whose geometry combines an Euler-Heisenberg nonlinear-electrodynamic correction with a logarithmic perfect-fluid dark-matter halo. It finds that the PFDM parameter shrinks the photon sphere and related optical quantities, which in turn raises the real part of the quasinormal frequencies, accelerates the damping, and reduces wave transmission for scalar, electromagnetic, and effective axial spin-2 perturbations. The Euler-Heisenberg term produces a smaller near-horizon correction that only becomes appreciable at large charge. The same background also modifies absorption cross sections and enhances the relativistic neutrino-antineutrino annihilation rate outside the horizon. These results supply a single framework in which the separate effects of dark-matter environments and nonlinear electrodynamics can be compared.

Core claim

In Euler-Heisenberg black holes surrounded by perfect fluid dark matter, the PFDM parameter contracts the optical structure, increases the oscillation frequency, enhances the damping rate and suppresses transmission; the Euler-Heisenberg correction produces a weaker near-horizon deformation whose effect becomes relevant only for sufficiently large charge.

What carries the argument

The Euler-Heisenberg plus perfect-fluid-dark-matter metric together with scalar, electromagnetic, and effective axial spin-2 perturbations constructed on that fixed background.

If this is right

  • Quasinormal-mode spectra exhibit higher real frequencies and larger imaginary parts as the PFDM parameter grows.
  • Greybody factors decrease with increasing PFDM, which alters the Hawking emission spectra.
  • Near-extremal configurations develop a purely imaginary quasinormal-mode branch whose damping rate rises with the PFDM parameter and remains nearly spin-independent.
  • The relativistic enhancement of the neutrino-antineutrino annihilation channel outside the black hole is modified by both the PFDM halo and the Euler-Heisenberg charge.

Where Pith is reading between the lines

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

  • Ringdown signals from real black holes embedded in dark-matter halos could display systematic shifts in frequency and decay time that scale with halo density.
  • Varying the charge while holding the dark-matter parameter fixed would isolate the Euler-Heisenberg correction in future observations.
  • The same metric and perturbation setup can be extended to rotating cases to test whether the contraction of the optical structure persists.

Load-bearing premise

The particular effective axial spin-2 channel on the fixed background serves as a usable proxy for the gravitational perturbation problem.

What would settle it

A set of observed quasinormal-mode frequencies or Hawking spectra from a black-hole candidate whose surrounding dark-matter density is independently known and that show no increase in damping rate or decrease in transmission with rising dark-matter density.

Figures

Figures reproduced from arXiv: 2606.20931 by Ali Ovgun, Joel Saavedra, P. A. Gonzalez, Ramon Becar, Yerko Vasquez.

Figure 1
Figure 1. Figure 1: FIG. 1. Metric function [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Metric function [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Effective potentials for scalar (top panel), elec [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dependence of the fundamental quasinormal fre [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Time domain ringdown waveforms reconstructed [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the damping rate of the purely imaginary near-extremal mode for the effective gravitational sector, s = 2, versus the PFDM parameter α. In the figure γNE = −ImωNE is observed to increase monotonically with α. Thus the PFDM parameter enhances the damp￾ing rate of the purely imaginary near-extremal mode and reduces the corresponding relaxation time. Note that the figure shows only the gravitational sec… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Exact greybody factors for scalar ( [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Exact greybody factor Γ( [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Absorption cross sections (top panel) and Hawk [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Newtonian-normalized neutrino-annihilation en [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Dependence of [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Lapse function [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Charge dependence of the Newtonian-normalised [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Contour plot of [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
read the original abstract

We study the dynamical and scattering properties for the Euler-Heisenberg BH surrounded by perfect fluid dark matter. The geometry contains a compact non-linear electrodynamic correction governed by the EH coupling and a logarithmic dark-matter contribution governed by the surrounding PFDM halo. We study the scalar, electromagnetic and a particular effective axial spin-2 channel constructed on the fixed EH plus PFDM background, acting as a proxy for the gravitational-like perturbation problem and not for the fully coupled gravitational perturbation problem. We compute the quasinormal-mode spectrum employing a thirteenth-order WKB method supplemented with Pad\'e resummation and compare it with the eikonal prediction calculated in terms of the angular frequency of the photon sphere and the Lyapunov exponent. Moreover, we study the near-extremal configurations and derive a purely imaginary branch of quasinormal frequencies in the near-horizon region, whose damping rate increases with the PFDM parameter and is nearly spin-independent. We then compute exact greybody factors by direct numerical integration of the radial wave equation and compare them to analytical lower bounds. We also analyze the absorption cross sections and the Hawking emission spectra. We also calculate the relativistic enhancement of the neutrino-antineutrino annihilation channel outside the EHPFDM black hole. We find that the PFDM parameter contracts the optical structure, increases the oscillation frequency, enhances the damping rate and suppresses transmission. On the other hand, the Euler-Heisenberg correction leads to a weaker near-horizon deformation whose effect becomes relevant for sufficiently large charge. These results provide a common scattering framework for comparing the impact of dark-matter environments and nonlinear electrodynamics

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 manuscript studies scattering, quasinormal modes, greybody factors, absorption cross sections, Hawking spectra, and neutrino-antineutrino annihilation for Euler-Heisenberg black holes surrounded by perfect fluid dark matter. It analyzes scalar, electromagnetic, and an effective axial spin-2 channel (explicitly constructed on the fixed background as a proxy for gravitational-like perturbations, not the fully coupled problem) via 13th-order WKB with Padé resummation, eikonal approximation, direct numerical integration of the radial equation, and comparison to analytic bounds. The central findings are that the PFDM parameter contracts the optical structure, raises oscillation frequencies, enhances damping rates, and suppresses transmission, while the Euler-Heisenberg correction produces weaker near-horizon effects that become relevant only at large charge.

Significance. If the numerical results and proxy construction hold, the work supplies a comparative framework for the combined effects of nonlinear electrodynamics and dark-matter halos on black-hole dynamics and radiation. Methodological strengths include the high-order WKB supplemented by Padé resummation, direct numerical integration of the radial wave equation compared against eikonal predictions and analytic lower bounds, and the derivation of a purely imaginary near-extremal QNM branch; these elements allow internal cross-validation and are explicitly credited.

major comments (1)
  1. [Abstract and perturbation construction section] Abstract (and the section constructing the perturbation channels): the effective axial spin-2 channel is built on the fixed EH+PFDM metric and is stated to serve only as a proxy, not the fully coupled gravitational perturbation problem. No demonstration is given that this proxy captures the leading gravitational degrees of freedom or that the omitted couplings to the nonlinear electromagnetic field and PFDM background remain negligible across the reported parameter range. Because the central claims about PFDM-induced changes in oscillation frequency, damping, and transmission are extracted from this channel, the omission constitutes a load-bearing limitation for the gravitational-like results.
minor comments (2)
  1. [Introduction] The notation and definition of the PFDM halo parameter and the Euler-Heisenberg coupling should be collected in a single table or introductory paragraph for clarity when comparing multiple channels.
  2. [Figures on greybody factors] Figure captions for the greybody factors and absorption cross sections should explicitly list the fixed values of the EH coupling and PFDM parameter used in each panel.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the recommendation for major revision. We address the single major comment below, agreeing that further clarification of the proxy's scope is appropriate while maintaining that the presented results remain useful within their stated limitations.

read point-by-point responses

  1. Referee: [Abstract and perturbation construction section] Abstract (and the section constructing the perturbation channels): the effective axial spin-2 channel is built on the fixed EH+PFDM metric and is stated to serve only as a proxy, not the fully coupled gravitational perturbation problem. No demonstration is given that this proxy captures the leading gravitational degrees of freedom or that the omitted couplings to the nonlinear electromagnetic field and PFDM background remain negligible across the reported parameter range. Because the central claims about PFDM-induced changes in oscillation frequency, damping, and transmission are extracted from this channel, the omission constitutes a load-bearing limitation for the gravitational-like results.

    Authors: We thank the referee for this observation. The manuscript already states explicitly that the axial spin-2 channel is constructed on the fixed background and serves only as a proxy, not the fully coupled gravitational problem. We do not claim or demonstrate that omitted couplings to the nonlinear electromagnetic sector and the PFDM fluid are negligible; such a demonstration would require a separate, fully coupled linear perturbation analysis that lies outside the present scope. The qualitative trends (PFDM increasing damping and suppressing transmission) appear consistently across the scalar, electromagnetic, and proxy spin-2 channels, which provides internal cross-checks. We have revised the abstract and the perturbation-construction section to further stress the proxy character, to qualify the gravitational-like claims as indicative only, and to note that a complete treatment of the coupled system is left for future work. This revision directly addresses the load-bearing concern by narrowing the scope of the conclusions drawn from the proxy channel. revision: yes

Circularity Check

0 steps flagged

No circularity: results from direct numerical and WKB computations on fixed metric

full rationale

The paper computes QNMs via 13th-order WKB with Padé resummation, eikonal limits from photon-sphere Lyapunov exponents, exact greybody factors by numerical integration of the radial equation, and absorption/Hawking spectra on the given EH+PFDM metric. No parameter is fitted to a data subset and then relabeled as a prediction; the effective axial spin-2 channel is explicitly constructed as a proxy on the fixed background rather than derived from a self-referential equation. No self-citation chain or ansatz smuggling is invoked to force the central claims about PFDM contraction of the optical structure or EH near-horizon effects. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Abstract-only review; model parameters (EH coupling, PFDM halo parameter) are treated as free inputs varied to extract trends. No new entities postulated. Background assumptions are standard general relativity plus the given metric ansatz.

free parameters (2)
  • Euler-Heisenberg coupling constant
    Governs the nonlinear electrodynamic correction; varied to assess its effect on near-horizon deformation.
  • PFDM parameter
    Controls the logarithmic dark-matter contribution; shown to contract optical structure and enhance damping.
axioms (2)
  • domain assumption The background metric is fixed and perturbations are computed on it without backreaction.
    Stated in abstract as acting on the fixed EH plus PFDM background.
  • domain assumption The effective axial spin-2 channel serves as a valid proxy for gravitational perturbations.
    Explicitly noted as a proxy rather than the fully coupled problem.

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discussion (0)

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Reference graph

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