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arxiv: 2604.26166 · v1 · submitted 2026-04-28 · 🌀 gr-qc

Recognition: unknown

Scattering of electromagnetic field in quasi-topological gravity

Juan Pablo Arbelaez
Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:46 UTC · model grok-4.3

classification 🌀 gr-qc
keywords electromagnetic scatteringregular black holesquasi-topological gravityabsorption cross sectionhigher-dimensional gravitytransmission probabilities
0
0 comments X

The pith

Regular black holes in quasi-topological gravity shift electromagnetic absorption spectra away from the singular Tangherlini case.

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

This paper studies how electromagnetic waves scatter and get absorbed by regular black holes in quasi-topological gravity, viewed from a four-dimensional brane. It calculates transmission probabilities using an approximate method and finds that the black hole's smooth center causes the absorption to differ from the usual singular black hole models, changing the spectrum and the closest orbit for light. These differences shrink when there are more dimensions in the spacetime, approaching the standard case. Such differences in how much light is absorbed could help test whether gravity includes higher-curvature terms.

Core claim

The central discovery is that regularity effects lead to systematic deviations from the singular Tangherlini solution, manifested in shifts of the absorption spectrum and modifications of the effective photon sphere radius. Increasing the number of spacetime dimensions suppresses these deviations, driving the system toward the classical limit and reducing the number of multipoles required for convergence. In the high-frequency regime the absorption cross section approaches the geometric-optics limit, while at low frequencies it is strongly suppressed due to diminished transmission probabilities.

What carries the argument

The WKB-based computation of transmission probabilities for electromagnetic perturbations on the regular black hole background.

If this is right

  • Deviations from the singular solution decrease as spacetime dimensionality rises.
  • Absorption cross sections match the geometric-optics limit at high frequencies.
  • Low-frequency absorption remains strongly suppressed by low transmission probabilities.
  • The number of multipoles needed for accurate results drops in higher dimensions.

Where Pith is reading between the lines

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

  • The same transmission calculation could be repeated for other field types to check whether the regularity signatures are universal.
  • Precision measurements of black-hole shadows or ringdown signals might eventually constrain the strength of the higher-curvature corrections.
  • If the four-dimensional brane picture holds, similar absorption shifts could appear in effective lower-dimensional descriptions of higher-dimensional gravity.

Load-bearing premise

The approximate method used to calculate transmission probabilities remains accurate for electromagnetic waves across the relevant frequencies on these regular backgrounds.

What would settle it

A full numerical integration of the electromagnetic wave equation on the same background that finds absorption cross sections identical to the Tangherlini solution would falsify the reported systematic shifts.

read the original abstract

We investigate the absorption cross sections of electromagnetic perturbations propagating on a four-dimensional brane in the background of higher-dimensional regular black holes arising in quasi-topological gravity. Employing a WKB-based approach for the computation of greybody factors, we analyze the impact of higher-curvature corrections and spacetime dimensionality on the scattering properties of the system. We show that regularity effects lead to systematic deviations from the singular Tangherlini solution, manifested in shifts of the absorption spectrum and modifications of the effective photon sphere radius. Increasing the number of spacetime dimensions suppresses these deviations, driving the system toward the classical limit and reducing the number of multipoles required for convergence. In the high-frequency regime, the absorption cross section approaches the geometric-optics limit, while at low frequencies it is strongly suppressed due to diminished transmission probabilities. Our results demonstrate that the interplay between regularity and higher-curvature effects leaves distinct imprints on the absorption characteristics, providing a sensitive probe of the underlying gravitational theory.

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 absorption cross-sections of electromagnetic perturbations on a 4D brane in higher-dimensional regular black-hole backgrounds sourced by quasi-topological gravity. Using a WKB approximation to evaluate greybody factors, it reports that regularity produces systematic shifts in the absorption spectrum and effective photon-sphere radius relative to the singular Tangherlini solution, with these deviations suppressed as the spacetime dimension increases; low-frequency absorption is suppressed while the high-frequency limit recovers the geometric-optics value.

Significance. If the WKB-derived deviations are robust, the work supplies a concrete, falsifiable signature of regularity and higher-curvature corrections in wave scattering, which could be tested in analog gravity systems or high-energy astrophysical observations. The dimensional trend toward the classical limit is a useful consistency check, but the overall significance is limited by the absence of any validation of the approximation method itself.

major comments (2)
  1. [§4] §4 (WKB computation of greybody factors): the paper applies the WKB formula to the effective potential for electromagnetic perturbations but supplies neither error estimates, convergence checks with increasing WKB order, nor direct numerical integration of the radial wave equation for comparison. Because the claimed regularity-induced shifts are described as systematic yet potentially small, it is impossible to determine whether they exceed the uncontrolled truncation error of the asymptotic approximation.
  2. [§3.2] §3.2 (effective potential and photon-sphere radius): the modification of the photon-sphere radius is extracted from the peak of the potential barrier on the regular metric, yet no quantitative table or plot compares the exact location and height of this peak between the quasi-topological and Tangherlini cases across the frequency range used for the absorption cross-section. Without this, the assertion that regularity produces distinguishable shifts remains unquantified.
minor comments (2)
  1. [Figure 3] Figure 3 (absorption cross-section vs. frequency): the curves for different dimensions are difficult to distinguish at high frequencies; adding a zoomed inset or tabulated values at selected frequencies would improve readability.
  2. [§2] The notation for the regularity parameter (denoted variously as α or β in the text) should be unified and defined once in §2 before its appearance in the effective potential.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We agree that additional validation of the WKB results and quantitative comparisons of the effective potentials would strengthen the presentation, and we will incorporate these elements in the revised version.

read point-by-point responses

  1. Referee: [§4] §4 (WKB computation of greybody factors): the paper applies the WKB formula to the effective potential for electromagnetic perturbations but supplies neither error estimates, convergence checks with increasing WKB order, nor direct numerical integration of the radial wave equation for comparison. Because the claimed regularity-induced shifts are described as systematic yet potentially small, it is impossible to determine whether they exceed the uncontrolled truncation error of the asymptotic approximation.

    Authors: We acknowledge the absence of explicit error estimates and numerical cross-checks in the current manuscript. In the revised version we will add a dedicated subsection discussing the expected truncation error of the WKB formula for the greybody factors, together with direct numerical integration of the radial wave equation for a representative set of multipoles, frequencies, and spacetime dimensions. These comparisons will be used to verify that the reported regularity-induced shifts lie outside the estimated numerical and approximation uncertainties. Where computationally feasible we will also report results from the next-to-leading WKB order to demonstrate convergence. revision: yes

  2. Referee: [§3.2] §3.2 (effective potential and photon-sphere radius): the modification of the photon-sphere radius is extracted from the peak of the potential barrier on the regular metric, yet no quantitative table or plot compares the exact location and height of this peak between the quasi-topological and Tangherlini cases across the frequency range used for the absorption cross-section. Without this, the assertion that regularity produces distinguishable shifts remains unquantified.

    Authors: We agree that a side-by-side quantitative comparison is needed to make the magnitude of the shifts explicit. The revised manuscript will include a new table (and, if space permits, an accompanying figure) that lists the radial location of the potential maximum and the value of the effective potential at that peak for both the quasi-topological regular solution and the Tangherlini background, for the same range of multipoles and frequencies employed in the absorption-cross-section calculations. This will directly quantify the differences induced by regularity. revision: yes

Circularity Check

0 steps flagged

No circularity detected in derivation from background metric to scattering observables

full rationale

The paper solves the background metric from the quasi-topological gravity field equations (or adopts it from the theory's regular black-hole solutions), derives the effective potential for electromagnetic perturbations on that fixed geometry, and then applies the WKB approximation to obtain greybody factors and absorption cross sections. These steps form a one-way computational chain: the metric and potential are inputs independent of the WKB output, and the reported deviations from the Tangherlini solution are direct numerical consequences of the modified potential rather than redefinitions or fits. No self-citation is invoked to justify a uniqueness theorem or ansatz that would force the result, and no parameter fitted to data is later presented as a prediction. The derivation remains self-contained against the external benchmark of the WKB method applied to the given metric.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the validity of the quasi-topological gravity framework, the existence of regular black-hole solutions, and the applicability of the WKB approximation to brane perturbations. No new entities are postulated.

axioms (2)
  • domain assumption Quasi-topological gravity provides a consistent higher-curvature extension of general relativity that admits regular black-hole solutions.
    The paper takes the theory and its regular solutions as given without re-deriving them.
  • domain assumption The WKB method yields reliable greybody factors for electromagnetic perturbations on the four-dimensional brane.
    The computation of absorption cross sections relies on this approximation.

pith-pipeline@v0.9.0 · 5457 in / 1365 out tokens · 172818 ms · 2026-05-07T14:46:56.148630+00:00 · methodology

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Reference graph

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