arxiv: 2605.03659 · v1 · submitted 2026-05-05 · 🌀 gr-qc

Recognition: unknown

Long-lived massive scalar modes, grey-body factors, and absorption cross sections of the Reissner--Nordstr\"om-like brane-world black hole

Zainab Malik

Authors on Pith no claims yet

Pith reviewed 2026-05-07 13:59 UTC · model grok-4.3

classification 🌀 gr-qc

keywords quasinormal modesbrane-world black holestidal chargegrey-body factorsabsorption cross sectionsmassive scalar fieldsReissner-Nordström-like metricquasi-resonant regime

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The pith

Tidal charge from extra dimensions drives massive scalar quasinormal modes around brane-world black holes toward arbitrarily long lifetimes.

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

This paper studies quasinormal modes of massive scalar fields in a brane-world black hole modified by a tidal charge from extra dimensions. It uses WKB calculations and time-domain evolution to find how the tidal charge, field mass, and multipole number affect the effective potential barrier. Positive tidal charge lowers the barrier, increases transmission and absorption, and moves the modes into a quasi-resonant regime with arbitrarily long lifetimes. The long-lived behavior cannot be seen directly in time profiles because asymptotic tails appear early and mask the ringing. These results matter for understanding black hole stability and wave scattering in modified gravity.

Core claim

Combining semiclassical WKB calculations with time-domain evolution, we determine the range of parameters for which the effective potential keeps the single-barrier shape needed for reliable analysis. We find that increasing positive tidal charge lowers the barrier, drives the spectrum closer to the quasi-resonant regime, and enhances transmission and absorption, whereas increasing the field mass or multipole number makes the barrier less transparent and shifts absorption to higher frequencies. Our results indicate the onset of an arbitrarily long-lived quasinormal-mode regime, although this behavior cannot be followed directly in the time-domain profiles because the asymptotic tails set in太

What carries the argument

The shape of the effective potential barrier in the wave equation for massive scalar perturbations, which controls the quasinormal frequencies and grey-body factors through WKB approximation.

If this is right

Positive tidal charge lowers the potential barrier and boosts transmission and absorption of the scalar field.
Higher scalar field mass or multipole number makes the barrier less transparent and moves absorption to higher frequencies.
The quasinormal modes enter an arbitrarily long-lived regime as positive tidal charge grows.
Time-domain evolution cannot reveal the long-lived ringing because asymptotic tails dominate early.

Where Pith is reading between the lines

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

Extra-dimensional tidal charge may increase stability of black holes to scalar perturbations compared to standard general relativity.
Frequency-domain techniques are required to access the long-lived regime, as time-domain signals are masked.
The same barrier-lowering mechanism could appear in other modified-gravity black hole solutions with extra parameters.

Load-bearing premise

The effective potential maintains a single-barrier shape over the parameter range needed for reliable WKB and scattering analysis.

What would settle it

A calculation showing that the effective potential develops multiple barriers for sufficiently large positive tidal charge would invalidate the WKB-based claim of arbitrarily long-lived modes.

Figures

Figures reproduced from arXiv: 2605.03659 by Zainab Malik.

**Figure 1.** Figure 1: FIG. 1. Representative effective potentials as functions of the view at source ↗

**Figure 3.** Figure 3: FIG. 3. Damping rate view at source ↗

**Figure 4.** Figure 4: FIG. 4. Time-domain profile view at source ↗

**Figure 5.** Figure 5: FIG. 5 view at source ↗

**Figure 6.** Figure 6: FIG. 6 view at source ↗

**Figure 7.** Figure 7: shows the corresponding partial and total absorption cross sections for a representative fixed mass µ = 0.2 and three values of the tidal-charge parameter. In each panel the black curve represents the total absorption cross section, while the colored curves show the partial contributions from individual multipoles. (a) 1 2 3 4 W M 50 100 150 ΣM2 (b) 1 2 3 4 W M 20 40 60 80 ΣM2 (c) 1 2 3 4 W M 20 40 60 … view at source ↗

**Figure 8.** Figure 8: FIG. 8 view at source ↗

read the original abstract

We study quasinormal modes, including the quasi-resonant regime, grey-body factors, and absorption cross sections of a massive scalar field in a Reissner--Nordstr\"om-like brane-world black hole endowed with a tidal-charge parameter induced by extra-dimensional effects. Combining semiclassical WKB calculations with time-domain evolution, we determine the range of parameters for which the effective potential keeps the single-barrier shape needed for a reliable quasinormal-mode and scattering analysis. We find that increasing positive tidal charge lowers the barrier, drives the spectrum closer to the quasi-resonant regime, and enhances transmission and absorption, whereas increasing the field mass or multipole number makes the barrier less transparent and shifts absorption to higher frequencies. Our results indicate the onset of an arbitrarily long-lived quasinormal-mode regime. At the same time, this behavior cannot be followed directly in the time-domain profiles, because the asymptotic tails set in too early and mask the late-time ringing.

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.

Desk Editor's Note private letter to a colleague

Positive tidal charge drives massive scalar modes toward arbitrarily long lifetimes in this brane-world RN setup, but the claim sits at the edge of the single-barrier window where WKB is justified and time-domain data offers no independent check.

read the letter

The paper computes quasinormal modes, grey-body factors, and absorption cross sections for massive scalars on a Reissner-Nordström-like brane-world black hole with tidal charge. It reports that positive tidal charge lowers the effective potential barrier, moves the frequencies closer to the quasi-resonant regime, and increases transmission and absorption, while higher field mass or multipole number does the opposite. The authors combine WKB with time-domain evolution and explicitly map the parameter range where the potential keeps a single barrier shape required for reliable use of those methods. They conclude that the spectrum shows the onset of arbitrarily long-lived modes as the tidal charge grows positive, though the time-domain ringing is masked by early tails so the long-lived behavior cannot be seen directly in the profiles. This combination of tidal-charge dependence, massive field, and the long-lived regime for this metric is new. The work is careful in stating the single-barrier condition and in showing how the parameters affect the scattering quantities. The calculations follow standard techniques without obvious algebraic slips in the abstract and described approach. The soft spot is that the long-lived regime occurs precisely as the barrier height drops toward zero, which is the boundary of the single-barrier window they enforce. If the potential develops extra turning points or changes shape before the imaginary part reaches zero, the WKB frequencies lose their justification. The time-domain runs do not resolve this because tails dominate early. The paper therefore rests the central claim on an extrapolation near the edge of its stated validity range. This is a niche calculation aimed at people working on black-hole perturbations in extra-dimensional models. A reader who needs concrete numbers for grey-body factors or absorption in tidal-charge spacetimes will find the scans useful. The paper is coherent enough on its own terms to deserve a serious referee, who should be asked to verify the potential shape right at the claimed long-lived boundary and to check whether any additional turning points appear. I would send it to peer review with that focus.

Referee Report

2 major / 2 minor

Summary. The manuscript studies quasinormal modes (including the quasi-resonant regime), grey-body factors, and absorption cross sections of a massive scalar field on a Reissner-Nordström-like brane-world black hole with tidal charge. It combines WKB calculations with time-domain evolution to identify the parameter window in which the effective potential retains a single-barrier shape, reports that positive tidal charge lowers the barrier and drives Im(ω) toward zero while enhancing transmission and absorption, and notes that time-domain profiles are masked by early power-law tails.

Significance. If the single-barrier condition is shown to persist into the limit of arbitrarily small Im(ω), the results would establish a concrete mechanism by which extra-dimensional tidal charge can produce long-lived massive scalar modes, with possible implications for black-hole stability and late-time gravitational-wave signals. The explicit restriction to the validated single-barrier domain and the dual-method approach constitute methodological strengths.

major comments (2)

[analysis of effective potential and single-barrier range] The claim of an 'arbitrarily long-lived quasinormal-mode regime' (abstract) is obtained from WKB as the barrier height approaches zero with rising positive tidal charge. This limit lies at the edge of the explicitly determined single-barrier parameter window. The manuscript must demonstrate—via explicit potential profiles, turning-point counts, or a quantitative boundary scan—that no additional local minimum or multiple barriers appear before Im(ω) becomes arbitrarily small; otherwise the WKB frequencies lose their justification precisely in the claimed regime.
[time-domain section and WKB results] Time-domain evolution is acknowledged to be masked by early tails and therefore supplies no independent confirmation of the long-lived modes. Because the central claim rests on WKB alone in the low-barrier limit, the paper should report WKB error estimates, convergence tests, or comparison with an alternative method (e.g., continued-fraction or Leaver) inside the validated window.

minor comments (2)

Label the tidal-charge parameter consistently (e.g., β or Q_t) in all figures and equations; its allowed range should be stated once in the introduction.
Include the precise numerical boundary values of the tidal charge at which the potential ceases to be single-barrier, together with the corresponding WKB frequencies, so readers can judge how close the long-lived regime lies to the breakdown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive report. The comments correctly identify the need for explicit verification that the single-barrier structure persists into the low-barrier limit and for additional validation of the WKB results. We address both points below and will incorporate the requested material in the revised manuscript.

read point-by-point responses

Referee: The claim of an 'arbitrarily long-lived quasinormal-mode regime' (abstract) is obtained from WKB as the barrier height approaches zero with rising positive tidal charge. This limit lies at the edge of the explicitly determined single-barrier parameter window. The manuscript must demonstrate—via explicit potential profiles, turning-point counts, or a quantitative boundary scan—that no additional local minimum or multiple barriers appear before Im(ω) becomes arbitrarily small; otherwise the WKB frequencies lose their justification precisely in the claimed regime.

Authors: We agree that an explicit demonstration is required. In the revised manuscript we will add a dedicated subsection with effective-potential plots for a sequence of increasing positive tidal-charge values up to the boundary of the single-barrier domain. These profiles, together with a quantitative scan of the number and location of turning points, confirm that the potential retains a single barrier with no additional local minima or inflection points that would invalidate the WKB approximation. The reported onset of arbitrarily long-lived modes is therefore approached asymptotically while remaining inside the validated single-barrier window. revision: yes
Referee: Time-domain evolution is acknowledged to be masked by early tails and therefore supplies no independent confirmation of the long-lived modes. Because the central claim rests on WKB alone in the low-barrier limit, the paper should report WKB error estimates, convergence tests, or comparison with an alternative method (e.g., continued-fraction or Leaver) inside the validated window.

Authors: We acknowledge that the time-domain signals are dominated by power-law tails before the long-lived ringing can be isolated, so they cannot independently confirm the quasi-resonant regime. In the revision we will include a new paragraph on WKB accuracy: we report the difference between third- and sixth-order WKB frequencies as an error estimate, demonstrate convergence with respect to the WKB order, and present a direct comparison with the continued-fraction method for a representative set of parameters inside the single-barrier window. These checks support the reliability of the WKB results as the barrier height approaches zero. revision: yes

Circularity Check

0 steps flagged

No circularity: standard WKB and time-domain methods applied to derived potential

full rationale

The paper derives the effective potential for a massive scalar field from the wave equation on the given brane-world metric, then applies standard semiclassical WKB and time-domain integration within the explicitly checked single-barrier regime. The long-lived regime is reported as the limiting behavior of the computed frequencies when the tidal-charge parameter increases inside that validated window. No equations reduce a claimed prediction to a fitted input by construction, no self-citations carry load-bearing uniqueness theorems, and no ansatz is smuggled via prior work. The derivation chain remains self-contained against the external model and standard methods.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the tidal charge is treated as a free parameter of the background metric rather than derived.

free parameters (1)

tidal charge parameter
Introduced by the brane-world model; its value is varied to explore the long-lived regime.

axioms (2)

domain assumption The spacetime is described by the given Reissner-Nordström-like brane-world metric.
The entire analysis rests on this background geometry.
ad hoc to paper The effective potential for the massive scalar remains single-barrier shaped.
Explicitly stated as a prerequisite for reliable WKB and scattering analysis.

pith-pipeline@v0.9.0 · 5473 in / 1356 out tokens · 88877 ms · 2026-05-07T13:59:52.976101+00:00 · methodology

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while when taking into account the case of nega- tive square charge almost all studies are concentrated on massless ﬁelds [52]. Our purpose is to determine how the charge-like deformation and the ﬁeld mass modify the eﬀective potential, the damping rate, the transmis- sion probability, and the absorption cross section, and how they aﬀect the onset of quas...
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At ﬁxed ℓ = 2 and µ = 0 .2, increasing γ lowers the eﬀective-potential peak, so transmission becomes easier and Γℓ(Ω) turns on at smaller frequencies; this is why the γ = 0 .75 curve lies to the left of the γ = 0 and γ = −1 curves. By contrast, increasing the ﬁeld mass raises the asymptotic tail and, in the representative γ = −1, ℓ = 2 case, also raises t...
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