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arxiv: 2603.28557 · v2 · pith:OLHFJS5Enew · submitted 2026-03-30 · 🌀 gr-qc

Eikonal quasinormal modes, greybody factors and shadow of charged accelerating black holes

Filipe Moura , Francisco Silva This is my paper

Pith reviewed 2026-05-22 10:32 UTC · model grok-4.3

classification 🌀 gr-qc
keywords quasinormal modeseikonal limitaccelerating black holesgreybody factorsblack hole shadownull geodesicscharged black holes
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The pith

Quasinormal modes of accelerating black holes in the eikonal limit are determined by the angular velocity and Lyapunov exponent of their unstable circular null geodesics.

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

The paper shows that for non-rotating accelerating black holes, whether neutral or charged, the high-frequency quasinormal modes of test fields follow the same relation to light-orbit properties as they do for ordinary spherical black holes. Specifically, the mode frequencies are set by the angular speed of the circular photon orbit and the rate at which nearby orbits fly apart. The authors calculate these modes and the associated greybody factors for scalar fields and find the formulas work for perturbations of any spin. They also find the size of the shadow the black hole casts. The expressions reduce to the standard ones for Reissner-Nordstrom black holes when the acceleration vanishes.

Core claim

The quasinormal modes in the eikonal limit for accelerating black holes are related to the angular velocity of the circular null geodesics and to the corresponding Lyapunov exponent in exactly the same way as for spherically symmetric black holes. This relation holds for both neutral and charged cases, with results universal across field spins, and the shadow radius is also determined from the photon sphere.

What carries the argument

The direct correspondence between eikonal quasinormal mode frequencies and the angular velocity Ω plus Lyapunov exponent λ of unstable circular null geodesics, via ω = l Ω − i (n + 1/2) λ.

If this is right

  • The quasinormal modes and greybody factors for accelerating black holes can be obtained from geodesic calculations alone in the eikonal regime.
  • The shadow radius follows from the location of the unstable photon orbit in these metrics.
  • The same geodesic-based formulas apply to fields of arbitrary spin.
  • Setting the acceleration parameter to zero recovers the known results for Reissner-Nordstrom black holes.

Where Pith is reading between the lines

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

  • This indicates the eikonal QNM-geodesic link is insensitive to the acceleration term in the metric.
  • Similar extensions might apply to other black hole solutions with non-standard asymptotics.
  • Direct numerical verification of the predicted frequencies for specific acceleration values would test the claim.

Load-bearing premise

The accelerating black hole metrics have well-defined unstable circular null geodesics that can be analyzed to extract their angular velocity and Lyapunov exponent for direct use in the standard eikonal formula.

What would settle it

A numerical computation of the quasinormal mode frequencies for an accelerating black hole in the large angular momentum limit that does not match the values predicted from its null geodesic angular velocity and Lyapunov exponent would falsify the claim.

read the original abstract

We show that the quasinormal modes, in the eikonal limit, for accelerating (non-rotating) black holes, are related to the angular velocity of the circular null geodesics and to the corresponding Lyapunov exponent, in the same way as the ones for spherically symmetric black holes are. We compute those quasinormal modes and greybody factors for neutral and charged accelerating black holes, considering massless test scalar fields, and we show that the results are universal for perturbations of any spin. We also determine the radius of the shadow cast by these black holes. Our results for charged black holes are valid for the Reissner-Nordstrom solution simply by setting the acceleration to zero.

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. The paper claims that the eikonal quasinormal modes for charged accelerating (non-rotating) black holes are related to the angular velocity of the circular null geodesics and the corresponding Lyapunov exponent in exactly the same way as for spherically symmetric black holes. It computes these modes and greybody factors for massless scalar fields, asserts that the results are universal for perturbations of any spin, and determines the shadow radius. The results are stated to reduce to the Reissner-Nordström solution upon setting the acceleration parameter to zero.

Significance. If the central relation holds without additional acceleration-dependent corrections, the work extends the geometric eikonal correspondence to a broader family of black-hole metrics that include an acceleration horizon. This offers a practical route to estimating ringdown frequencies from null geodesics and supplies concrete greybody and shadow results. The explicit reduction to the Reissner-Nordström limit and the claimed spin universality constitute clear strengths that would be valuable if the derivations are confirmed.

major comments (2)
  1. [§3] §3 (Eikonal quasinormal modes): The assertion that the frequencies are given by the standard expressions ω_R = l Ω and ω_I = (n + 1/2) λ with no further A dependence must be supported by an explicit derivation of the radial wave equation. Because the metric lacks spherical symmetry and the radial coordinate is not areal, the effective potential may acquire extra factors from the acceleration parameter; the peak location and its second derivative should be shown to coincide exactly with the geodesic quantities.
  2. [§4] §4 (Greybody factors): The transmission coefficients are extracted after separation of variables, yet the presence of the acceleration horizon alters the asymptotic structure. The boundary conditions at the acceleration horizon and their effect on the greybody factor integral should be stated explicitly and shown to reduce correctly when A → 0.
minor comments (3)
  1. The abstract states that results are 'universal for perturbations of any spin'; the text should clarify whether this is demonstrated by explicit calculation for spin-0,1,2 or by a general argument.
  2. Figure captions for the shadow and greybody plots should list the specific values of mass, charge, and acceleration used in each panel.
  3. [§5] A short paragraph comparing the obtained Lyapunov exponents with those of the Reissner-Nordström limit would help readers assess the magnitude of acceleration effects.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comments point by point below, providing the requested clarifications and indicating revisions that will be incorporated to strengthen the derivations.

read point-by-point responses

  1. Referee: [§3] §3 (Eikonal quasinormal modes): The assertion that the frequencies are given by the standard expressions ω_R = l Ω and ω_I = (n + 1/2) λ with no further A dependence must be supported by an explicit derivation of the radial wave equation. Because the metric lacks spherical symmetry and the radial coordinate is not areal, the effective potential may acquire extra factors from the acceleration parameter; the peak location and its second derivative should be shown to coincide exactly with the geodesic quantities.

    Authors: We acknowledge the referee's point that an explicit derivation is required given the absence of spherical symmetry and the non-areal nature of the radial coordinate. In the revised manuscript we will add a dedicated subsection deriving the radial wave equation for the massless scalar field after separation of variables. We will then compute the effective potential explicitly, locate its maximum, and evaluate the second derivative at that point. This calculation confirms that the peak coincides with the radius of the unstable circular null geodesic and that the curvature yields precisely the Lyapunov exponent λ with no residual A-dependent prefactors in the eikonal limit. The resulting expressions for ω_R and ω_I therefore remain identical to the standard geometric formulae. revision: yes

  2. Referee: [§4] §4 (Greybody factors): The transmission coefficients are extracted after separation of variables, yet the presence of the acceleration horizon alters the asymptotic structure. The boundary conditions at the acceleration horizon and their effect on the greybody factor integral should be stated explicitly and shown to reduce correctly when A → 0.

    Authors: We agree that the boundary conditions at the acceleration horizon must be stated explicitly. In the revised version we will specify that the wave function satisfies purely ingoing boundary conditions at the event horizon and appropriate (outgoing or decaying) conditions at the acceleration horizon. We will also demonstrate analytically that, as A → 0, the acceleration horizon recedes to spatial infinity, the metric functions reduce to those of the Reissner-Nordström solution, and the greybody factor integral recovers the standard expression for that spacetime. This limit check will be included as an explicit appendix calculation. revision: yes

Circularity Check

0 steps flagged

Standard eikonal formula applied to independently computed null geodesics; no reduction to inputs by construction

full rationale

The paper computes the angular velocity Ω and Lyapunov exponent λ of unstable circular null geodesics directly from the accelerating black hole metric (via the effective potential for null geodesics), then inserts these quantities into the established eikonal quasinormal-mode expressions ω_R = l Ω and ω_I = (n + 1/2) λ that were previously derived for spherically symmetric cases. This insertion is presented as an extension rather than a re-derivation or fit; the metric functions, geodesic equations, and resulting Ω/λ are obtained from the line element without presupposing the final QNM values. No self-citation chain, ansatz smuggling, or parameter fitting that forces the output is evident in the derivation chain. The claim of universality for any spin is likewise obtained by explicit computation of greybody factors and shadow radius from the same geodesic data. The overall derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the standard general-relativity assumption that the given accelerating black-hole metrics are solutions of the Einstein equations with appropriate matter or cosmological-constant terms, and that linear perturbation theory around these backgrounds is well-defined. No new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The accelerating black-hole metrics admit circular null geodesics whose angular velocity and Lyapunov exponent determine the eikonal quasinormal modes exactly as in the spherically symmetric case.
    This is the load-bearing premise that allows the known spherical formula to be reused without modification.

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Reference graph

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