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arxiv: 2508.11096 · v1 · submitted 2025-08-14 · 🌀 gr-qc

Echoes and quasinormal modes of asymmetric black bounces

Alana C. L. Santos , Leandro A. Lessa , Roberto V. Maluf , Gonzalo J. Olmo This is my paper

Pith reviewed 2026-05-18 22:17 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black bouncesquasinormal modesgravitational wave echoesasymmetric spacetimesReissner-Nordströmscalar perturbationsgeneral relativity
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0 comments X

The pith

Asymmetric black bounces recover the Reissner-Nordström solution externally and generate no gravitational wave echoes.

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

The paper examines quasinormal modes and echoes for symmetric and asymmetric black bounce spacetimes sourced by anisotropic fluids in general relativity. Symmetric horizonless cases can develop multiple potential barriers that produce echoes whose details depend on the regularization parameter and fluid density. Asymmetric models, however, match the Reissner-Nordström geometry outside the core region whether bounded or unbounded inside, and they exhibit no echoes. This similarity in wave emission properties makes the asymmetric bounces difficult to distinguish from ordinary charged black holes on the basis of gravitational-wave signals alone.

Core claim

Asymmetric black bounce solutions recover the Reissner-Nordström geometry in their external region. Depending on the sign of a parameter they are either bounded or unbounded inside, yet both variants display qualitatively the same wave-emission behavior as Reissner-Nordström black holes and produce no echoes, in contrast to certain symmetric horizonless bounces that generate echoes from multiple barriers.

What carries the argument

Effective potential for massless scalar fields, constructed directly from the given black-bounce line elements and used to compute quasinormal-mode frequencies via WKB, Pöschl-Teller, and time-domain methods.

If this is right

  • Symmetric horizonless black bounces can produce echoes whose strength and timing depend on the fluid energy density and the minimal-radius parameter a.
  • Asymmetric black bounces remain indistinguishable from Reissner-Nordström configurations by their quasinormal-mode spectra or echo signatures.
  • Both bounded and unbounded asymmetric models share the same qualitative wave-emission properties.
  • Echoes appear only when the effective potential develops multiple barriers, which occurs in certain symmetric but not asymmetric cases.

Where Pith is reading between the lines

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

  • Wave-based tests may miss deviations from standard black holes if the underlying model is an asymmetric bounce.
  • Other perturbation channels or late-time tails could still reveal differences even when echoes are absent.
  • The result motivates checking whether the same potential structure persists for higher-spin fields or in modified-gravity extensions.

Load-bearing premise

The effective potential follows from the black-bounce metrics for massless scalar fields without extra assumptions about the fluid or regularization that would reshape the barrier structure or echo formation.

What would settle it

Observation of echoes or their absence in the ringdown of gravitational waves from a candidate that externally matches Reissner-Nordström but is suspected to be an asymmetric black bounce.

Figures

Figures reproduced from arXiv: 2508.11096 by Alana C. L. Santos, Gonzalo J. Olmo, Leandro A. Lessa, Roberto V. Maluf.

Figure 1
Figure 1. Figure 1: FIG. 1. Graphical representation of [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The effective potential (2a) and time evolution of the massless scalar field (2b) for the [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The effective potential (left panels) and time evolution of the massless scalar field (right [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The effective potential (left panels) and time evolution of the massless scalar field (right [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Graphical representation of [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Effective potential (6a) and time evolution of the massless scalar field (6b) for the asymmetric [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Graphical representation of [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Graphical representation of [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Graphical representation of [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
read the original abstract

We study quasinormal modes and echoes of symmetric and asymmetric black bounce solutions generated by anisotropic fluids within the framework of general relativity. We derive the effective potential governing massless scalar fields and compute the corresponding quasinormal mode spectra using three independent methods: sixth-order WKB, P\"oschl-Teller and time-domain evolution. Our results show that symmetric black bounce configurations with horizons yield a standard single-barrier potential, while horizonless solutions may exhibit multiple potential barriers that generate gravitational wave echoes. These echoes are sensitive to model parameters such as the fluid energy density and the regularizing parameter $a$ that defines the minimal $2$-sphere. The asymmetric models considered recover the Reissner-Nordstr\"om solution in their external region but can be bounded or unbounded in the inside, depending on the sign of a parameter. Both cases have similar qualitative properties as far as wave emission is concerned but show no echoes. This makes it very difficult to distinguish them from standard Reissner-Nordstr\"om configurations.

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 manuscript studies quasinormal modes and echoes of symmetric and asymmetric black bounce spacetimes sourced by anisotropic fluids in general relativity. It derives the effective potential for massless scalar perturbations from the given metrics and computes the spectra via three independent techniques: sixth-order WKB, Pöschl-Teller fitting, and time-domain integration. The central results are that symmetric horizonless configurations can develop multiple barriers producing echoes, while asymmetric models recover the Reissner-Nordström exterior exactly, retain a horizon, and display only standard ringdown plus power-law tails with no echoes, rendering them difficult to distinguish from RN black holes via wave emission.

Significance. If the results hold, the work clarifies the observational distinguishability of black-bounce models, showing that asymmetric versions are effectively indistinguishable from RN in echo searches. The cross-validation across three numerical methods is a clear strength that bolsters reliability of the reported spectra and the no-echo conclusion for the asymmetric cases.

major comments (2)
  1. The time-domain evolution section does not report grid-resolution or time-step convergence tests, nor error estimates on the extracted waveforms. This is load-bearing for the central claim that asymmetric models produce no echoes, as small numerical artifacts could mimic or mask late-time signals.
  2. No explicit validation is performed against the known Schwarzschild or RN quasinormal frequencies in the limit a → 0 or vanishing fluid density. Without this check, the implementation of the effective potential and the three solvers cannot be fully trusted for the no-echo distinction asserted in the abstract.
minor comments (3)
  1. The abstract states that echoes are sensitive to fluid energy density and a but does not quote the specific parameter values used for the displayed potentials or waveforms.
  2. Figure captions for the effective-potential plots should explicitly list the metric parameters (a, fluid density, charge) corresponding to each curve.
  3. A short paragraph comparing the obtained RN-limit frequencies to tabulated values in the literature would improve clarity without altering the main results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: The time-domain evolution section does not report grid-resolution or time-step convergence tests, nor error estimates on the extracted waveforms. This is load-bearing for the central claim that asymmetric models produce no echoes, as small numerical artifacts could mimic or mask late-time signals.

    Authors: We agree that explicit convergence tests and error estimates are important for the reliability of the time-domain results, particularly when asserting the absence of echoes. Although internal checks were performed during the development of the code to confirm stability of the waveforms under refinement, these details were omitted from the manuscript. In the revised version we will add a dedicated paragraph in the time-domain section reporting the grid resolutions and time steps employed, together with a brief discussion of the observed convergence and estimated numerical errors on the late-time signals. revision: yes

  2. Referee: No explicit validation is performed against the known Schwarzschild or RN quasinormal frequencies in the limit a → 0 or vanishing fluid density. Without this check, the implementation of the effective potential and the three solvers cannot be fully trusted for the no-echo distinction asserted in the abstract.

    Authors: We acknowledge the value of an explicit benchmark against the well-known Schwarzschild and Reissner-Nordström spectra. While the asymmetric metrics are constructed so that the exterior geometry reduces exactly to Reissner-Nordström (and the effective potential accordingly), we did not include a direct numerical comparison of the computed frequencies in the appropriate limits. In the revised manuscript we will add a short validation subsection (or appendix) that recovers the known Schwarzschild and RN quasinormal frequencies as a → 0 or the fluid density vanishes, thereby confirming the implementation of the potential and the three independent solvers. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation proceeds from given black-bounce metrics (with parameters a and fluid density as explicit inputs) to the effective potential via the standard GR reduction to a Schrödinger-like equation for massless scalars; quasinormal frequencies and echoes are then obtained by three independent external methods (6th-order WKB, Pöschl-Teller fit, time-domain integration) that do not feed back into the metric or potential. Asymmetric cases recover the RN exterior exactly, so the single-barrier potential and absence of echoes follow directly from the causal structure without any fitted outputs or self-referential definitions. No load-bearing step reduces to a self-citation chain or renames a known result as a new prediction; the computations remain self-contained against standard GR benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central results rest on the existence of the black bounce metrics generated by anisotropic fluids, the validity of the massless scalar perturbation equation in those backgrounds, and the numerical accuracy of the three QNM methods. No new entities are postulated beyond the model parameters a and fluid density.

free parameters (2)
  • regularizing parameter a
    Defines the minimal 2-sphere radius and controls the potential barrier structure; its value is chosen per model rather than derived.
  • fluid energy density
    Enters the metric functions and affects echo properties; treated as a free model parameter.
axioms (2)
  • domain assumption The spacetime is a solution of Einstein's equations sourced by an anisotropic fluid.
    Invoked to generate the symmetric and asymmetric black bounce metrics used throughout.
  • standard math Massless scalar field perturbations obey the standard wave equation on the given background metric.
    Basis for deriving the effective potential and computing quasinormal modes.

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