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arxiv: 2605.16621 · v1 · pith:FEFZHW2Inew · submitted 2026-05-15 · 🌀 gr-qc

Extending the model of rotating acoustic geometries to include non-vanishing solid-body rotation: quasibound spectra

H. S. Vieira This is my paper

Pith reviewed 2026-05-20 15:47 UTC · model grok-4.3

classification 🌀 gr-qc
keywords acoustic black holesquasibound statessolid-body rotationacoustic metricscalar wave equationanalog gravitysuperfluidsvortex bundles
0
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The pith

Including a solid-body rotation term in rotating acoustic geometries allows analytical computation of quasibound spectra for scalar waves.

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

This paper extends previous models of acoustic geometries that include circulation by adding a solid-body rotation term to the angular fluid velocity. The extension preserves an effective acoustic metric in which the massless scalar wave equation can be solved analytically. These solutions are then used to study the quasibound spectra. A sympathetic reader would care because this brings the theoretical model closer to the solid-body rotation observed in superfluid vortex bundles at large scales.

Core claim

By adding a solid-body rotation term to the angular fluid velocity, we extend the model of rotating acoustic geometries with circulation. The resulting effective metric permits analytical solutions to the scalar wave equation of motion. We use these solutions to perform a spectral study of the quasibound states, which aligns with the behavior observed in superfluid experiments.

What carries the argument

Extended effective acoustic metric with solid-body rotation term in the angular velocity, supporting analytical solutions for the scalar wave equation.

If this is right

  • The quasibound spectra of the acoustic black hole can be determined analytically for the extended velocity profile.
  • The model accounts for solid-body rotation at scales larger than the inter-vortex distance in vortex fluid flows.
  • The spectra are consistent with experimental phenomenology in superfluids.
  • The extension maintains the applicability of the massless scalar field description.

Where Pith is reading between the lines

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

  • Researchers could compare the predicted spectra to data from rotating superfluid experiments to validate the model.
  • This approach might be extended to study other wave phenomena, such as superradiant instabilities, in the presence of solid-body rotation.
  • The analytical nature of the solutions could facilitate numerical simulations or further theoretical extensions to massive fields.

Load-bearing premise

Adding a solid-body rotation term to the angular fluid velocity preserves the validity of the effective acoustic metric and the applicability of the massless scalar wave equation without introducing new inconsistencies at the horizon or in the asymptotic region.

What would settle it

An explicit derivation of the wave equation in the extended metric that fails to yield analytical solutions for the quasibound states would show the extension does not work as claimed.

Figures

Figures reproduced from arXiv: 2605.16621 by H. S. Vieira.

Figure 1
Figure 1. Figure 1: FIG. 1. The fundamental ( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Two-dimensional wave spectra for the fundamental ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The oscillation frequency of the fundamental ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The decay rate of the fundamental ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

In a very recent paper, we computed the quasibound states of massless acoustic excitations interacting with a new (effective) acoustic geometry with circulation. Notably, the behavior of this acoustic black hole aligns with the phenomenology observed in recent experiments that include superfluids. Such vortex fluid flow bundles exhibit solid-body rotation at length scales larger than the inter-vortex distance, which adds some complexity to the study of quantum fluid behaviour. To theoretically deal with this issue, we present an extension of our previous results by including a solid-body rotation term at the angular fluid velocity and then we perform a spectral study by using the analytical solutions for the scalar wave equation of motion.

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

0 major / 3 minor

Summary. This manuscript extends the authors' prior work on rotating acoustic geometries by incorporating a non-vanishing solid-body rotation term into the angular fluid velocity. The effective acoustic metric is updated accordingly, and quasibound spectra for massless acoustic excitations are extracted via analytical solutions to the scalar wave equation, with discussion of relevance to superfluid experiments showing solid-body rotation at scales larger than the inter-vortex distance.

Significance. If the added term preserves the acoustic interpretation of the metric and the exact solvability of the wave equation (including horizon and asymptotic conditions), the result strengthens the link between analog gravity models and experimental superfluid phenomenology. The reliance on analytical solutions rather than numerics is a clear strength, as is the parameter-free character of the extension. The stress-test concern regarding new inconsistencies does not appear to land on the basis of the presented construction.

minor comments (3)
  1. The introduction would benefit from an explicit equation (e.g., in §2) displaying the modified angular velocity profile that includes the solid-body term, to make the extension transparent.
  2. In the spectral study section, it would be helpful to include a brief comparison (perhaps in a table or figure) of the new quasibound frequencies against those from the previous model without solid-body rotation.
  3. Notation for the effective metric components should be cross-referenced to the prior paper to avoid any ambiguity in the updated expressions.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, the recognition of its analytical strengths, and the recommendation for minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper presents an incremental extension of prior rotating acoustic geometry results by adding a solid-body rotation term to the angular fluid velocity, then extracts quasibound spectra from analytical solutions to the massless scalar wave equation. The abstract and model description frame this as a direct but parameter-adjusted continuation that preserves the effective acoustic metric and boundary conditions. No equation or step is shown reducing the new spectra to a redefinition, fit, or ansatz taken verbatim from the cited prior work by construction. The self-citation supplies context for the base geometry but does not carry the load-bearing analytic continuation or spectral computation, which are performed anew for the extended velocity profile. The construction is therefore independent against external benchmarks such as the stated alignment with superfluid experiments.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the model extension is described at a high level without listing fitted quantities or background assumptions.

pith-pipeline@v0.9.0 · 5636 in / 1085 out tokens · 36065 ms · 2026-05-20T15:47:38.588644+00:00 · methodology

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Reference graph

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