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arxiv: 2512.23305 · v1 · submitted 2025-12-29 · ✦ hep-th · gr-qc

Bosonic and Fermionic love number of static acoustic black hole

Yongbin Du , Xiangdong Zhang This is my paper

Pith reviewed 2026-05-16 19:34 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords acoustic black holesLove numbersscalar perturbationsDirac perturbationsanalogue gravitytidal responseblack hole physics
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The pith

Acoustic black holes have generically nonzero scalar Love numbers in four dimensions while fermionic ones follow exact power laws.

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

The paper calculates static Love numbers for scalar and Dirac perturbations around static acoustic black holes in three and four dimensions. It shows that in four dimensions the scalar Love number is nonzero in general, while the fermionic Love number always takes the universal form of plus or minus four to the power of minus (angular momentum plus one half). In three dimensions a logarithmic term appears in the scalar solution, making the bosonic Love number zero when the azimuthal number is even but nonzero when odd, yet the fermionic Love number remains the simple power law four to the minus azimuthal number. These results come from imposing regularity at the horizon and matching the near-horizon solution to the far-field expansion to read off the ratio of decaying to growing modes. The findings highlight how analogue black hole systems respond differently to integer-spin and half-integer-spin tidal fields.

Core claim

By solving the perturbation equations for scalar and Dirac fields on the background of static acoustic black holes and imposing regularity at the horizon, the ratio of decaying to growing modes at large distance yields the Love numbers. In (3+1) dimensions the scalar Love number is generically nonzero, whereas the fermionic ones are given by F^{±1/2}_{ℓm} = ±4^{-(ℓ+1/2)}. In (2+1) dimensions the bosonic Love number vanishes for even m but is nontrivial for odd m due to a logarithmic structure, while the fermionic Love number is F_m = 4^{-m}.

What carries the argument

The Love number defined as the ratio of the coefficients of the decaying and growing solutions in the far-field expansion of the perturbation fields, determined after enforcing regularity at the acoustic horizon.

If this is right

  • Tidal responses of acoustic black holes depend on whether the perturbing field has integer or half-integer spin.
  • Fermionic Love numbers remain simple power laws even when the bosonic case develops logarithmic terms in lower dimensions.
  • The vanishing of bosonic Love numbers for even azimuthal numbers occurs only in three dimensions and is tied to the logarithmic structure.
  • Analogue gravity setups can in principle measure these specific spin-dependent tidal deformabilities.

Where Pith is reading between the lines

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

  • The exact power-law form for fermions may arise from the underlying conformal or spinor properties of the acoustic metric.
  • Logarithmic corrections seen in three dimensions could appear in other reduced-dimensionality analogue models.
  • Laboratory tests in fluid systems could directly probe the predicted parity dependence of bosonic responses.
  • The same matching procedure could be applied to rotating or time-dependent acoustic backgrounds to check for frequency-dependent differences.

Load-bearing premise

The perturbations admit solutions that are regular at the horizon and can be uniquely matched to a combination of growing and decaying modes at large distances.

What would settle it

A direct calculation showing that the scalar perturbation mode in four-dimensional acoustic black holes has zero ratio of decaying to growing amplitude for a generic choice of angular momentum would contradict the claim that the scalar Love number is generically nonzero.

read the original abstract

We compute static ($\omega\to0$) tilde Love numbers for scalar ($s=0$) and Dirac ($s=1/2$) perturbations of static acoustic black holes (ABHs) in (3+1) and (2+1) dimensions respectively. By imposing horizon regularity condition and matching to the large-radius expansion, we extract the ratio between decaying and growing modes. It turns out that in (3+1) dimensions the scalar Love number is generically nonzero for ABHs, while the Fermionic Love numbers follow a universal power-law form $F^{\pm1/2}_{\ell m}=\pm 4^{-(\ell+1/2)}$. In (2+1) dimensions the scalar field exhibits a strange logarithmic structure, causing the Bosonic Love number to vanish for even $m$ but remain nontrivial for odd $m$; In contrast, the Fermionic Love number in this case retains a simple power-law form $F_m=4^{-m}$ and is generically nonzero. These results provide insights into tidal response in analogue gravity systems and highlight qualitative differences between integer- and half-integer-spin fields.

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 manuscript computes static Love numbers for scalar (s=0) and Dirac (s=1/2) perturbations of static acoustic black holes in (3+1) and (2+1) dimensions. Horizon-regular solutions of the static wave equations are matched to the large-radius expansion to extract the ratio of decaying to growing modes. In (3+1)D the scalar Love number is reported as generically nonzero while the fermionic Love numbers obey the universal form F^{±1/2}_{ℓm}=±4^{-(ℓ+1/2)}; in (2+1)D the scalar solutions contain logarithmic terms that cause the bosonic Love number to vanish for even m (but remain nontrivial for odd m), while the fermionic Love number retains the simple power-law F_m=4^{-m}.

Significance. If the mode identifications and extractions are robust, the results supply exact, dimension-dependent expressions for tidal responses in analogue-gravity systems and underscore qualitative distinctions between integer- and half-integer-spin fields. The universal fermionic power laws constitute a concrete, falsifiable prediction that could be checked against numerical or experimental data in fluid analogues.

major comments (2)
  1. [Section on (2+1)D scalar perturbations] The (2+1)D scalar analysis: the indicial equation at infinity produces logarithmic terms for integer m. The claim that the Love number vanishes exactly for even m requires an explicit demonstration that the horizon-regular solution contains no component of the log-augmented non-decaying mode; without this step the vanishing result rests on an unverified classification of the asymptotic basis.
  2. [Method section and (3+1)D results] The extraction procedure (horizon regularity plus asymptotic matching) is stated without an error estimate or cross-check against known limits (e.g., the Schwarzschild Love number in the appropriate limit). This leaves the quoted numerical coefficients and the asserted universality open to possible contamination by sub-leading terms.
minor comments (2)
  1. [Introduction and notation] The notation F^{±1/2}_{ℓm} and F_m should be compared explicitly with the standard Love-number definitions used in the general-relativity literature to avoid confusion.
  2. [Setup] A brief statement of the acoustic metric and the precise form of the static wave operators would improve readability for readers outside analogue-gravity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will incorporate the suggested clarifications into a revised manuscript.

read point-by-point responses

  1. Referee: The (2+1)D scalar analysis: the indicial equation at infinity produces logarithmic terms for integer m. The claim that the Love number vanishes exactly for even m requires an explicit demonstration that the horizon-regular solution contains no component of the log-augmented non-decaying mode; without this step the vanishing result rests on an unverified classification of the asymptotic basis.

    Authors: We agree that an explicit demonstration is required to confirm the absence of the log-augmented growing mode. In the revised version we will construct the horizon-regular solution explicitly, substitute it into the full asymptotic basis (including the logarithmic term), and show by direct coefficient matching that the prefactor of the non-decaying log-augmented mode vanishes identically for even m. This step will be added to the (2+1)D scalar section. revision: yes

  2. Referee: The extraction procedure (horizon regularity plus asymptotic matching) is stated without an error estimate or cross-check against known limits (e.g., the Schwarzschild Love number in the appropriate limit). This leaves the quoted numerical coefficients and the asserted universality open to possible contamination by sub-leading terms.

    Authors: We acknowledge that the current presentation lacks quantitative error control. In the revision we will augment the matching procedure with an explicit truncation-error estimate obtained by retaining the next two orders in the large-radius expansion and recomputing the Love-number ratio. Although the acoustic metric does not reduce directly to Schwarzschild, we will also verify the procedure against the known analytic Love numbers for the (3+1)D Schwarzschild case in the appropriate parameter limit to confirm consistency of the extraction method. revision: yes

Circularity Check

0 steps flagged

No circularity: results obtained from direct boundary-value solution of static perturbation equations

full rationale

The derivation proceeds by writing the static (ω→0) scalar and Dirac equations on the acoustic black-hole background, imposing regularity at the horizon, and reading the Love number from the coefficient ratio in the large-r asymptotic expansion. These steps are standard linear ODE boundary-value problems whose solutions are not defined in terms of the Love numbers themselves. The reported power-law forms (F^{±1/2}_{ℓm}=±4^{-(ℓ+1/2)} and F_m=4^{-m}) and the even-m vanishing in (2+1)D emerge from the indicial structure and explicit integration; they are not fitted parameters renamed as predictions, nor do they rely on load-bearing self-citations or ansätze imported from prior work. The calculation is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the acoustic metric for static black holes, the standard wave equations for scalar and Dirac fields in curved spacetime, and the conventional boundary conditions of regularity at the horizon plus asymptotic flatness at infinity. No new entities or fitted parameters are introduced in the abstract.

axioms (2)
  • domain assumption Horizon regularity condition for perturbations
    Standard requirement in black hole perturbation theory to select physically acceptable solutions.
  • domain assumption Asymptotic matching to large-radius expansion
    Standard technique to isolate the ratio of decaying to growing modes that defines the Love number.

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