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arxiv: 2508.03380 · v2 · submitted 2025-08-05 · 🌀 gr-qc · quant-ph

Squeezed Quasinormal Modes from Nonlinear Gravitational Effects

Sreenath K. Manikandan , Frank Wilczek This is my paper

Pith reviewed 2026-05-19 01:01 UTC · model grok-4.3

classification 🌀 gr-qc quant-ph
keywords gravitational wavesblack hole ringdownquasinormal modessqueezingnonlinear effectshigher harmonicsSchwarzschild black hole
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0 comments X

The pith

Nonlinear gravitational effects in black hole ringdowns produce about one percent squeezing in gravitational waves.

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

The paper estimates how much squeezing nonlinear gravity can create in the waves emitted during the ringdown phase after a black hole merger. It draws on known ratios of higher harmonics to compute this effect within the weakly perturbative regime for a Schwarzschild black hole. A sympathetic reader would care because this offers a concrete way to think about quantum-like features emerging from classical nonlinear gravity in strong-field settings. If the estimate holds, it suggests that future detectors could in principle pick up these subtle squeezed states as a signature of the underlying dynamics.

Core claim

We estimate the degree of squeezing possible in gravitational waves due to nonlinear gravitational effects in the weakly perturbative regime. Using the predicted amplitude ratios for higher harmonic generation in the ringdown phase of a black hole merger event, we estimate the relevant degree of squeezing produced by a Schwarzschild singularity to be of the order of one percent.

What carries the argument

Higher harmonic generation in quasinormal modes, which induces squeezing through nonlinear gravitational interactions during the ringdown phase.

Load-bearing premise

The estimation assumes that previously calculated amplitude ratios for higher harmonics can be directly used in the squeezing calculation without significant corrections from strong-field dynamics or back-reaction.

What would settle it

A numerical relativity simulation computing the actual squeezing parameter in the ringdown of a black hole merger that yields a value far from one percent would falsify the estimate.

read the original abstract

We estimate the degree of squeezing possible in gravitational waves due to nonlinear gravitational effects in the weakly perturbative regime. Using the predicted amplitude ratios for higher harmonic generation in the ringdown phase of a black hole merger event, we estimate the relevant degree of squeezing produced by a Schwarzschild singularity to be of the order of one percent.

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 estimates the degree of squeezing in gravitational waves that can arise from nonlinear gravitational effects in the weakly perturbative regime. It takes published amplitude ratios for higher-harmonic generation in the ringdown of a black-hole merger, inserts them into a squeezing calculation for a Schwarzschild singularity, and reports an order-of-magnitude result of one percent.

Significance. If the central estimate survives scrutiny, the work would supply a concrete, falsifiable link between classical nonlinear gravity and quantum squeezing in the ringdown signal. Such a result could motivate targeted searches in future high-precision gravitational-wave data and would illustrate how perturbative nonlinearities can seed observable quantum features without requiring a full quantum-gravity treatment.

major comments (2)
  1. [Estimation paragraph (post-abstract)] The one-percent squeezing figure is obtained by direct substitution of external amplitude ratios into the squeezing formula (see the estimation paragraph following the abstract). Because those ratios originate from linear or weakly nonlinear ringdown calculations, the substitution implicitly assumes that back-reaction and strong-field corrections near the singularity remain negligible; no self-consistent solution of the nonlinear wave equation with the squeezed state is presented to verify this assumption at the quoted precision.
  2. [Weakly perturbative regime discussion] The manuscript states that the calculation is performed inside the weakly perturbative regime, yet the local curvature near the Schwarzschild singularity is strong. It is therefore necessary to show explicitly (perhaps via an order-of-magnitude estimate or a controlled expansion) that the additional phase shifts or amplitude corrections generated by the same nonlinear interactions that produce the harmonics do not exceed the one-percent level.
minor comments (2)
  1. [Notation and definitions] Define the squeezing parameter and its relation to the harmonic amplitude ratios in a single, self-contained equation so that the numerical insertion can be reproduced without external references.
  2. [Results paragraph] Add a brief error-propagation estimate or sensitivity analysis for the input amplitude ratios; even a one-sentence statement would clarify the robustness of the one-percent figure.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. Our work provides an order-of-magnitude estimate of squeezing in gravitational waves from nonlinear effects in the black-hole ringdown, based on published higher-harmonic amplitude ratios. We address each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: The one-percent squeezing figure is obtained by direct substitution of external amplitude ratios into the squeezing formula (see the estimation paragraph following the abstract). Because those ratios originate from linear or weakly nonlinear ringdown calculations, the substitution implicitly assumes that back-reaction and strong-field corrections near the singularity remain negligible; no self-consistent solution of the nonlinear wave equation with the squeezed state is presented to verify this assumption at the quoted precision.

    Authors: We agree that the estimate substitutes amplitude ratios from the existing literature into the squeezing formula and that those ratios are derived from linear or weakly nonlinear calculations. The manuscript presents this as an order-of-magnitude estimate under the assumption that back-reaction remains small in the weakly perturbative regime. We will revise the estimation paragraph to state these assumptions explicitly and to note that a full self-consistent solution of the nonlinear wave equation including the squeezed state is not provided. Such a solution would constitute a substantial separate investigation. revision: partial

  2. Referee: The manuscript states that the calculation is performed inside the weakly perturbative regime, yet the local curvature near the Schwarzschild singularity is strong. It is therefore necessary to show explicitly (perhaps via an order-of-magnitude estimate or a controlled expansion) that the additional phase shifts or amplitude corrections generated by the same nonlinear interactions that produce the harmonics do not exceed the one-percent level.

    Authors: The referee correctly identifies that curvature is strong near the singularity while the ringdown calculation assumes weak perturbations at larger radii. The nonlinear harmonic generation we consider occurs in the wave zone where the metric perturbation is small. In the revised manuscript we will add a brief order-of-magnitude argument showing that strong-field corrections to phase and amplitude are suppressed by the smallness of the perturbation amplitudes (typically ≲ 10^{-2}), remaining below the one-percent level for the parameters of interest. This discussion will be placed in the section addressing the weakly perturbative regime. revision: yes

standing simulated objections not resolved
  • A fully self-consistent solution of the nonlinear wave equation that includes the squeezed state and verifies the absence of back-reaction at the quoted precision.

Circularity Check

0 steps flagged

No significant circularity; estimation uses external amplitude ratios as independent input

full rationale

The paper estimates squeezing by inserting predicted amplitude ratios for higher harmonics in black hole ringdown into a squeezing calculation in the weakly perturbative regime. The abstract and available text present these ratios as given predictions from the literature on ringdown, without deriving or fitting them internally. No self-definitional equations, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The central result is an order-of-magnitude estimate relying on external benchmarks, making the paper self-contained against independent inputs rather than reducing to its own outputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard assumptions of black-hole perturbation theory and the validity of using external harmonic-amplitude predictions; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Nonlinear gravitational effects remain small enough in the ringdown phase to be treated within the weakly perturbative regime.
    Invoked when the authors use predicted amplitude ratios to estimate squeezing.

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