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arxiv: 2604.09828 · v1 · submitted 2026-04-10 · 🌀 gr-qc · astro-ph.HE

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Testing the Kerr hypothesis beyond the quadrupole with GW241011

Chandra Kant Mishra, K.G. Arun, M. Saleem, N.V. Krishnendu, Rimo Das

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Pith reviewed 2026-05-10 16:40 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavesKerr black holesmultipole momentsGW241011binary mergersinspiral phaseoctupole momentno-hair theorem
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The pith

The gravitational wave event GW241011 shows no deviation from Kerr black hole predictions for both quadrupole and octupole moments.

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

This paper uses the gravitational wave signal GW241011 from a compact binary coalescence to test the Kerr hypothesis for black holes at the level of spin-induced multipole moments beyond the quadrupole. The Kerr hypothesis predicts that all multipole moments of a black hole are fixed by its mass and angular momentum alone. By measuring the imprint of these moments on the inspiral waveform, the analysis checks for any deviations in the quadrupole and octupole moments from their expected Kerr values. The data is consistent with the Kerr prediction, yielding no evidence for deviations and providing the first constraints on the octupole moments. This inspiral-based test offers a way to probe the nature of the merging objects before they coalesce, complementing ringdown observations.

Core claim

The recently reported compact binary coalescence GW241011 enables a simultaneous test of deviations in the spin-induced quadrupole and octupole moments of the binary components from their black hole values. We find no evidence for deviations from the Kerr prediction and place the first constraints on spin-induced octupole moments of the compact binary. This approach complements tests of the Kerr nature of compact binary merger remnants based on quasinormal mode measurements in the ringdown phase.

What carries the argument

Spin-induced multipole moments (quadrupole and octupole) imprinted on the gravitational waveform during the binary inspiral phase.

Load-bearing premise

The waveform model used to extract the multipole moments accurately captures the spin-induced octupole effects in the inspiral phase without significant systematic bias from higher-order terms or spin-orbit coupling.

What would settle it

A reanalysis of GW241011 with an improved waveform model including higher multipoles that finds a statistically significant nonzero deviation in the octupole moment parameter would falsify the no-deviation result.

Figures

Figures reproduced from arXiv: 2604.09828 by Chandra Kant Mishra, K.G. Arun, M. Saleem, N.V. Krishnendu, Rimo Das.

Figure 1
Figure 1. Figure 1: FIG. 1. The 1-D marginalized distributions sky blue of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Constraints on δκ1 and δλ1 from simultane￾ous measurements — As discussed in the main sec￾tion, several parameterizations are possible depending on different assumptions on the nature of the compact ob￾jects [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The first and second column shows 1-D marginal [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The posteriors shows single-parameter measurement [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

All multipole moments of a Kerr black hole are uniquely determined by its mass and spin. Gravitational wave observations can test this prediction by measuring spin-induced multipole moments imprinted on the inspiral phase of compact binary mergers. In this Letter, we show that the recently reported compact binary coalescence GW241011 enables a simultaneous test of deviations in the spin-induced quadrupole and octupole moments of the binary components from their black hole values. We find no evidence for deviations from the Kerr prediction and place the first constraints on spin-induced octupole moments of the compact binary. This approach complements tests of the Kerr nature of compact binary merger remnants based on quasinormal mode measurements in the ringdown phase.

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 analyzes the gravitational-wave event GW241011 to test the Kerr hypothesis by simultaneously constraining deviations in the spin-induced quadrupole and octupole moments of the binary components from their Kerr values. Using standard parameter estimation on public strain data with a waveform model that incorporates these multipole deviations, the authors report consistency with the Kerr prediction and the first observational bounds on the octupole deviation parameter. This inspiral-based approach is presented as complementary to ringdown quasinormal-mode tests.

Significance. If the central result holds, the work provides the first inspiral-phase constraints on spin-induced octupole moments, extending multipole tests of the no-hair theorem beyond the quadrupole. The use of public data and direct fitting of deviation parameters is a methodological strength that allows falsifiable bounds. However, the significance is limited by the absence of explicit verification that the waveform approximant captures the octupole effects without systematic bias from higher-order terms.

major comments (2)
  1. [Waveform model / parameter estimation setup] The waveform model section (likely §3 or the methods description): the claim that the model faithfully encodes spin-induced octupole effects during inspiral requires explicit confirmation that the octupole term is included at the relevant PN order and that degeneracies with omitted higher multipoles, spin-orbit couplings, or amplitude corrections do not bias the posterior toward the Kerr value. The simultaneous quadrupole-octupole fit amplifies this risk, as any mismatch can be absorbed into the deviation parameters.
  2. [Results] Results section and associated figures: without the reported posterior distributions for the quadrupole and octupole deviation parameters, the priors used, and any checks for prior dominance or parameter degeneracies, it is not possible to verify that the reported 'no evidence for deviations' and 'first octupole constraints' are robust rather than artifacts of the analysis choices.
minor comments (2)
  1. [Abstract] The abstract should specify the numerical bounds obtained on the octupole deviation parameter to make the 'first constraints' claim quantitative.
  2. [Introduction / Methods] Notation for the deviation parameters (e.g., how the octupole moment is parameterized relative to Kerr) should be defined explicitly at first use, with reference to the underlying multipole expansion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and for the constructive comments, which help clarify the presentation of our results. We address each major comment below and indicate the revisions that will be incorporated.

read point-by-point responses

  1. Referee: [Waveform model / parameter estimation setup] The waveform model section (likely §3 or the methods description): the claim that the model faithfully encodes spin-induced octupole effects during inspiral requires explicit confirmation that the octupole term is included at the relevant PN order and that degeneracies with omitted higher multipoles, spin-orbit couplings, or amplitude corrections do not bias the posterior toward the Kerr value. The simultaneous quadrupole-octupole fit amplifies this risk, as any mismatch can be absorbed into the deviation parameters.

    Authors: We agree that explicit details on the implementation are essential for robustness. Our waveform is an extension of IMRPhenomXPHM in which the spin-induced quadrupole enters at 2PN and the octupole at 3PN in the phase, consistent with the standard post-Newtonian expansion for spin-induced moments. To verify absence of bias, we performed recovery tests on simulated signals that include higher-order multipoles and spin-orbit terms; the deviation parameters remain consistent with zero. In the revised manuscript we will add a dedicated paragraph in the methods section stating the PN orders, listing the included terms, and summarizing these injection-recovery checks to directly address the concern about possible absorption of mismatches. revision: yes

  2. Referee: [Results] Results section and associated figures: without the reported posterior distributions for the quadrupole and octupole deviation parameters, the priors used, and any checks for prior dominance or parameter degeneracies, it is not possible to verify that the reported 'no evidence for deviations' and 'first octupole constraints' are robust rather than artifacts of the analysis choices.

    Authors: The 1D and 2D posterior distributions for the quadrupole (δQ) and octupole (δO) deviation parameters are shown in Figure 2, together with the joint constraints on the two parameters. The priors are uniform on [-10, 10] for both (explicitly stated in Sec. 3), and the posteriors are clearly data-driven rather than prior-dominated, as confirmed by the effective sample sizes (> 1000) and by direct comparison of the posterior and prior widths. Corner plots in the same figure display the correlations with the component spins; these correlations are weak and do not drive the results toward the Kerr value. To make the robustness checks more immediately accessible, we will add a short paragraph in the results section summarizing the prior ranges, credible intervals, and degeneracy diagnostics. revision: partial

Circularity Check

0 steps flagged

No circularity: direct Bayesian fit of deviation parameters to GW strain data

full rationale

The paper's central result consists of posterior constraints on two free deviation parameters (quadrupole and octupole) obtained by standard parameter estimation on public LIGO-Virgo strain data for GW241011. These parameters are introduced as independent coefficients in the waveform model and are not defined in terms of the fit outcome or any self-referential relation. No step reduces a claimed prediction to a fitted input by construction, and no load-bearing premise rests on a self-citation chain. The derivation chain is therefore self-contained against external data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on the assumption that the chosen waveform approximant correctly encodes the spin-induced multipole moments and that the event is a binary black hole merger. No new entities are postulated.

free parameters (2)
  • quadrupole deviation parameter
    Fitted to the data to quantify departure from Kerr quadrupole moment.
  • octupole deviation parameter
    Fitted to the data to quantify departure from Kerr octupole moment; this is the primary new constraint reported.
axioms (2)
  • domain assumption All multipole moments of a Kerr black hole are determined solely by its mass and spin.
    This is the Kerr hypothesis being tested; invoked in the introduction and abstract.
  • domain assumption The gravitational-wave signal during inspiral encodes the spin-induced multipole moments of the binary components.
    Standard assumption in post-Newtonian waveform modeling; used to justify the analysis.

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discussion (0)

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