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REVIEW 4 major objections 4 minor 72 references

Relativistic reflection spectra of super-spinning black holes

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Two Seyfert galaxies prefer a non-Kerr spacetime with black hole spin beyond the Kerr limit.

desk verdict Useful new model implementation, but the paper's own numbers do not support the 3-sigma claim for Swift J0501.9-3239; the Ark 120 result is the one that holds up. read the letter →

arxiv 1908.05177 v2 pith:KDXQQPXZ submitted 2019-08-14 gr-qc astro-ph.HE

Biao Zhou , Ashutosh Tripathi , Askar B. Abdikamalov , Dimitry Ayzenberg , Cosimo Bambi , Sourabh Nampalliwar , Menglei Zhou This is my paper · ORCID
classification gr-qcastro-ph.HE
keywords relativisticreflectionspectroscopysuper-spinningblackholesnon-KerrspacetimesdeformationparameterX-raySeyfertgalaxiesSuzakuholespin
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether compact objects previously classified as near-extremal Kerr black holes are genuinely described by general relativity's Kerr metric. The authors extend their relativistic reflection model to a parametric non-Kerr spacetime in which black holes can have dimensionless spin $|a_*| > 1$, and fit Suzaku X-ray spectra of four Seyfert galaxies known for very high spin estimates. For two sources, Ton S180 and 1H0419-577, the data remain consistent with the Kerr solution. For Ark 120 and Swift J0501.9-3239, the Kerr solution is not recovered at the $3\sigma$ level, with $\Delta\chi^2$ improvements of 20.40 and 6.86 over the Kerr fit, and MCMC analyses confirm the preference for the non-Kerr spacetime. The authors stress that systematic uncertainties, especially the assumed radial emissivity profile of the reflection component, may account for the apparent detection.

What carries the argument

The load-bearing object is the parametric non-Kerr metric introduced in Ref. [52], here restricted to $m_1 = m_2 = M(1 + \alpha M^2/r^2)$ in Boyer-Lindquist-like coordinates. The deformation parameter $\alpha$ controls deviations from Kerr ($\alpha = 0$ recovers Kerr); for $\alpha > 0$, the equation $\Delta = r^2 - 2m_2 r + a^2 = 0$ has real roots even when $|a_*| > 1$, so the spacetime describes a rotating black hole rather than a naked singularity, with event-horizon and ISCO radii that can be smaller than in Kerr. The observed reflection spectrum is computed with the transfer-function method as implemented in the relxill_nk model, tabulated over a grid of spin $a_*$, deformation parameter $\alpha$, and inclination angle, and the fit marginalizes over disk emissivity parameters. An MCMC analysis using the Goodman-Weare ensemble sampler confirms the best-fit regions for the two sources that prefer the non-Kerr solution.

What would settle it

Refit the Ark 120 and Swift J0501.9-3239 Suzaku spectra with an extended-corona Comptonisation component added to the model, since the paper itself raises partial Comptonisation to explain residuals above 8 keV. If $\alpha$ and $a_*$ then return to the Kerr values within $1\sigma$, the claimed super-spinning detection was an artifact of the missing component; if they remain above the Kerr bound at $3\sigma$, the non-Kerr interpretation stands.

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Extended reading notes

Core claim

The paper's central claim is that the spacetime around the compact object in Ark 120, and with weaker significance in Swift J0501.9-3239, is better described by a non-Kerr metric with deformation parameter $\alpha > 0$ and spin parameter $|a_*| > 1$ than by the Kerr metric of general relativity. In the metric family used here, when $m_1 = m_2 = M(1 + \alpha M^2/r^2)$, positive $\alpha$ allows the event horizon to exist for spins above the Kerr bound, and the innermost stable circular orbit can lie inside the Kerr ISCO radius. Fitting this model to Suzaku data, the authors find $\Delta\chi^2 = 20.40$ for Ark 120 and $\Delta\chi^2 = 6.86$ for Swift J0501.9-3239 in favor of the non-Kerr model, with best-fit values $a_* = 1.242^{+0.022}_{-0.018}$ and $\alpha = 0.213^{+0.030}_{-0.011}$ for Ark 120 and $a_* = 1.131^{+0.019}_{-0.036}$ and $\alpha = 0.137^{+0.003}_{-0.003}$ for Swift J0501.9-3239. MCMC analyses give $a_* = 1.16^{+0.09}_{-0.13}$, $\alpha = 0.20^{+0.11}_{-0.08}$ for Ark 120 and $a_* = 1.11^{+0.12}_{-0.08}$, $\alpha = 0.12^{+0.09}_{-0.14}$ for Swift J0501.9-3239 at 90% confidence. The Kerr hypothesis is not recovered at $3\sigma$ for these two sources, while the other two remain consistent with Kerr.

Load-bearing premise

The claimed non-Kerr detection rests on the assumed mathematical form for how the disk's reflected brightness declines with radius; if the real profile differs from the fitted power-law forms, the measurement of $\alpha$ is biased and the apparent preference for super-spinning black holes could vanish.

Editorial extensions

If this is right

  • If the detections hold, the central objects of Ark 120 and Swift J0501.9-3239 are the first astrophysical candidates for super-spinning black holes, with event horizons present despite $|a_*| > 1$, requiring physics beyond the Kerr hypothesis of Einstein's gravity.
  • All four sources in this sample had spins stuck at the model boundary $a_* \leq 0.998$ under the Kerr assumption; allowing $\alpha$ free moves the best fits above 1, suggesting that boundary-stuck measurements are a warning sign of model breakdown rather than a sign of maximal Kerr spin.
  • The large $\Delta\chi^2$ for Ark 120 shows that X-ray reflection spectroscopy can, in principle, distinguish Kerr from non-Kerr spacetimes with existing data if the source and emissivity model are well chosen.
  • Confirmation will require higher-quality data, in particular broad-band coverage such as XMM-Newton plus NuSTAR, to pin down the reflection component above 8 keV and reduce modeling degeneracies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable consequence of the paper's systematic-uncertainty caveat is that refitting Ark 120 with a grid-free or physically motivated emissivity profile, such as a lamppost corona geometry, should move $\alpha$ back toward 0 if the detection is an artifact; if $\alpha$ remains positive, the super-spinning interpretation is strengthened.
  • The same parametric spacetime could be applied to other near-extremal spin measurements from reflection spectroscopy; if boundary-stuck spins are generic, other sources previously reported at $a_* \simeq 0.998$ may also migrate to $|a_*| > 1$ when $\alpha$ is freed.
  • Because the metric also admits naked-singularity solutions for other parameter combinations, these fits double as a test of whether the central object possesses an event horizon, linking X-ray reflection constraints to black-hole existence.
  • The paper does not propose a top-down theory that produces $\alpha > 0$ naturally; if the detections survive systematic scrutiny, they would motivate such theories and a search for independent signatures of super-spinning horizons.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper constructs a relativistic reflection model in the parametric non-Kerr spacetime of Lin et al. (2015), in which m1=m2=M(1+αM^2/r^2) and positive α permits black-hole solutions with dimensionless spin |a*| > 1. The model is implemented in the public package relxill_nk. The authors fit Suzaku observations of four Seyfert galaxies (Ton S180, Ark 120, 1H0419-577, and Swift J0501.9-3239) that were previously modeled as near-extremal Kerr black holes. For each source they compare a Kerr fit (a* ≤ 0.998, α = 0) with a fit where a* and α are free. They find that Ton S180 and 1H0419-577 remain consistent with Kerr, while Ark 120 and Swift J0501.9-3239 show chi-square improvements of Δχ2 = 20.40 and 6.86, respectively. The abstract states that for these two sources "the Kerr solution is not recovered at 3-sigma". The paper also presents MCMC results for Ark 120 and Swift, and discusses systematic uncertainties, particularly the choice of the disk emissivity profile.

Significance. This work extends an existing public X-ray reflection model to a spacetime family that admits super-spinning black holes, and applies it to real data. The step is valuable in itself: it makes a falsifiable prediction within a parametric extension of Kerr and demonstrates how apparent near-extremal spins can be re-interpreted in a deformed metric. The paper is transparent about the limitations of the model, including the emissivity profile and the modest quality of Suzaku data. However, the significance of the claimed detection is not uniform across the two sources, and at least one of the two headline detections (Swift J0501.9-3239) is not supported by the quoted statistics. The central claim as stated in the abstract therefore needs a statistical correction.

major comments (4)
  1. [Section V, Eq. (11), Table II] The claim that Kerr is excluded at 3-sigma for Swift J0501.9-3239 is not supported by the paper's own numbers. For one additional free parameter, the 3-sigma threshold is Δχ2 = 9; the reported Δχ2 = 6.86 corresponds to roughly 2.6-sigma. Moreover, the MCMC 90% interval reported in Eq. (11), α = 0.12+0.09−0.14, includes α = 0. To substantiate a 3-sigma exclusion the authors should report the 3-sigma credible interval from the MCMC chains and state the Δχ2 threshold used. Without this, the abstract's claim for Swift should be removed or weakened.
  2. [Table II (Swift row) and Eq. (11)] There is an inconsistency between the best-fit value and errors for α of Swift J0501.9-3239 in Table II (α = 0.137+0.003−0.003) and the MCMC result in Eq. (11) (α = 0.12+0.09−0.14). These are very different uncertainties. If the table errors are correct, the MCMC result would need to be explained; if the MCMC is correct, the table contains a typographical error. This needs to be corrected or reconciled.
  3. [Section V, first paragraph] The statement that "the best-fit values that were stuck at 0.998 in Ref. [50] moved to a* > 1 for all sources" is misleading in the context of the paper's own significance levels. For Ton S180 and 1H0419-577 the Δχ2 improvements are only 2.21 and 0.79, respectively, so the best-fit a* > 1 values are within the 90% confidence region and are consistent with Kerr. The movement of the best-fit value alone is not evidence for a non-Kerr spacetime.
  4. [Abstract and Section V] The headline claim that Kerr is not recovered at 3-sigma for Ark 120 is also presented without sufficient hedging, given the authors' own statement in Section V that "it is possible that a simple power-law or a broken power-law are not enough to fit the Suzaku data of Ark 120, and this may cause the apparent detection of a non-vanishing α". The abstract should reflect this acknowledged systematic dependence, or the paper should provide a quantitative estimate of this systematic error.
minor comments (4)
  1. [Section V, final paragraph] There is a typo: "we also not that" should read "we also note that".
  2. [Reference [65]] Reference [65] is cited as "in preparation"; if the work has now appeared, please replace it with the published version, otherwise the citation is not verifiable.
  3. [Figures 7 and 8 captions] The captions say "1-σ and 3-σ limits" but do not specify which vertical lines correspond to which confidence level; please clarify the plotting convention and state the parameter ranges shown.
  4. [Section V, confidence-level discussion] The text uses "3-σ" without defining whether this refers to one or two relevant parameters; since the Δχ2 between Kerr and non-Kerr models involves one additional free parameter, the threshold Δχ2=9 should be stated explicitly to avoid confusion with the two-parameter 99% contours in Fig. 5 (Δχ2=9.21).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the non-Kerr metric is an adopted parametric ansatz from prior literature, and the Kerr-exclusion claim is a data-fit result, not a construction-level tautology.

full rationale

The paper's derivation chain is: adopt the Lin et al. metric (Eqs. 1-4), tabulate Cunningham transfer functions, fit Suzaku data, and compare chi-squared. Nothing in this chain defines the deformation parameter alpha in terms of the measured reflection spectrum, nor fits alpha to a subset and then predicts the same subset. The claim that Ark 120 and Swift J0501.9-3239 prefer a non-Kerr spacetime is an empirical model-comparison result, and the paper explicitly discusses systematic uncertainties that could bias it. Self-citations to relxill_nk and the metric paper are present, but the model is public and the metric is an explicit parameterization, so these citations are supporting tools rather than an unverified uniqueness theorem that forces the conclusion. The abstract's 3-sigma statement for Swift appears hard to reconcile with Delta chi2 = 6.86 and the reported 90% MCMC interval alpha = 0.12(+0.09/-0.14), which includes zero; that is a statistical/correctness concern, not circularity. No equation in the paper reduces to its own input by construction.

Assumptions & free parameters 7 free parameters · 4 assumptions · 1 invented entities

The central claim depends on the fitted spin a* and deformation alpha, on the adopted parametric spacetime from Ref. [52], and on the disk emissivity model. The paper has no free parameters in the sense of a derivation from first principles, but the data analysis includes many fitted spectral parameters. The strongest load-bearing assumptions are the ad hoc metric and the emissivity profile, both acknowledged as potential sources of systematic bias.

free parameters (7)
  • a* (dimensionless spin parameter) = Ton S180: 1.0018; Ark 120: 1.242; 1H0419-577: 1.029; Swift J0501.9: 1.131
    Central parameter of the analysis; best-fit values exceed the Kerr limit for all four sources when alpha is free.
  • alpha (deformation parameter) = Ton S180: 0.004; Ark 120: 0.213; 1H0419-577: 0.02; Swift J0501.9: 0.137
    Central parameter that measures deviation from Kerr; nonzero values drive the claimed non-Kerr result.
  • Disk inclination i = Ton S180: 37.5 deg; Ark 120: 17 deg; 1H0419-577: 54 deg; Swift J0501.9: 13.3 deg
    Affects the relativistic line shape and is degenerate with spin and deformation.
  • Ionization parameter log xi = Ton S180: 3.305; Ark 120: 3.07; 1H0419-577: 1.55; Swift J0501.9: 2.87
    Determines the shape of the reflection spectrum and is fitted freely.
  • Iron abundance A_Fe = Ton S180: 4.2; Ark 120: 3.8; 1H0419-577: <0.75; Swift J0501.9: 3.35
    Fitted freely; affects the iron line strength and can trade against the reflection normalization.
  • Emissivity profile parameters q_in and R_br = q_in: 9.9, 8.0, 7.6, 9.64; R_br: 3.24 and 4.6 for Ton S180 and Ark 120
    The assumed emissivity profile is a major systematic; Section V states it may cause the apparent non-vanishing alpha.
  • Power-law photon index Gamma and component normalizations = Gamma: 2.45, 2.48, 2.38, 2.366
    Continuum nuisance parameters fitted freely in all models.
assumptions (4)
  • ad hoc to paper The Lin et al. spacetime in Eq. (1) with m1 = m2 = M(1 + alpha M^2 / r^2) is the appropriate parametric extension of Kerr and admits black holes with |a*| > 1 for alpha > 0.
    Adopted from Ref. [52] with no underlying gravity theory; the black-hole boundary in Eq. (5) and Figure 1 defines the allowed parameter region.
  • domain assumption The accretion disk is geometrically thin and optically thick, its inner edge is at the ISCO radius, and the reflection spectrum is computed with the relxill transfer-function approach.
    Stated in Sections III and V; deviations from this disk model can bias the measured spin and deformation parameters.
  • domain assumption The radial emissivity profile is a power-law or a broken power-law, with the choice made per source based on best fit.
    Section IV describes the choice; Section V explicitly says this choice may produce the apparent detection of non-vanishing alpha.
  • domain assumption XSPEC chi-squared statistics and the MCMC sampler reliably find the global minimum of the fit.
    Section IV notes the XSPEC minimizer has problems and produces islands in the confidence contours; the MCMC is used to mitigate this.
invented entities (1)
  • Super-spinning black hole solutions with |a*| > 1 in the Lin et al. metric
    purpose: Provide a non-Kerr spacetime that can fit apparent near-extremal spin measurements without saturating the Kerr bound.
    These are parametric solutions from Ref. [52]; the paper's fits provide no independent falsifiable handle outside the adopted metric and disk model.

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Cite this review

Pith. "Pith review of Relativistic reflection spectra of super-spinning black holes." pith.science (2026). https://pith.science/paper/KDXQQPXZ

@misc{pith2026190805177,
  author       = {Pith},
  title        = {Pith review of: Relativistic reflection spectra of super-spinning black holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KDXQQPXZ}},
  note         = {Machine review of arXiv:1908.05177}
}
abstract

We construct a relativistic reflection model in a non-Kerr spacetime in which, depending on the value of the deformation parameter of the metric, there are black hole solutions with spin parameter $|a_*| > 1$. We apply our model to fit Suzaku data of four Seyfert galaxies (Ton S180, Ark 120, 1H0419-577, and Swift J0501.9-3239). These galaxies host at the center supermassive black holes that were previously interpreted as near-extremal Kerr black holes. For Ton S180 and 1H0419-577, our measurements are still consistent with the Kerr hypothesis. For Ark 120 and Swift J0501.9-3239, the Kerr solution is not recovered at 3-$\sigma$. We discuss our results and possible systematic uncertainties in the model.

Figures

Figures reproduced from arXiv: 1908.05177 by the authors.

Figure 1
Figure 1. FIG. 1. Contour levels of the radial coordinates of the event horizon [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The left panel shows the grid points in the FITS file for the spin parameter [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Data-to-best-fit-model ratios for the four sources of our study when the spectra are described by a power-law component [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Spectra of the best fit models with the corresponding components (upper panels) and data to best-fit model ratios [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Constraints on the spin parameter [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Source spectra, background spectra, and folded models of the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Histograms of the spin parameter [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Histograms of the spin parameter [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

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