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Limits on the existence of totally reflective exotic compact objects with current and future gravitational-wave detectors

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

Pith's one-line read This paper argues that the spins of 104 gravitational-wave-detected compact objects cap the fraction of totally reflecting exotic compact objects in the merging population at 71 percent (90% credibility), because such horizonless objects…

desk verdict A clean, reproducible population-level ECO bound from resolved CBC spins, but the headline 71%/59% limit is a marginal bound over a log-uniform epsilon prior, not a pointwise statement over the stated range. read the letter →

arxiv 2502.07675 v1 pith:B7NZJYGL submitted 2025-02-11 gr-qc

classification gr-qc
keywords exoticcompactobjectsergoregioninstabilityblackholemimickersgravitationalwaveastronomyspindistributionpopulationinferenceGWTC-3EinsteinTelescope
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 tries to establish that the measured spin distribution of 104 compact objects in the LIGO–Virgo–KAGRA catalog GWTC-3 puts a firm ceiling on how many of the detected mergers could be exotic compact objects (ECOs) with perfectly reflecting surfaces that replace black-hole event horizons. The physical mechanism is the ergoregion instability: a spinning horizonless object loses energy exponentially if its spin exceeds a critical value set by its compactness, so any ECO must arrive at merger with spin below that threshold. Because two detected events, GW190517_055101 and GW191109_010717, are fast-spinning, they cannot be ECOs, which drives the limits: fewer than 71% (polar perturbations) or 59% (axial) of the population can be such ECOs at 90% credibility, tightening to 28% and 25% for ultracompact ECOs. The paper also shows that one day of Einstein Telescope data could push the ceiling below 20%.

What carries the argument

The load-bearing ingredient is the ergoregion-instability critical spin, $\chi_{\rm crit}(\epsilon) = \pi(1+q)/(m\,|\log_{10}\epsilon|)$ with $q=1$ (polar) or $q=2$ (axial) and $m=2$, which acts as a sharp upper cap on the spin of any totally reflecting ECO. Above this spin the object rapidly sheds angular momentum through gravitational radiation until it approaches $\chi_{\rm crit}$, so the population model redistributes any ECO formed above the cap into a Gaussian pile-up near $\chi_{\rm crit}$. This cap, inserted into a hierarchical Bayesian mixture of black holes and ECOs that share a common $\beta$ distribution of formation spins, is what turns the observed spin distribution into a bound on the ECO fraction.

What would settle it

Detecting a single horizonless compact object with a measured spin above the critical value $\chi_{\rm crit}(\epsilon)$ for its inferred compactness (for example, a totally reflecting surface with $\epsilon \approx 10^{-10}$ forbids spins above about 0.2) would falsify the premise that such objects cannot exist with high spins, which is the physical input behind the population limits. Conversely, with enough events, the predicted pile-up of ECO spins just below $\chi_{\rm crit}$ should appear if a substantial ECO fraction exists; its absence at the predicted location would contradict the model's spin distribution.

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Extended reading notes

Core claim

The central claim is that totally reflective ECOs, defined by a surface at $r = r_+(1+\epsilon)$ and reflectivity $|\mathcal{R}|^2 = 1$, are limited to a minority fraction of the observed compact-binary-coalescence population. The argument rests on the analytic critical spin $\chi_{\rm crit}(\epsilon) = \pi(1+q)/(m\,|\log_{10}\epsilon|)$ for the $l=m=2$ ergoregion instability: ECOs with spin above $\chi_{\rm crit}$ spin down to roughly $\chi_{\rm crit}$ on cosmologically short timescales, so a population containing such ECOs must have a dearth of fast-spinning members. Fitting a mixture model with a $\beta$-distributed formation spin common to ECOs and black holes to 104 objects from GWTC-3 yields 90% upper limits $f_{\rm ECO} < 0.71$ (polar) and $f_{\rm ECO} < 0.59$ (axial) for $\epsilon \in [10^{-42}, 10^{-3}]$, and $f_{\rm ECO} < 0.28/0.25$ for $\epsilon < 10^{-30}$. The limits are driven by GW190517_055101 and GW191109_010717, whose primary spins exceed the maximum critical spin the model allows, and they are roughly twice as strong as those obtained from the non-detection of a stochastic gravitational-wave background from ECO spin loss. For the future, the paper predicts that with about 200 binary detections from the Einstein Telescope—roughly a day of observing—the ECO fraction can be constrained below 20%.

Load-bearing premise

The constraints assume that ECOs and black holes are formed with spins drawn from a single common beta distribution; if ECOs form with systematically different spins (for example, lower ones), the upper limits on the ECO fraction would be weakened or invalidated.

Editorial extensions

If this is right

  • The limits imply that, at 90% credibility, any theory in which more than about 70% of detected binary black hole mergers are totally reflective ECOs with $\epsilon$ down to $10^{-42}$ is disfavored by the GWTC-3 spin data.
  • GW190517_055101 and GW191109_010717 are effectively identified as black holes, since their spins exceed the maximum allowed for ECOs; subsequent fast-spinning detections will sharpen the constraint.
  • Spin-population limits on ECOs are about twice as tight as those from the non-detection of the stochastic gravitational-wave background, establishing the spin distribution as the more sensitive current probe of horizonless objects.
  • With next-generation detectors, roughly one day of Einstein Telescope observations (about 200 detections) should reduce the 90% upper limit on the ECO fraction to below 20%, and to a few percent if the underlying binary black hole population is high-spin.
  • The method is not limited to the specific reflectivity model: any model that imposes an upper spin cap on compact objects can be tested with the same mixture-population analysis.

Reading between the lines

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

  • If ECOs form through channels that systematically damp their spins (for example, accretion or tidal locking), the shared-beta-distribution assumption would be violated and the quoted limits could substantially weaken; the paper's own caveat makes this the main open point.
  • The same spin-cap logic transfers directly to superradiance-induced spin-down from ultralight bosons, suggesting a unified population-level probe of both horizon-scale and beyond-Standard-Model physics.
  • A testable extension would be to search for the predicted pile-up of ECO spins near $\chi_{\rm crit}$ with the higher-SNR, higher-statistics O4/O5 event sets, turning the current upper limit into a targeted detection test.
  • The forecast that one day of Einstein Telescope data beats years of current observations indicates that the spin-distribution approach could become the strongest robust test of horizonless compact objects before the end of the decade.
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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

3 major / 6 minor

Summary. The paper proposes a hierarchical Bayesian population model in which a fraction fECO of compact binaries are totally reflective exotic compact objects. Using the ergoregion-instability critical spin chi_crit(epsilon), ECOs with formation spin above chi_crit are assumed to spin down to a Gaussian distribution centered on chi_crit, while BH formation spins and ECO formation spins are drawn from a common beta distribution. Applying this model to 52 CBCs from GWTC-3 (104 compact objects), the authors report 90% credible upper limits fECO < 71% (polar) and < 59% (axial) after marginalizing over a log-uniform prior on epsilon in [10^-42, 10^-3], tighter limits of 28% and 25% for epsilon < 10^-30, and projections for the Einstein Telescope using simulated low-spin and high-spin BBH populations. The constraints are driven primarily by the high measured spins of GW190517_055101 and GW191109_010717.

Significance. If the result holds, this is one of the first resolved-CBC population limits on the abundance of totally reflective ECOs using the ergoregion instability, and it is complementary to stochastic-background, ringdown, and echo searches. The hierarchical Bayesian framework is standard, the use of public GWTC-3 posterior samples and injection-based selection effects is appropriate, and the ET forecast provides a useful quantitative projection. The main limitation is that the headline constraints are conditional on the assumed common formation-spin distribution for BHs and ECOs and on the log-uniform prior for epsilon, so the advertised numbers are model- and prior-dependent rather than pointwise statements in epsilon.

major comments (3)
  1. [Sec. 2, Eq. (1)] Equation (1) writes chi_crit = pi(1+q)/(m |log10 epsilon|), but the numerical values quoted in Table 2 (chi_crit in [0.03, 0.45] for polar and [0.05, 0.68] for axial perturbations over epsilon in [10^-42, 10^-3]) and shown in Fig. 1 correspond to the natural logarithm, |ln epsilon|, not |log10 epsilon|. As written, Eq. (1) overestimates chi_crit by a factor of ln(10) ~ 2.303 and prevents a reader from reproducing the subsequent analysis. Please correct the base of the logarithm, or if the original reference uses natural log, define it explicitly in the text.
  2. [Abstract; Sec. 4.2, Eq. (25) and Fig. 6] The headline limits fECO < 71% (polar) and < 59% (axial) are 90% credible bounds on fECO after marginalizing over the log-uniform prior on epsilon given in Table 2, and the ultracompact limits are similarly obtained under the prior restricted to epsilon < 10^-30. These are not pointwise statements that hold for every epsilon in [10^-42, 10^-3]; the joint posterior in the left panel of Fig. 6 shows that larger fECO becomes allowed as epsilon approaches 10^-3. The abstract and conclusions should state explicitly that the limits are marginalized over a log-uniform prior on epsilon, or alternatively report conditional upper limits at fixed epsilon values so that the prior-averaged nature of the constraint is transparent. As written, the phrase 'if ECOs have epsilon in [10^-42, 10^-3]' overstates the uniformity of the bound.
  3. [Sec. 3.1, Eq. (7); Sec. 6] The constraints rely on the assumption that ECOs and BHs are formed with spins drawn from the same beta distribution (Eq. 7). The paper acknowledges in Sec. 3 that this is a simplistic assumption, but the conclusion section does not restate it. If ECO formation produces systematically lower spins than BH formation, the reported fECO upper limits could be substantially weakened. Please add an explicit caveat in the conclusions that the constraints are conditional on this common formation-spin assumption.
minor comments (6)
  1. [Sec. 4.1, Eq. (24)] The denominator in Eq. (24) should be fECO p(chi_M | ECO, Lambda) + (1 - fECO) p(chi_M | BH, Lambda), not the unweighted sum p(chi_M | ECO, Lambda) + p(chi_M | BH, Lambda). As written, the per-event ECO probabilities reported in Table 1 are not correctly normalized; this does not affect the main fECO upper limits but should be corrected.
  2. [Sec. 3.1] The word 'marginilize' should be 'marginalize'.
  3. [Abstract] The notation 'epsilon in [10^-42 - 10^-3]' is ambiguous; please use '10^-42 to 10^-3' or an en dash.
  4. [Fig. 6] In the right panel, the axis label 'f UL ECO' should be typeset as fECO^UL, and the caption should state explicitly that the curve is computed with a truncated log-uniform prior on epsilon below the indicated threshold.
  5. [Table 3] The header 'BBH vs log10B' is confusing; clarify that the entries are log10 Bayes factors in favor of the BBH model relative to the listed model.
  6. [Sec. 4.2] The phrase 'fastly spinning' should be 'rapidly spinning'.

Circularity Check

0 steps flagged · score 0.0 of 10

The inference is self-contained: fECO limits are derived from a hierarchical fit of independent LVK spin measurements to a model whose ECO spin cap chi_crit is an external analytic result; no central prediction reduces to an input by construction.

full rationale

The central derivation chain is not circular. The ECO critical spin chi_crit(eps) is taken from Eq. (1), attributed to the prior analytic calculation of Ref. [38]; it is a parameter-free theoretical input with stated assumptions and does not encode the observed spin data or fECO, so the self-citation (Maggio is a co-author) is not load-bearing in a way that forces the result. The observed spin magnitudes are independent LVK posterior samples from GWTC-2.1 and GWTC-3, and the fECO upper limits follow from a genuine hierarchical Bayesian likelihood with selection effects (Eqs. (20)-(21), (25)), not from reinserting the fitted quantity. The paper explicitly flags its two main modeling assumptions: the common beta formation-spin distribution for BHs and ECOs (Eq. (7), 'could be similar') and the independence of mass/spin/redshift distributions ('we make this simplistic assumption'); these are limitations and prior assumptions, not circular reductions. The only in-sample element is the per-event ECO probability in Eq. (24), which uses the hierarchical posterior computed from the same events; the paper itself states that formally the event should be excluded and argues the effect is negligible. This caveat affects a secondary classification table, not the headline fECO limits, which are driven by the high-spin measurements of GW190517_055101 and GW191109_010717. The forecast section is a standard self-consistent injection study with simulated BBH populations and does not present a physical prediction that reduces to its inputs. The skeptical concern about the log-uniform prior on epsilon is a Bayesian prior-marginalization interpretation issue, not a circularity. Overall, no step in the derivation is equivalent to its own inputs by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities: ECOs, the ergoregion instability, and the critical-spin formula all come from prior literature. The free parameters are the population-hyperparameters of the spin model (alpha, beta, fECO, epsilon, sigma), with sigma being the most ad hoc. The main axiomatic burden is the shared formation-spin distribution for BHs and ECOs, plus the mapping from epsilon to a sharp critical spin via the cited formula. The forecast section additionally assumes specific injected beta distributions for the simulated BBH populations.

free parameters (4)
  • sigma = prior U[0.005, 0.5]
    Width of the Gaussian used to model the ECO spin after spin-down around the critical spin (Eq. 15). There is no first-principles derivation for this width; it is an ad hoc agnostic choice.
  • fECO = inferred, 90% upper limit 0.71 (polar) / 0.59 (axial)
    Fraction of the population that is ECOs. This is the target of the inference, not a nuisance parameter, but it is still fitted to data.
  • alpha, beta (formation spin beta distribution) = inferred with priors U[1.1, 10]
    Shape parameters of the beta distribution describing the formation spins of both BHs and ECOs. They are fitted to the observed spin distribution.
  • epsilon (through chi_crit) = prior LU[10^-42, 10^-3]
    Compactness parameter setting the critical spin via Eq. (1). It is a model parameter inferred from the data, and its prior range maps to chi_crit in [0.03, 0.45] (polar) or [0.05, 0.68] (axial).
assumptions (5)
  • domain assumption ECOs and BHs are formed with the same spin distribution, a beta distribution with shared alpha and beta (Eq. 7).
    Stated in Sec. 3.1: 'We assume that both ECOs and classical BHs are formed with spins drawn from a common distribution... the astrophysical formation mechanisms... could be similar.' This is load-bearing because the inferred fECO limits compare the observed spins against this shared formation distribution.
  • domain assumption The ergoregion critical spin formula chi_crit(eps) = pi(1+q)/(m |log10 eps|) from Ref. [38] is valid for perfectly reflecting ECOs with l=m=2.
    Invoked as Eq. (1) with a citation to Ref. [38]. The entire analysis maps the model parameter epsilon to a sharp spin cutoff through this formula.
  • domain assumption The ergoregion instability triggers and spins the ECO down to chi approximately chi_crit on timescales that are not cosmologically relevant, for all formation spins above chi_crit.
    Stated in Sec. 2: 'regardless of epsilon, initial mass and spin of the ECO, the ergoregion instability will be triggered if chi > chi_crit on a time that is not cosmologically relevant.' This justifies replacing the spin of every ECO above the threshold with a value near chi_crit.
  • domain assumption The mass and redshift distributions are independent of the spin distribution and of the nature of the objects; mass and redshift parameters are fixed to canonical values from Ref. [17].
    In Sec. 3.2 the rate model factorizes masses, spins and redshift, and the paper fixes the Power Law + Peak and redshift parameters. The paper acknowledges that possible mass-spin correlations exist in the literature and discusses their effect qualitatively.
  • ad hoc to paper A Gaussian distribution N(chi_crit, sigma) adequately describes the final ECO spin after the spin-down, with the same sigma for all ECOs.
    Introduced in Eq. (15) as an 'agnostic gaussian distribution' for the final ECO spin. There is no physical derivation of this distribution or of the universal sigma.

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Pith. "Pith review of Limits on the existence of totally reflective exotic compact objects with current and future gravitational-wave detectors." pith.science (2026). https://pith.science/paper/B7NZJYGL

@misc{pith2026250207675,
  author       = {Pith},
  title        = {Pith review of: Limits on the existence of totally reflective exotic compact objects with current and future gravitational-wave detectors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B7NZJYGL}},
  note         = {Machine review of arXiv:2502.07675}
}
abstract

Exotic compact objects (ECOs) are a theorized class of compact objects that solve the paradoxes of black holes by replacing the event horizon with a physical surface located at $r=r_+(1+\epsilon)$ from the would-be horizon at $r_+$. Spinning horizonless objects are prone to the ergoregion instability, which would prevent their existence if their spin is higher than a critical threshold. In this paper, we set upper limits on the existence of a population of merging ECOs from the spin distribution of the population of compact binary coalescences (CBCs) detected by the LIGO, Virgo and KAGRA collaboration. Using spin measurements from 104 compact objects, we find that if ECOs have $\epsilon \in [10^{-42}-10^{-3}]$ and their surface is totally reflective, the population of CBCs cannot be composed (at 90% credible level) by more than 71% (59%) of ECOs for polar (axial) perturbations. If we restrict the ECOs to be ultracompact ($\epsilon<10^{-30}$), at 90% credible level, ECOs cannot compose more than 28% and 25% of the CBC population for polar and axial perturbations. The constraints from current data are a factor of two more precise than the ones obtained from a non-detection of a stochastic GW background due to spin loss. We also study how next generation gravitational-wave detectors, such as the Einstein Telescope, can constrain the ECO population. We find that 1 day of data taking would be enough to constrain the fraction of ECOs to be lower than 20% for $\epsilon \in [10^{-42}-10^{-3}]$.

Figures

Figures reproduced from arXiv: 2502.07675 by the authors.

Figure 1
Figure 1. Critical spin for the ergoregion instability as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Conceptual model to construct the spin distribution at merger of CBCs composed [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Spin magnitude distribution for one of the two compact objects in the binary with [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Marginal posterior on log10(ϵ) for the case in which the population of compact objects observed during O3 is composed by ECOs with totally reflective surfaces. The dashed vertical line indicates the 90% credible level lower limit. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 crit 0 5 1…
Figure 5
Figure 5. Figure 5: Implied posteriors from the events detected during O3 on the critical spin magnitude [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Left: Joint posterior distribution on log10(ϵ) and fECO from the CBCs detected during O3 with a FAR< 0.25 yr−1 . The coloured area indicates the 90% C.I. The figure also reports the marginal posteriors for the two population parameters. Right: 90% credible upper limits…
Figure 7
Figure 7. Figure 7: Left panel: Spin magnitude distribution reconstructed for the overall population from the GW events detected during O3 for the ECOs-only, BBHs-only and mixture cases. Middle panel: Spin magnitude distribution reconstructed for the BBH population from the GW events dete…
Figure 8
Figure 8. Figure 8: 68.3% credible interval fractional error on the spin magnitude (vertical axis) versus [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Marginal posteriors on ϵ and fECO for the simulated low spin (top row) and high spin (bottom-row) BBH populations. The contours indicate the 90% credible interval of the posteriors and the colors mark posteriors obtained with a different number of GW events. able to co…
Figure 10
Figure 10. Figure 10: Left panels: Spin magnitude distribution reconstructed for the overall population from the GW events detected during O3 for the BBHs-only and mixture cases. Middle panels: Spin magnitude distribution reconstructed for the BBH population from the GW events detected dur…

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