{"id":"444ee68e-df9c-43c5-8087-0e10b1945ea6","arxiv_id":"2508.19874","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Hot-spot images and polarization around extreme parametrized black hole models are nearly identical to Schwarzschild, so tighter observations are needed to constrain these models.","lead":"The paper simulates glowing hot-spots orbiting four modified black hole spacetimes and finds their images and polarization signals look nearly the same as for an ordinary Schwarzschild black hole. The takeaway is that current telescopes are unlikely to tell these modified models apart from standard black holes without more precise observations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The conclusion that hot-spot observables cannot constrain JP/KZ models rests on non-rotating metrics; spin can alter exactly the higher-order image sector that drives all reported differences, so the near-degeneracy may not survive for Sgr A*.","rationale":"The reader identified the non-rotating simplification as the weakest assumption, and I agree that this is the most load-bearing gap. The central claim is plausible for the specific spherical models simulated, but the paper states the conclusion in a way that invites extrapolation to Sgr A*, a rotating source. Since all reported parameter sensitivity flows through the secondary-image sector, and spin is known to affect exactly that sector through frame dragging and asymmetric critical curves, the lack of a rotating test is a real soft spot. I do not think this invalidates the paper's modest and carefully hedged conclusion for the models analyzed; it does mean the broader inference about observability with current instruments is not yet established. The reader's verdict of CONDITIONAL already captures this, so my read does not change the verdict. A concrete rotating-metric rerun would settle whether the concern is fatal or simply a scope limitation.","tokens_in":15541,"tokens_out":7421,"duration_ms":87702,"concrete_test":"Rerun the Sec. III.D numerical setup with a rotating counterpart of the JP metric (e.g., a/M=0.9, with the same leading deformation scale ε3) and a rotating Kerr baseline, at i=80°, and compute the maximum separation in the temporal centroid, QU-loop, and EVPA curves between the deformed and Kerr models. If the separation remains below current GRAVITY/EHT polarimetric and astrometric accuracy, the near-degeneracy extends to the rotating case; if it exceeds it, the paper's conclusion is limited to a=0 and would need to be revised. For a full check, the deformation parameters should be re-calibrated to the EHT 2σ shadow-size constraint at the chosen spin before comparing observables.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that the selected JP/KZ spacetimes are nearly indistinguishable from Schwarzschild in hot-spot astrometry and polarimetry, so current EHT/GRAVITY observations cannot meaningfully constrain these parametrized models. The most load-bearing assumption in this argument is that the spherically symmetric, non-rotating metrics of Eqs. (2.1) and (2.5) capture the observable differences of the actual target, Sgr A*. The EHT 2σ shadow-size constraints used to set the parameter ranges, ε∈[-5,11.4] and η∈(-32/27,2], are applied to static metrics, whereas Sgr A* is believed to be rotating. Spin introduces frame dragging, an asymmetric photon ring, and spin-dependent critical-curve geometry, so the same deformation parameters can produce larger or differently located changes in the secondary-image position and polarization than in the spherical case. The paper itself finds in Sec. IV.B that all model differences are mediated by the size and position of the secondary and higher-order images. Spin modifies precisely that sector. Therefore, the extrapolation from 'these spherical models deviate little from Schwarzschild' to 'parametrized models cannot be constrained by hot-spot observations' is insecure. The conclusion may still be correct, but the paper does not test it, and the central claim is stated more broadly than the simulations support.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses the GYOTO ray-tracing code to simulate synchrotron-emitting spherical hot-spots on circular equatorial Keplerian orbits at r=8M around four static, spherically symmetric parametrized black hole metrics: two extreme Johanssen-Psaltis models (epsilon=-5 and epsilon=11.4) and two extreme Konoplya-Zhidenko models (eta=-32/27 and eta=2), whose shadow sizes lie within the EHT 2-sigma constraints. It computes time-integrated Stokes I,Q,U maps, temporal fluxes and magnitudes, centroid tracks, QU-loops and EVPA for inclinations of 20 degrees and 80 degrees, comparing each observable with the Schwarzschild case. The paper finds that the astrometric observables are qualitatively similar to Schwarzschild with small quantitative differences, that JP models deviate more than KZ models, and that some polarimetric differences at high inclination are noticeable but short-lived. The authors conclude that current observations cannot meaningfully constrain these parametrized models and that more precise observations, such as GRAVITY+ and ngEHT, would be needed.","tokens_in":15923,"tokens_out":7472,"duration_ms":83318,"significance":"If the result holds, the paper provides a useful caution for attempts to use hot-spot astrometry and polarimetry to constrain deviations from the Kerr/Schwarzschild geometry: within the static, spherically symmetric JP and KZ families compatible with the EHT shadow-size bound, the observable imprints are strongly degenerate with Schwarzschild. The paper makes productive use of a public ray-tracing code, compares multiple Stokes observables, and isolates the secondary/higher-order image channel as the source of model differences. These are concrete strengths. However, the absence of quantitative deviation metrics, resolution/convergence checks, and rotating spacetimes means the significance is currently more limited than the abstract and conclusion suggest; it is a proof-of-principle for the specific static metrics tested rather than a general statement about constraining parametrized black holes from hot-spot observations.","major_comments":[{"comment":"The central claim that the parametrized models 'deviate only slightly' from Schwarzschild is supported only by visual inspection of Figs. 4 and 5. No quantitative deviation metric (e.g., mean or peak difference in centroid position, QU-loop displacement, or EVPA curve), no comparison with GRAVITY/EHT astrometric or polarimetric uncertainties, and no statistical significance is reported. For example, the statement that 'the deviations in the EVPA are barely noticeable' (Sec. IV.D) is not backed by a number. Because the conclusion that 'more precise observations are needed' is the main message, this omission is load-bearing.","section":"Secs. IV.C and V"},{"comment":"All spacetimes used are static and spherically symmetric (Eqs. (2.1) and (2.5)), yet the analysis is framed as an alternative model for Sgr A* and the conclusion is stated broadly for 'parametrized BH models'. The authors themselves trace every deviation to differences in the size and position of secondary and higher-order images (Sec. IV.B). Spin changes precisely this sector through frame dragging, an asymmetric photon ring, and a spin-dependent critical curve. Therefore the extrapolation from these spherical metrics to rotating Sgr A* is not justified. The conclusions should either be restricted to the static JP/KZ models tested, or the analysis should be extended to at least one rotating parametrized metric.","section":"Secs. II, III.D, and V"},{"comment":"The simulations use a single resolution of 1000x1000 pixels, and the light-ring contribution is described as 'barely visible in the images due to pixelation' (Sec. IV.B). Since the quantitative model differences are attributed to the size and position of secondary and higher-order images, a convergence check (e.g., with 2000x2000 or higher resolution) or subpixel centroiding is needed to establish that the small differences in Fig. 4 are physical rather than numerical artifacts. No error bars or resolution study is provided.","section":"Secs. III.D and IV.B"},{"comment":"Only a single orbital radius, r_o = 8M, is simulated. The flux, size, and position of secondary images depend on the emission radius, so the near-degeneracy with Schwarzschild may be specific to this radius. Testing at least one additional radius (e.g., r_o = 6M or 10M), or providing an argument for why the conclusions are radius-independent, would materially strengthen the generality of the central claim.","section":"Sec. III.D"}],"minor_comments":[{"comment":"The two-argument inverse tangent is written as 'atan' but should be 'atan2' to match Eq. (3.3).","section":"Eq. (3.10)"},{"comment":"The acronym EVPA is defined inconsistently as 'Electric Field Position Angle' in the abstract and as 'Electric Vector Position Angle' in Sec. III.B; please use one definition throughout.","section":"Abstract and Sec. III.B"},{"comment":"The normalization scale F_min is not precisely defined. State explicitly whether it is the global minimum of the flux over all models, all times, and all pixels; otherwise the magnitude normalization is ambiguous.","section":"Eq. (3.7)"},{"comment":"The statement that the coefficient epsilon_2 is 'experimentally strongly constrained' is not quantified. Either give the relevant bound or cite the specific constraint used.","section":"Sec. II.A"},{"comment":"Typos: 'Rezzola-Zidenko' should be 'Rezzolla-Zhidenko', and 'fidutial' in Sec. III.D should be 'fiducial'.","section":"Introduction"},{"comment":"Please specify the orbital period T used to normalize the time axis, and state whether the Keplerian angular velocity is obtained from the g_tt component of each metric.","section":"Sec. III.D"},{"comment":"The text quotes time intervals such as 't/T in [0.05, 0.40]' for the deviations; marking these intervals directly in the relevant panels of Figs. 4 and 5 would make the claims easier to verify.","section":"Sec. IV.C"},{"comment":"The color/point coding of the time parameter t/T is not explained in the caption; please clarify how the shading maps to time.","section":"Fig. 6"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First application of hot-spot astrometric/polarimetric observables to the JP and KZ parametrized metrics, using GYOTO with synchrotron emission. The central result — that within the EHT 2σ shadow bounds the static JP/KZ models tested look nearly Schwarzschild in these observables — is believable from the figures. Deviations are traced cleanly to the size/position of the secondary image, which is a nice physical explanation. The paper is honest about EVPA being hard to use at high inclination, and the conclusion is modest in its own words.\n\nThe soft spots are real, though none of them sink the paper on its own terms. The biggest is the absence of any quantification: 'minor quantitative deviations' is never translated into, say, a centroid shift in microarcseconds or a percentage change in QU-loop area. For a paper whose stated motivation is to inform future ngEHT/GRAVITY+ observations, that's a missing number. There are also no convergence checks or error bars, and no released code or data, so reproducibility relies on GYOTO itself.\n\nThe spin issue is the one that makes me hesitate about the broader conclusion. All model differences are mediated by higher-order images, and spin is known to change that sector substantially. The paper only considers spherical static metrics, so the step from 'these static models are degenerate' to 'parametrized models cannot be constrained by hot-spot observations' is an extrapolation. The authors do say 'the models analyzed,' but the framing in the abstract and final paragraph points at Sgr A* and future observing campaigns, where rotation is expected. That gap should be acknowledged and ideally closed with at least one rotating example or a quantitative argument about why spin won't resurrect the differences.\n\nThe parameter ranges come from their own earlier photon-ring/shadow paper [60]. That is a self-citation, but the hot-spot observables here are forward-modeled rather than fitted, so there's no circularity in the comparison. The range choice is also reasonable as a 'most extreme allowed' test.\n\nOverall: a legitimate first application, useful for the hot-spot community. It deserves a serious referee, but the revision should add quantitative measures of the deviations and an explicit discussion of the rotating case before the near-degeneracy is treated as a robust result.","headline":"A careful but limited hot-spot study: the near-degeneracy with Schwarzschild is real for the static JP/KZ spacetimes tested, but the paper doesn't quantify it and quietly drops spin, so the broad conclusion about constraining parametrized models overreaches.","tokens_in":16358,"tokens_out":2886,"would_cite":true,"duration_ms":34675,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83C10","83B05"],"pacs":["04.70.-s"],"model":"deepseek-v4-flash","headline":"Hot-spot astrometry and polarimetry around the most extreme allowed JP and KZ parametrized black holes deviate only slightly from Schwarzschild, so these observables cannot yet constrain the models.","keywords":["hot-spots","parametrized black holes","Johanssen-Psaltis metric","Konoplya-Zhidenko metric","ray tracing","polarimetry","Stokes parameters","Sgr A* flares"],"falsifier":"A high-cadence, polarimetrically resolved observation of a bright Sgr A* flare that resolves the secondary image and tracks the QU-plane: if the centroid track width and the high-inclination QU-loop show the left-side crossing predicted for the positive-JP model rather than Schwarzschild, the near-degeneracy claim would be refuted.","tokens_in":1922,"feed_emoji":"🕳️","tokens_out":1873,"duration_ms":103040,"temperature":0.7,"pith_summary":"This paper asks whether orbiting hot-spot flares, the bright blobs observed near Sgr A*, can tell parametrized black hole spacetimes apart from the standard Schwarzschild solution. Using ray tracing with polarized synchrotron emission for the two most extreme Johanssen-Psaltis and Konoplya-Zhidenko metrics allowed by current shadow-size bounds, it finds that all astrometric and polarimetric observables are nearly identical to Schwarzschild. The small differences trace to the size and position of higher-order lensed images, not the primary image. Some qualitative polarization differences appear at high inclination, but only during a short fraction of the orbit. The conclusion is that hot-spot observations as currently achievable cannot meaningfully constrain these parametrized models; more precise instruments are needed.","feed_headline":"Flare images of altered black holes look nearly Schwarzschild","feed_subtitle":"Simulated hot-spot observables stay close to Schwarzschild, so current data cannot constrain these models.","key_machinery":"The load-bearing objects are two spherically symmetric parametrized metric families. The Johanssen-Psaltis metric is ds2 = f_S(1+h_JP)dt2 + (1+h_JP)/f_S dr2 + r2 dΩ2 with h_JP = sum_k epsilon_k (M/r)^k, whose first non-trivial coefficient is epsilon_3 = epsilon. The Konoplya-Zhidenko metric is ds2 = -f_KZ dt2 + f_KZ^{-1} dr2 + r2 dΩ2 with f_KZ = 1 - [1+h_KZ] 2M/r and h_KZ = (1/2) sum_k eta_k (M/r)^k, whose first non-trivial coefficient is eta_2 = eta. These families carry the free parameters fixed by shadow-size bounds. The analysis mechanism is polarized ray tracing with GYOTO, which parallel-transports the synchrotron polarization vector along null geodesics and produces Stokes I, Q, U ima","core_discovery":"The authors select four spherically symmetric parametrized black hole metrics, two from the Johanssen-Psaltis family with epsilon = -5 and 11.4, and two from the Konoplya-Zhidenko family with eta = -32/27 and 2, the extremes allowed by Event Horizon Telescope 2-sigma shadow-size constraints. They simulate a synchrotron-emitting hot-spot on a circular Keplerian orbit at radius 8M with a vertical magnetic field, using the ray-tracing code GYOTO, and compute time-integrated Stokes I, Q, U images, temporal centroid and magnitude, QU-loops, and EVPA at 20 and 80 degree inclinations. The observational properties deviate only slightly from Schwarzschild: primary-image intensity and polarization are","pith_inferences":["An implicit consequence is that hot-spot observables are sensitive mainly to the photon-sphere critical-curve radius, not to the full metric; metrics sharing the same critical curve would be nearly indistinguishable in these observables regardless of other differences.","The spherically symmetric, non-rotating assumption likely understates the separability of rotating configurations; including spin could shift the secondary image and break the degeneracy in ways this setup does not capture.","A natural extension is to scan orbital radius and magnetic-field geometry: closer orbits, such as 6M, would amplify higher-order image contributions and may make the JP and KZ deviations detectable, while toroidal fields would change the two-loop structure of the QU-track.","The finding that EVPA is practically unusable at high inclination is a practical warning for flare-monitoring campaigns: QU-loop morphology, not EVPA, is the more promising target observable for metric discrimination."],"forward_implications":["Even the most extreme JP and KZ metrics allowed by current 2-sigma shadow bounds produce hot-spot images whose primary component is indistinguishable from Schwarzschild; all departures come from higher-order lensed images.","Astrometric observables scale with the radial size of the secondary-image track: models with smaller secondary tracks show narrower centroid loops and dimmer temporal fluxes, models with larger tracks show the opposite.","At high inclination the QU-loop of the positive-JP model shows a left-side crossing absent in the negative-JP and Schwarzschild models, but this distinction occupies only a short portion of the orbit.","The JP parametrization produces larger deviations than KZ, the positive-JP model deviating the most; the KZ models remain very close to Schwarzschild in both astrometry and polarimetry.","Because the deviations are tiny or fleeting, constraining parametrized metrics with hot-spot flares requires next-generation sensitivity or a combination of time-averaged shadow and hot-spot measurements."],"supporting_citations":[{"why":"Defines the Johanssen-Psaltis parametrized metric family used for two of the four spacetime models.","marker":"[46]"},{"why":"Defines the Konoplya-Zhidenko parametrized metric family used for the other two spacetime models.","marker":"[47]"},{"why":"Earlier analysis constraining the JP parameter epsilon from shadow-size bounds; this paper extends that analysis to hot-spot observables.","marker":"[60]"},{"why":"Gives the GYOTO ray-tracing software that performs null-geodesic integration and polarimetric transport for the simulations.","marker":"[63, 64]"},{"why":"GRAVITY observations of the Sgr A* polarized flare that set the vertical magnetic-field configuration and provide the observational baseline.","marker":"[71]"},{"why":"ALMA observations of Sgr A* polarization used to anchor the magnetic-field geometry and the QU-loop comparison.","marker":"[84]"},{"why":"Event Horizon Telescope measurement of the shadow size that supplies the 2-sigma bounds fixing the parameter ranges of the models.","marker":"[78]"},{"why":"Establishes the framework connecting general relativistic effects to observed polarization, the basis for extracting polarimetric observables.","marker":"[73]"},{"why":"Provides the definitions and usage of temporal QU-loops and related polarimetric observables adopted in the analysis.","marker":"[87]"}],"fun_headline_variants":["Hot-spot flares can't distinguish exotic black holes from Schwarzschild","Black hole hot-spot observables show only slight Schwarzschild deviation","Simulated black hole flares mimic Schwarzschild too closely for constraints","Altered black hole hot-spots leave nearly identical polarimetric signatures"],"cache_read_input_tokens":18048,"weakest_assumption_plain":"The simulations take the central object to be a spherically symmetric, non-rotating parametrized metric and place the hot-spot on a single fixed circular equatorial orbit at 8M with a vertical magnetic field; if Sgr A*'s actual spin or the flare's orbital and magnetic geometry shifts the higher-order images, the near-Schwarzschild degeneracy derived here may not hold.","fun_headline_variants_meta":{"raw":{"variants":["Hot-spot flares can't distinguish exotic black holes from Schwarzschild","Black hole hot-spot observables show only slight Schwarzschild deviation","Simulated black hole flares mimic Schwarzschild too closely for constraints","Altered black hole hot-spots leave nearly identical polarimetric signatures"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000326,"raw_usage":{"total_tokens":1739,"prompt_tokens":897,"completion_tokens":842,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":641,"completion_tokens_details":{"reasoning_tokens":768}},"tokens_in":641,"tokens_out":842,"duration_ms":7357,"temperature":1.0,"reasoning_tokens":768,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T15:22:04.842659+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A high-cadence, polarimetrically resolved observation of a bright Sgr A* flare that resolves the secondary image and tracks the QU-plane: if the centroid track width and the high-inclination QU-loop show the left-side crossing predicted for the positive-JP model rather than Schwarzschild, the near-degeneracy claim would be refuted.","supporting_citations":[{"cited_title":"Johannsen and D","cited_arxiv_id":null,"evidence_quote":"Defines the Johanssen-Psaltis parametrized metric family used for two of the four spacetime models."},{"cited_title":"Konoplya and A","cited_arxiv_id":null,"evidence_quote":"Defines the Konoplya-Zhidenko parametrized metric family used for the other two spacetime models."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"ALMA observations of Sgr A* polarization used to anchor the magnetic-field geometry and the QU-loop comparison."},{"cited_title":"Bertotti, L","cited_arxiv_id":null,"evidence_quote":"Event Horizon Telescope measurement of the shadow size that supplies the 2-sigma bounds fixing the parameter ranges of the models."},{"cited_title":"Wielgus, et.al., Astron","cited_arxiv_id":null,"evidence_quote":"Establishes the framework connecting general relativistic effects to observed polarization, the basis for extracting polarimetric observables."},{"cited_title":"Radiative processes in astrophysics","cited_arxiv_id":null,"evidence_quote":"Provides the definitions and usage of temporal QU-loops and related polarimetric observables adopted in the analysis."}],"review_version":1}