{"id":"fda7d677-c2f8-4625-b070-71d72214297c","arxiv_id":"2608.01413","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"For a rotating Lorentz-violating black hole, increasing the LV parameter shrinks and broadens Sgr A*'s image ring, and EHT data bound the parameter over a spin-dependent range.","lead":"The paper simulates 230 GHz images of Sgr A* assuming a spacetime that breaks Lorentz symmetry, and finds that the Lorentz-violating parameter shrinks the bright ring diameter while widening and brightening the ring. The authors use the EHT measured ring diameter to place a model-dependent range on the parameter.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (1) does not reduce to Kerr at l=0: printed g_tφ has an a^2 factor, so the LV baseline and the resulting EHT l-range rest on a mistranscribed metric.","rationale":"The paper's central claim is that the LV parameter l produces systematic, observable changes in the bright ring of Sgr A* and can be constrained from EHT diameter measurements. Every quantitative result flows from the spacetime metric in Eq. (1). The reader's weakest assumption was that this metric is a valid and correctly transcribed rotating Horava solution. My stress-test confirms this is the most load-bearing point, and it is even more concrete than the reader stated: the printed metric is internally inconsistent with the paper's own Kerr-limit claim. Setting l=0 should recover Kerr, but Eq. (1)'s g_tφ term still contains a^2 and does not match the Kerr form; the g_φφ term also differs. This is not an external or philosophical worry but a checkable algebraic inconsistency. If the manuscript were the only specification of the spacetime, the simulations could not be reproduced, and the derived l-range would be tied to an unspecified metric. I therefore agree with the reader's CONDITIONAL verdict: the concern is real, but it may be resolved by a typographical correction or by pointing to the exact form used in the code. Credit is due for the otherwise systematic REX-based analysis and the explicit EHT comparison, but the central numerical claim is only as secure as the metric transcription.","tokens_in":11295,"tokens_out":8554,"duration_ms":73641,"concrete_test":"Rerun one GRRT image with l=0 using (a) the printed Eq. (1) and (b) the Kerr metric; compare the extracted ring diameter d and width w. More directly, substitute Eq. (1) into the low-energy Horava field equations with a symbolic algebra system (e.g., xAct) and compare with Ref. [50]; if [50]'s g_{tφ} is -4(l+1) M a r sin^2θ/ρ^2 (not a^2), then Eq. (1) is mistyped. Recompute Fig. 4 with the corrected metric and check whether the l-range and its spin-dependence shift.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II presents Eq. (1) as the rotating LV black hole metric, with g_{tφ} = -4(l+1) M a^2 r sin^2θ/ρ^2 and Σ^2 = (r^2+a^2)ρ^2 + 2M a^2 r sin^2θ. The text then states 'This solution can be returned to the Kerr solution when l=0.' Setting l=0 gives g_{tφ} = -4 M a^2 r sin^2θ/ρ^2, whereas the Kerr metric in Boyer-Lindquist coordinates has g_{tφ} = -2 M a r sin^2θ/ρ^2 (and a different g_{φφ}). Thus the printed metric does not have the claimed Kerr limit; the discrepancy is not a small normalization but an extra power of a in the frame-dragging term, and it is dimensionally inconsistent if a has the standard length dimension. All subsequent ring quantities and the EHT-derived allowed range for l in Figs. 4–6 are computed in this spacetime. If the simulations used the printed metric, they are not comparing against a Kerr baseline; if they used a corrected metric, Eq. (1) is mistranscribed and the paper does not specify which was coded. Either way, the central claim and the l constraint are not reproducible from the manuscript as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies 230 GHz images of Sgr A* produced by a semi-analytic radiatively inefficient accretion flow (RIAF) around a rotating Lorentz-violating (LV) black hole in low-energy Hořava gravity. Using the EHT REx algorithm on ray-traced and blurred images, it reports that increasing the LV parameter l decreases the bright-ring diameter and increases ring width, luminosity, azimuthal asymmetry, and orientation angle; that spin and disk thickness affect these trends; and that comparing with EHT's Sgr A* diameter (51.8 ± 2.3 μas) yields a model-dependent allowed l range. It also analyzes how l shifts peak positions and widths of the n=0 primary image and n=1 photon ring for Keplerian, mixed, and radial free-fall flows.","tokens_in":11615,"tokens_out":12227,"duration_ms":117600,"significance":"The forward-modeling strategy is sensible and connects a modified-gravity parameter to a specific EHT observable. The use of a semi-analytic RIAF, thermal synchrotron emissivity, and the REx ring extractor is appropriate, and the paper explicitly scans multiple spins, disk thicknesses, and l values. If Eq. (1) were correctly transcribed and the simulations rerun, the qualitative trends could provide a useful template for LV searches in horizon-scale images. However, the paper gives no code or data release, and the central line element as printed is internally inconsistent, which currently prevents reproducibility and undermines the physical interpretation of the LV constraints.","major_comments":[{"comment":"The metric as printed does not have the claimed Kerr limit. Setting l=0 gives g_{tφ} = -4 M a^2 r sin^2θ / ρ^2, whereas Kerr in Boyer-Lindquist coordinates has g_{tφ} = -2 M a r sin^2θ / ρ^2. Thus the statement that the solution 'can be returned to the Kerr solution when l=0' is false for the printed line element; the extra power of a also makes g_{tφ} dimensionally inconsistent if a is the usual specific angular momentum. Because every ray-tracing result and the EHT-derived allowed range for l (Figs. 1-6 and the Section V summary) are computed in this spacetime, the central claim is not reproducible from the manuscript. The authors must verify the metric against Ref. [50], correct the transcription, and rerun the simulations; as written the paper cannot be accepted.","section":"Section II, Eq. (1)"},{"comment":"The allowed-range analysis only propagates the 1σ statistical diameter uncertainty (51.8 ± 2.3 μas) for fixed fiducial model parameters (Table I). The diameter d varies by only a few μas over the quoted l ranges, so EHT systematic uncertainties (calibration, imaging, source variability) and model uncertainties in n_{e,0}, T_{e,0}, κ, inclination, and disk thickness could shift or erase the allowed range. The abstract and Section V present the l interval as a constraint rather than as a conditional illustration. This conclusion should be softened or supplemented by an explicit systematic-error treatment.","section":"Section III, Fig. 4"}],"minor_comments":[{"comment":"'Radiation ineffective accretion flows' should be 'radiatively inefficient accretion flows'; this typo appears in the title, abstract, and summary.","section":"Title, Abstract, Section V"},{"comment":"The sentence 'From grr = ∆r/ρ² = 0' is garbled. The horizon condition is Δ=0, i.e. g^{rr}=0, not g_{rr}=0; please fix the notation.","section":"Section II, Eq. (2)"},{"comment":"'Isohypse' appears to be a typo for 'isophote' or 'isocontour' in the description of temperature contours.","section":"Section IV, Fig. 7"},{"comment":"The label 'Lv parameter' should be 'LV parameter'.","section":"Fig. 6 label"},{"comment":"The definition of ring width w as 'FWHM[I(r,θ)-I_floor]' is ambiguous: it should specify the radial coordinate over which the FWHM is computed, and the role of the azimuthal average.","section":"Section III, Eq. (8)"}],"recommendation":"major_revision","confidential_remarks":"The decisive issue is the transcription of Eq. (1). I cannot determine from the manuscript whether the code used the metric as printed or a corrected version; the authors must clarify this before resubmission. Given the scale of the numerical parameter study, correcting the metric and rerunning is a substantial but potentially fixable task, so I have chosen major_revision rather than reject. If the printed a^2 in g_{tφ} is not a typo, the paper should be rejected because the LV interpretation and EHT constraints would be baseless."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"If you only look at one thing: check Eq. (1). The paper claims the rotating Lorentz-violating black hole metric reduces to Kerr at l=0, but the printed g_tφ is -4 M a^2 r sin^2θ/ρ^2, not -4 M a r sin^2θ/ρ^2. That extra factor of a means the l=0 baseline is not Kerr. This is load-bearing. The paper's central result—the EHT-derived allowed range for the LV parameter l—is computed in this spacetime. If the simulations used the printed metric, they are not comparing against a Kerr baseline; if they used the correct Devecioglu-Park metric, then Eq. (1) is mistranscribed and the manuscript does not say which was coded. Either way, the numbers in Figs. 4–6 are not reproducible from the text.\n\nI want to give credit where it's due. The study is a competent forward-model exercise: RIAF model, thermal synchrotron, ray tracing, REX ring extraction, and a transparent comparison with the EHT Sgr A* diameter. The qualitative trends (diameter decreases with l; width, asymmetry, orientation, brightness ratio increase) hang together, and the paper does not oversell the constraints beyond the fixed fiducial parameters. As far as I can tell, this is a genuine new application of the established pipeline to the Horava black hole, not a repackaged calculation.\n\nThe other soft spots are minor by comparison. The l constraint is conditional on ne,0, Te,0, H, and a with no propagation of systematics, and no code or data are released. Standard for the genre, but it limits how much weight the EHT bound can carry. The authors also lean entirely on [50] for the metric without an independent check of the geodesic structure; a quick l=0 limit check would have caught the issue.\n\nNet: the reviewer's conditional verdict is right in spirit, but the metric typo makes the central quantitative claim unsupported as written. I would send this to peer review, because the topic is relevant and the problem is potentially fixable, but with a strong request to correct Eq. (1), rerun or confirm the simulations, and report whether any numbers change. As it stands, I would not cite it or treat the l constraint as reliable.","headline":"The parameter study is competent, but Eq. (1) as printed does not reduce to Kerr at l=0, so the EHT-based l constraint is not reproducible from the manuscript.","tokens_in":12125,"tokens_out":6363,"would_cite":false,"duration_ms":55871,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.70.Dy","95.30.Sf","97.60.Lf"],"model":"deepseek-v4-flash","headline":"A single Lorentz-violating parameter in a rotating black hole metric shrinks Sgr A*'s bright-ring diameter while widening, brightening, and asymmetrizing the ring, and the measured diameter can be turned into an allowed range for that param","keywords":["Lorentz violation","black hole image","Sgr A*","bright ring","radiatively inefficient accretion flow","synchrotron radiation","photon ring","Lorentz-violating gravity"],"falsifier":"Substitute Eq. (1) into the field equations of the low-energy Lorentz-violating gravity theory and verify it as an exact solution; a failed check would show the $l$-dependence is an artifact of the metric ansatz. Observationally, measure the Sgr A* ring at higher resolution and compare the diameter and width changes as the accretion state varies: if the diameter does not shrink while the width grows along the suggested $l$ direction, the predicted correlations are excluded.","tokens_in":11168,"feed_emoji":"🕳️","tokens_out":12960,"duration_ms":112005,"temperature":0.7,"pith_summary":"This paper tries to establish that Lorentz violation leaves a measurable imprint on the bright ring of Sgr A* images. Working with a rotating black hole metric from a low-energy Lorentz-violating gravity theory and a radiatively inefficient accretion flow model, it claims that increasing the Lorentz-violating parameter $l$ monotonically shrinks the ring diameter while increasing its width, brightness, azimuthal asymmetry, and orientation angle, and that these trends grow with black hole spin and disk thickness. It then uses the measured ring diameter of Sgr A* to derive allowed ranges for $l$ that depend on spin and disk thickness, and shows that nonzero $l$ shifts and narrows the allowed spin range. A sympathetic reader would care because this turns a single image observable into a concrete, quantifiable constraint on Planck-scale Lorentz symmetry breaking.","feed_headline":"Lorentz violation shrinks Sgr A*'s ring but widens and brightens it","feed_subtitle":"A Lorentz-violating metric parameter reshapes Sgr A*'s ring, turning its image into a Planck-scale test.","key_machinery":"The load-bearing object is the rotating Lorentz-violating black hole metric of Eq. (1), whose time-time and off-diagonal $t\\varphi$ components carry the parameter $l$ multiplied by powers of the spin $a$; this product structure makes $l$ mimic spin effects without being identical to them. Around this spacetime the paper places a semi-analytic radiatively inefficient accretion flow (RIAF) with power-law electron density and temperature profiles, a disk-thickness parameter $H$, and velocities interpolated between Keplerian and radial free-fall. Images are produced by general-relativistic ray tracing of thermal synchrotron emission, blurred to observational resolution, and the ring features are","core_discovery":"The paper's central claim is that the Lorentz-violating parameter $l$ in the rotating black hole metric produces a systematic, spin-like change in the simulated 230 GHz image of Sgr A*: the bright-ring diameter decreases monotonically with $l$, while the ring's width, intensity, azimuthal asymmetry, orientation angle, and brightness asymmetry all increase. Because $l$ enters the metric functions in products with the spin parameter $a$, its imaging effects track those of spin. Comparing the simulated ring diameter with the observed value $51.8 \\pm 2.3\\,\\mu\\mathrm{as}$, the paper derives, for each disk thickness, an allowed interval in $l$ that first broadens and then contracts as $a$ grows an","pith_inferences":["The paper implicitly treats $l$ and $a$ as degenerate in the ring diameter; an independent measurement of Sgr A*'s spin, for instance from quasi-periodic variability or jet orientation, would break that degeneracy and sharpen the $l$ bound.","The same RIAF-plus-ring-extraction pipeline could be applied to other Lorentz-violating black hole solutions to test whether the monotonic diameter/width/asymmetry trends are generic to Lorentz violation or specific to this metric's particular coupling structure.","The semi-analytic flow is a fixed idealization; replacing it with turbulent GRMHD snapshots would test whether the claimed $l$ trends survive realistic velocity and magnetic-field fluctuations before the bounds are used as exclusion limits."],"forward_implications":["The observed Sgr A* ring diameter can be translated, at fixed disk thickness, into an allowed interval for the Lorentz-violating parameter $l$, so a single image measurement becomes a quantitative bound on Lorentz violation.","Nonzero $l$ narrows the allowed spin range of the black hole: negative $l$ pushes spin upward and positive $l$ pushes it downward, meaning the two parameters are observationally entangled.","Thicker disks shrink the predicted ring diameter and amplify the $l$-dependence of the diameter, so disk thickness must be known or marginalized before a reliable $l$ constraint can be quoted.","The primary image and $n=1$ photon ring respond differently to $l$: their peak positions and widths decrease with $l$ except in narrow angular windows, and Keplerian versus radial free-fall flows produce different sensitivities, so future resolution of these subcomponents could separate Lorentz violation from flow geometry."],"supporting_citations":[{"why":"Supplies the rotating Lorentz-violating black hole metric, Eq. (1), that the entire image simulation is built on.","marker":"[50]"},{"why":"Provides the semi-analytic RIAF model with electron density and temperature profiles, disk thickness parameter $H$, and Keplerian/free-fall velocity interpolation.","marker":"[22]"},{"why":"Underlies the general-relativistic ray-tracing used to compute 230 GHz synchrotron images.","marker":"[53]"},{"why":"Provides the fitted formulas for synchrotron emission, absorption, and Faraday effects used in the polarized radiative transfer.","marker":"[61]"},{"why":"Introduces the ring-extraction algorithm from which the paper's diameter, width, orientation, and asymmetry measures are taken.","marker":"[19]"},{"why":"Supplies the measured Sgr A* bright-ring diameter, $51.8 \\pm 2.3\\,\\mu\\mathrm{as}$, against which the allowed $l$ range is derived.","marker":"[5]"},{"why":"Defines the primary image versus photon-ring decomposition used in the peak-position analysis.","marker":"[18]"}],"fun_headline_variants":["LV thins Sgr A* ring, widens its glow","Lorentz violation reshapes Sgr A* ring image","Sgr A* ring reveals LV via size and brightness","LV changes Sgr A* ring diameter and luminosity","LV parameter alters Sgr A* ring's shape and shine"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"Everything rests on the rotating Lorentz-violating metric being a genuine, correctly transcribed solution of the underlying gravity theory, especially the off-diagonal term where $a^2$ appears; if that metric is not an exact solution or contains a typographical error, the quoted ring properties and the derived allowed range for $l$ are invalid.","fun_headline_variants_meta":{"raw":{"variants":["LV thins Sgr A* ring, widens its glow","Lorentz violation reshapes Sgr A* ring image","Sgr A* ring reveals LV via size and brightness","LV changes Sgr A* ring diameter and luminosity","LV parameter alters Sgr A* ring's shape and shine"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000246,"raw_usage":{"total_tokens":1437,"prompt_tokens":864,"completion_tokens":573,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":503}},"tokens_in":608,"tokens_out":573,"duration_ms":5778,"temperature":1.0,"reasoning_tokens":503,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:11:53.550958+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Substitute Eq. (1) into the field equations of the low-energy Lorentz-violating gravity theory and verify it as an exact solution; a failed check would show the $l$-dependence is an artifact of the metric ansatz. Observationally, measure the Sgr A* ring at higher resolution and compare the diameter and width changes as the accretion state varies: if the diameter does not shrink while the width grows along the suggested $l$ direction, the predicted correlations are excluded.","supporting_citations":[{"cited_title":"Rotating Black Holes in a Viable Lorentz-Violating Gravity: Finding Exact Solutions Without Tears","cited_arxiv_id":"2402.02253","evidence_quote":"Supplies the rotating Lorentz-violating black hole metric, Eq. (1), that the entire image simulation is built on."}],"review_version":1}