{"id":"c1532812-86de-497d-99a7-ee9b486e0037","arxiv_id":"2411.10315","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Ray-traced images of the Kerr-Newman-MOG black hole show that the MOG parameter α enlarges and rounds the shadow, and its effect beats that of the electric charge Q.","lead":"General relativity's shadow images for a charged, spinning black hole in modified gravity (MOG) are computed with a backward ray-tracing code. The modified gravity parameter α enlarges and rounds the shadow more strongly than the electric charge Q shrinks it.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed dominance of α over Q is not established: the paper compares equal numerical values (α=0.5 vs Q=0.5) even though the metric depends on Q² and α(1+α), so the conclusion may be an artifact of parameter normalization.","rationale":"The paper's ray-tracing is standard and the qualitative statement that α enlarges and rounds the shadow follows from the metric; I see no internal inconsistency in the geodesic equations. The reader's conditionality on the adopted metric is fair, but the more immediate load-bearing soft spot is that the paper's headline comparison is not normalized. The metric itself shows why: Q² and α(1+α) contributions differ by a factor of three at equal numerical values, and α additionally enters the linear term. Figures and tables do not quantify the ratio of effects; the claim \"α plays a dominant role\" is essentially a restatement of the metric's parameter structure under an arbitrary convention. My proposed test is cheap and uses the paper's own pipeline. If the test shows comparable effects, the abstract's last sentence should be revised. If it confirms dominance even with matched contributions, the reader's verdict could stand. Since this is a computational check, and the reader's CONDITIONAL already flags lack of code and data, I recommend keeping the verdict CONDITIONAL but adding the normalization test as an explicit requirement. I partially disagree with the reader's choice of weakest assumption: metric provenance is a legitimate external concern, but the internal comparison issue is the one that directly undermines the stated central claim as written.","tokens_in":22331,"tokens_out":7560,"duration_ms":73306,"concrete_test":"Recompute the shadow radius, inner-shadow area, and δs for the same observer setup using three comparisons: (1) fixed Q/M=0.5, scan α; (2) fixed α=0.5, scan Q; (3) matched constant contribution Q=√(α(1+α)), so Q≈0.866 when α=0.5. Also repeat Fig. 9 with Q fixed rather than Q=0.3Qe while α varies. If α's effect on observables remains several times larger than Q's at matched Δ-perturbation strengths, the dominance claim is robust; if Q's effect becomes comparable or larger, the claim is an artifact of comparing equal numbers, and the conclusion should be weakened to \"α and Q act in opposite directions with comparable strength under suitable normalizations\".","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that α dominates Q in shaping the image is not quantitatively established because the paper never defines a physically meaningful \"same parameter level\". In the assumed metric, Δ = r² − 2(1+α)r + a² + Q² + α(1+α) (with M=GN=1), so Q enters only through Q² while α enters both through the linear term −2αr and through α(1+α). Figure 9 compares α=0.5 with Q=0.5, i.e. constant contributions of 0.75 vs 0.25, and α also changes the horizon radius and photon-sphere scale. It is therefore unsurprising—and not a physical discovery—that α shows a larger effect at equal numerical values. Moreover, in Figs 1–8 the charge is fixed as Q=0.3Qe with Qe=√(1+α−a²), so Q itself grows as α is varied, mixing the two parameters. The concluding sentence of Section 5 explicitly says the dominance \"can also be seen from the metric equations\", which confirms that the effect is partly an artifact of how the parameters appear in Δ rather than a robust, separately quantified result. Without either a matched-Δ comparison (e.g., Q=√(α(1+α))), or a percent-change table for shadow radius and inner-shadow area as each parameter is varied independently, the strongest claim is conditional on an arbitrary normalization.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the shadow and thin accretion disk images of the Kerr-Newman black hole in modified gravity (MOG), using a backward ray-tracing method. Working with the KN-MOG metric given by Eqs. (2.1)-(2.2), the authors compute shadow boundaries, deviation rates, photon trajectories, redshift maps, and intensity distributions for various values of the spin a, charge Q, and MOG parameter α. They report that increasing α enlarges the shadow and inner shadow, makes the D-shaped shadow more circular, decreases the deviation rate δs, and increases the redshifted regions, while increasing Q has the opposite but weaker effects. The paper concludes that α plays a dominant role in shaping the observable image of the KN-MOG black hole.","tokens_in":22633,"tokens_out":7122,"duration_ms":69756,"significance":"If the KN-MOG metric is indeed the correct charged rotating solution of scalar-tensor-vector gravity, the paper provides a useful catalogue of possible observational signatures that could distinguish MOG black holes from Kerr/Kerr-Newman black holes. The ray-tracing machinery is standard, but it is applied to a spacetime that has not been extensively studied in this context, and the explicit trend tables (e.g., Table 1) for shadow radius and deformation as functions of α are helpful for future comparisons with EHT-like observations. The paper does not release its code or provide convergence tests, which limits reproducibility, but the qualitative trends are consistent with the known Kerr and Kerr-Newman limits when α=0 or Q=0. The main shortcoming is that the central claim of α-dominance over Q rests on an ill-defined parameter comparison, as detailed in the major comments.","major_comments":[{"comment":"The central claim that α has a greater effect than Q 'at the same parameter level' is not quantitatively established. In Δ = r^2 - 2(1+α)r + a^2 + Q^2 + α(1+α), with G_N=M=1, α appears linearly in the 2(1+α)r term and quadratically in the constant term, while Q appears only quadratically. Comparing α=0.5 with Q=0.5 compares constant contributions of 0.75 and 0.25, and moreover α shifts the horizon and photon-sphere radii. A meaningful comparison would match the metric contributions (e.g., Q = sqrt(α(1+α))), or report fractional changes in shadow radius and inner-shadow area as each parameter is varied by the same relative amount. Without such a control, the 'dominant role' conclusion is an artifact of the chosen parameter normalization, and the statement in Section 5 that the dominance 'can also be seen from the metric equations' confirms that the numerical finding is not independent of the parameterization.","section":"§5, Fig. 9, Eqs. (2.1)-(2.2)"},{"comment":"The KN-MOG metric is adopted from Ref. [108] without derivation or any verification that it satisfies the scalar-tensor-vector gravity field equations. Since all subsequent results—shadow radii, images, the α-versus-Q comparison—depend on this metric, the assumption is load-bearing. If the true charged rotating MOG solution has a different radial dependence or a different coupling of α to the electromagnetic sector, the reported phenomenological conclusions would not apply to actual MOG black holes. The authors should either justify the metric's validity from the STVG action or explicitly frame the entire study as conditional on the metric proposed in Ref. [108].","section":"§2, Eqs. (2.1)-(2.2)"},{"comment":"The derivation of the critical impact parameters ξ(r) and η(r) is omitted; only the final expressions are given. These formulas are central to the shadow computation and are not obvious, involving the auxiliary quantities A and B. A brief derivation or a reference to a paper that derives these expressions for this specific spacetime should be provided so that the results can be verified and reproduced.","section":"§2, Eq. (2.7)"},{"comment":"The quantitative statements about shadow radii, deviation rates, and intensity distributions rely on numerical ray tracing, but no numerical details are reported: there is no description of the integration scheme, resolution, step size, or convergence tests, and the quantities in Table 1 are given without error estimates. This makes it difficult to assess the reliability of the reported variations (e.g., the change in R_s from 0.050695 to 0.079475). At minimum, the authors should state the numerical precision and show that the results are converged.","section":"Table 1 and Figs. 3-8"}],"minor_comments":[{"comment":"The explanation that a stronger electric field 'repels nearby light, reducing the degree of light bending' is physically misleading; in general relativity, light deflection is governed by spacetime curvature, and the charge affects the metric rather than exerting a direct repulsive force on photons. The qualitative trend (shrinking shadow with increasing Q) is correct, but the wording should be revised.","section":"§2, paragraph after Fig. 2"},{"comment":"The caption contains a typo: the second occurrence of 'For the left plane' should be 'For the right plane.'","section":"Fig. 2 caption"},{"comment":"The equations contain several notation and typesetting issues (e.g., \\(\\Sigma1^2\\) instead of \\(\\Sigma^2\\), overlong radical expressions, and undefined symbols such as \\(D\\) in Eq. (2.11)). A thorough editorial pass would improve readability.","section":"§2, Eqs. (2.6)-(2.12)"},{"comment":"The transition from Eq. (3.7) to the simplified form \\(\\sum_n f_n g_n^3 J_n\\) is not explained; in particular, the meaning of the \\(f_n\\) factor and the limit in which absorption is negligible should be stated explicitly.","section":"§3, Eq. (3.7)"},{"comment":"The description of the two 'tails' near the Einstein ring is vague. The authors should define what they mean by a 'tail' and specify whether it is a feature of the lensed image, the photon ring, or a coordinate artifact.","section":"§4, Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is a fairly standard ray-tracing application to a known spacetime, and the novelty lies mainly in the particular parameter study rather than in new methods. The main scientific concern is that the headline conclusion about α-dominance over Q is not robustly defined; however, the issue is fixable by adding a matched-parameter comparison and tempering the claims. The metric-validity concern is also real but can be addressed by a caveat and appropriate framing. Given that the paper is otherwise competently executed and the trends are plausible, I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the honest one-line take: this is a workmanlike ray-tracing study of the Kerr-Newman-MOG metric that produces a plausible qualitative catalog of shadow and thin-disk images, but its headline claim that the MOG parameter α dominates the charge Q is not actually established by the comparison the paper runs.\n\nWhat's genuinely new: the paper appears to be the first to produce thin-disk accretion images for the KN-MOG metric from Ref. [108], including direct and lensed images, inner-shadow behavior, redshift maps, and intensity cuts across a modest grid of a, Q, and α. The shadow computation is standard Hamilton-Jacobi, the limiting checks (α=0, Q=0) reduce to known Kerr values, and the observational-scale numbers are consistent with placing the observer at r_o=100. The qualitative effects — α enlarges and rounds the shadow, Q shrinks it, spin creates the D-shape and the tail-like features on the Einstein ring — are all plausible consequences of the assumed metric.\n\nThe soft spots, in order of importance. First, the central claim about the dominance of α over Q is confounded by the parameterization. In Δ = r² − 2(1+α)r + a² + Q² + α(1+α), α changes both the coefficient of r and adds a constant, while Q appears only through Q². Comparing α=0.5 with Q=0.5 is not comparing like with like; α is guaranteed to look bigger. The paper even concedes the point by saying the dominance 'can also be seen from the metric equations.' A matched comparison — e.g., varying Q and α so that the constant contribution to Δ is the same, or tabulating percent changes in shadow radius per unit change in each parameter — would be needed to support the claim. Second, there are no convergence tests, error bars, or resolution details for the ray-tracing, and no code or data beyond 'available on request.' Third, the abstract and introduction promise observational relevance to M87*/Sgr A*, but no quantitative comparison to the EHT data is made. Finally, because the metric is imported from Shaymatov et al., the entire study inherits the question of whether that metric is truly the correct charged rotating MOG solution; the authors should at least say this more clearly.\n\nWho is this for? A reader who wants a visual reference for what thin-disk images of this particular MOG model look like, or who needs a baseline for future MOG image studies. It is not a breakthrough, but it is a competent and honest calculation. I would send it to a referee, not desk-reject it, but the referee should press on the dominance claim and the missing numerical details.","headline":"A competent but incremental ray-tracing catalog for KN-MOG; the headline α-vs-Q dominance claim is undercut by unequal parameter normalization.","tokens_in":23186,"tokens_out":3402,"would_cite":false,"duration_ms":32397,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83C10"],"pacs":["04.70.-s","04.20.-q"],"model":"deepseek-v4-flash","headline":"The MOG parameter $\\alpha$, not the charge $Q$, is the dominant control of the shadow and accretion-disk image of a charged rotating black hole in modified gravity.","keywords":["black hole shadow","accretion disk image","Kerr-Newman black hole","modified gravity MOG","scalar-tensor-vector gravity","backward ray-tracing","inner shadow","photon ring"],"falsifier":"Derive the charged rotating black hole solution directly from the scalar-tensor-vector gravity action rather than adopting the additive $\\Delta$ term in (2.2), and recompute the shadow radius and $\\delta_s$ at the same value of $\\alpha$; if the electromagnetic sector couples to $\\alpha$ differently, or the radial function is not simply the KN function plus $Q^2$, the reported dominance of $\\alpha$ over $Q$ will not survive. Observationally, for a black hole with independently known mass and distance, a horizon-scale image whose shadow size and circularity are fitted with the KN-MOG family would settle the claim: if the best fit has $\\alpha\\simeq 0$ even though the image shows the larger, rounder shadow the paper attributes to $\\alpha$, the proposed signatures are not present.","tokens_in":22115,"feed_emoji":"🌑","tokens_out":8924,"duration_ms":84353,"temperature":0.7,"pith_summary":"The paper sets out to show that in a charged rotating black hole described by scalar-tensor-vector modified gravity (MOG), the modified-gravity parameter $\\alpha$ is the dominant knob controlling what an observer sees: raising $\\alpha$ enlarges the shadow and the inner shadow, rounds the spin-induced flat \"D\" edge, lowers the deviation from circularity, and expands the redshifted regions of the thin accretion disk image, while raising the charge $Q$ shrinks the shadow and acts noticeably more weakly. The motivation is that shadows and disk images are the practical observables that can distinguish modified gravity from general relativity, so a clean qualitative signature of $\\alpha$ matters for interpreting horizon-scale images. The claim is established by backward ray-tracing null geodesics in the KN-MOG metric (2.1) with a geometrically thin, optically thin accretion disk, and by directly comparing Kerr, Kerr-MOG, Kerr-Newman, and Kerr-Newman-MOG images at equal parameter levels.","feed_headline":"MOG parameter dominates black hole images over charge","feed_subtitle":"A ray-tracing study shows alpha enlarges shadows, rounds spin's D-shape, and beats charge in observable effect.","key_machinery":"The load-bearing object is the KN-MOG metric (2.1)-(2.2), whose radial function $\\Delta = r^2 - 2GMr + a^2 + Q^2 + G_N^2\\,\\alpha(1+\\alpha)M^2$ carries the modified-gravity effect as a single additive term alongside the charge. On top of this metric, the paper solves the Hamilton-Jacobi equation for null geodesics, imposes the photon-sphere conditions $R(r_p)=0$ and $dR/dr|_{r_p}=0$ to obtain the impact parameters $\\xi$ and $\\eta$, and projects them onto a zero-angular-momentum observer's screen through celestial coordinates. For the disk images, the thin accretion disk is modeled by circular geodesic motion outside the ISCO and plunge orbits inside it, with a radiative-transfer intensity formula including a redshift factor and a \"fudge factor\" normalized according to the inner-shadow literature. This combination turns the single metric term in $\\Delta$ into the qualitative features the paper reports.","core_discovery":"On its own terms, the paper's central result is that the MOG parameter $\\alpha$ plays a dominant role in the charged rotating MOG spacetime: at fixed charge, increasing $\\alpha$ from 0 to 0.7 increases the shadow radius at every spin (for $a=0.998$, from 0.051475 to 0.080038) and decreases the circularity deviation $\\delta_s$ (from 0.247953 to 0.084967), while the flat edge produced by fast spin gradually rounds back toward a circle. Charge $Q$ acts in the opposite direction, shrinking the shadow and the critical curve, and in side-by-side images at the same parameter level its effect is clearly smaller than that of $\\alpha$. For thin-disk illumination, the inner shadow and critical curve grow with $\\alpha$ and shrink with $Q$, the redshift regions expand with $\\alpha$, and the intensity profile shows a wider two-peak separation as $\\alpha$ grows; at large spin, $\\alpha$ increases the peak intensity and radiative flux, while at low spin it decreases them. A separate feature the paper reports is the appearance of two \"tails\" along the Einstein ring in celestial-sphere images, which elongate with spin $a$ and appear nearly independent of $\\alpha$.","pith_inferences":["A direct corollary the paper leaves implicit is a degeneracy: because $\\alpha$ rounds the shadow and lowers $\\delta_s$, modified gravity mimics a smaller effective spin, so shadow-based spin estimates that ignore $\\alpha$ will be biased low for a MOG universe.","The paper stops at qualitative and numerical signatures; a natural next step is to run a parameter-estimation pipeline on synthetic or real horizon-scale images to see whether posteriors prefer $\\alpha>0$ over the Kerr hypothesis.","Whether the additive $Q^2$ term is the true MOG electromagnetic coupling remains open outside this paper; if a full solution from the scalar-tensor-vector gravity action changes that term, the same ray-tracing machinery would need to be rerun, and the relative dominance of $\\alpha$ could shift.","The optically thin disk treatment with a normalized \"fudge factor\" suppresses absorption effects; extending the model to finite optical depth or thick disks could change the predicted peak intensities while leaving the shadow boundary statements intact."],"forward_implications":["At fixed spin and charge, a KN-MOG black hole casts a larger, rounder shadow than its Kerr-Newman counterpart, so a nearly circular shadow does not by itself imply low spin; it could mean a large $\\alpha$.","Because $\\alpha$ affects the shadow more strongly than $Q$ at equal parameter levels, attempts to measure electric charge from shadow size need to fit $\\alpha$ simultaneously or risk attributing MOG effects to charge.","Redshift maps of thin accretion disks expand with $\\alpha$ for both prograde and retrograde flows, giving an independent observable, beyond shadow shape, for detecting the modified-gravity parameter.","The spin-related Einstein-ring \"tails\" grow with $a$ but stay nearly unchanged in $\\alpha$, while shadow size and roundness respond strongly to $\\alpha$; this partial separation means spin and MOG effects can be disentangled in images.","In comparisons across the four spacetime families, Kerr-MOG has the largest inner shadow and Kerr-Newman the smallest, so inner-shadow size joins shadow radius as a discriminator among gravity models."],"supporting_citations":[{"why":"Supplies the KN-MOG metric (2.1)-(2.2) whose $\\Delta$ term carries the modified-gravity parameter; the whole calculation starts from this spacetime.","marker":"[108]"},{"why":"Original rotating black hole solution in scalar-tensor-vector gravity that the charged version extends and whose observational signatures are being probed.","marker":"[92]"},{"why":"Defines the shadow radius and deviation rate $\\delta_s$ used to quantify how $\\alpha$ enlarges and rounds the shadow in Table 1.","marker":"[110]"},{"why":"Provides the tetrad/camera model and backward ray-tracing scheme used for the shadow and accretion disk images.","marker":"[109]"},{"why":"Normalizes the fudge factor and supplies the inner-shadow interpretation used in the thin-disk intensity and redshift analysis.","marker":"[112]"},{"why":"Establishes the direct, lensed, and photon-ring decomposition of thin-disk images that the paper uses to identify observed rings.","marker":"[41]"}],"fun_headline_variants":["Alpha rounds black hole shadow, beats charge in images","MOG parameter reshapes black hole shadow and outshines charge","Charged rotating MOG black hole: alpha dominates shadow images","Spin's tails and alpha dominance in MOG black hole images","MOG's alpha rules black hole images, charge takes a back seat"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that Eq. (2.1), with the MOG parameter entering the metric only through the additive term $G_N^2\\,\\alpha(1+\\alpha)M^2$ alongside $Q^2$, is the actual charged rotating black hole solution of scalar-tensor-vector gravity; if the correct solution has a different coupling between $\\alpha$ and the electromagnetic field or a different radial structure, the reported dominance of $\\alpha$ over $Q$ is not guaranteed.","fun_headline_variants_meta":{"raw":{"variants":["Alpha rounds black hole shadow, beats charge in images","MOG parameter reshapes black hole shadow and outshines charge","Charged rotating MOG black hole: alpha dominates shadow images","Spin's tails and alpha dominance in MOG black hole images","MOG's alpha rules black hole images, charge takes a back seat"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000426,"raw_usage":{"total_tokens":2240,"prompt_tokens":1060,"completion_tokens":1180,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":676,"completion_tokens_details":{"reasoning_tokens":1092}},"tokens_in":676,"tokens_out":1180,"duration_ms":8680,"temperature":1.0,"reasoning_tokens":1092,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T19:45:07.991261+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Derive the charged rotating black hole solution directly from the scalar-tensor-vector gravity action rather than adopting the additive $\\Delta$ term in (2.2), and recompute the shadow radius and $\\delta_s$ at the same value of $\\alpha$; if the electromagnetic sector couples to $\\alpha$ differently, or the radial function is not simply the KN function plus $Q^2$, the reported dominance of $\\alpha$ over $Q$ will not survive. Observationally, for a black hole with independently known mass and distance, a horizon-scale image whose shadow size and circularity are fitted with the KN-MOG family would settle the claim: if the best fit has $\\alpha\\simeq 0$ even though the image shows the larger, rounder shadow the paper attributes to $\\alpha$, the proposed signatures are not present.","supporting_citations":[],"review_version":1}