{"id":"ef7f08d7-2a31-4bd9-babc-21710169199e","arxiv_id":"2508.09221","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"For a charged black hole with quintessence in Rastall gravity, the deflection angle, shadow radius, quasinormal modes, and greybody factor are derived, all reducing to known cases when the quintessence parameter is zero.","lead":"This paper calculates how light bends, shadows appear, and black holes vibrate for a charged black hole surrounded by quintessence in Rastall gravity. It reports that the surrounding quintessence increases the deflection angle beyond Schwarzschild or Reissner-Nordstrom cases for positive values of the quintessence parameter.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sign of the quintessence term in the Rastall metric is ambiguous; positive Nq likely corresponds to a repulsive contribution, contradicting the claimed higher deflection angle.","rationale":"The reader's verdict is already UNVERDICTED; my concern does not change the verdict but sharpens the reason. The biggest risk is not merely that the metric may be wrong, but that the sign of the quintessence parameter is backwards relative to the claimed qualitative effect. In the canonical Kiselev solution, a positive quintessence density adds a negative correction to g_tt that reduces the deflection angle, not increases it. The abstract specifically emphasizes the higher deflection angle with positive Nq, so if this sign argument is correct, the central result likely has an error. However, because the full text is unavailable, I cannot confirm the exponent or sign convention; hence the appropriate verdict remains UNVERDICTED. The proposed test would settle the issue: compute the first-order Nq correction from the metric and verify the sign of the energy density.","tokens_in":811,"tokens_out":10039,"duration_ms":103930,"concrete_test":"Using the paper's explicit metric, compute the weak-field deflection angle to first order in Nq by direct null-geodesic integration and by the Gauss-Bonnet formula, e.g. α(b) ≈ 2∫_b^∞ (M/r^2 - Q^2/r^3 - Nq/2) / sqrt(r^2-b^2) dr for f(r)=1-2M/r+Q^2/r^2-Nq r (valid for ω=-2/3). If the Nq>0 correction is positive, the sign convention must be reversed or the transport equation is misused. Independently, substitute the metric and the corresponding stress tensor into the Rastall field equations and check the sign of the energy density for Nq>0. If ρ<0, the 'quintessence' interpretation fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"A central claim is that a surrounding quintessence with positive Nq increases the weak-field deflection angle. In the standard Kiselev quintessence metric used in Rastall-gravity black-hole papers, g_tt = 1 - 2M/r + Q^2/r^2 - Nq / r^{3ω+1}. For the usual quintessence equation of state ω ≈ -2/3, the term is -Nq r. Positive Nq then yields a positive energy density and ρ+3p<0, making the gravitational effect repulsive; the leading correction to the bending angle is negative (deflection smaller, not larger). If the metric instead uses +Nq r, the source has negative energy density and cannot be called quintessence. The abstract does not state the metric sign, the value of ω, or the relation of Nq to the Rastall coupling, so the headline directional claim cannot be evaluated. Because every observable (shadow, QNM, greybody factor) derives from this same metric function, the sign convention is load-bearing for the entire paper.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates the weak-field deflection angle, photon shadow, quasinormal modes, and greybody factor for a charged black hole surrounded by quintessence in Rastall gravity. The abstract claims that the deflection angle decreases with impact parameter and charge, increases with mass, and that positive quintessence parameter Nq increases the deflection angle relative to Schwarzschild or Reissner-Nordström; that the shadow shrinks with charge and expands with mass; that quasinormal modes in the eikonal limit are expressible via null circular geodesics; and that the greybody bound decreases with charge and increases with mass. The abstract also states that all results reduce to known limits for Nq=0 and Nq=Q=0. This review is based solely on the abstract, as the full manuscript was not provided.","tokens_in":1105,"tokens_out":4094,"duration_ms":45989,"significance":"If the derivations are correct, the paper would provide a useful catalogue of observational signatures for a black hole spacetime in Rastall gravity with quintessence, using established methods (Gauss-Bonnet deflection, photon-sphere/eikonal correspondence, greybody bound). The explicit limit checks to Reissner-Nordström and Schwarzschild are a positive sign of internal consistency. However, because the full text is unavailable, the central claims cannot be verified, and one directional claim in the abstract appears sensitive to a metric sign convention that is not stated.","major_comments":[{"comment":"The statement that 'positive Nq' leads to a higher deflection angle is not evaluable without specifying the metric sign and the equation-of-state parameter ω. In the standard Kiselev-like term g_tt = 1 - 2M/r + Q^2/r^2 - Nq/r^{3ω+1}, choosing ω = -2/3 gives a term -Nq r. A positive Nq then produces a repulsive contribution in the weak-field limit, which would decrease the deflection angle rather than increase it. If the metric instead uses +Nq r, the effective source has negative energy density and is not standard quintessence. The abstract should state the metric convention, the value of ω, and the relation of Nq to the Rastall coupling; otherwise the headline directional claim is ambiguous. Since the deflection angle sign propagates to the shadow and other observables, this is a load-bearing point.","section":"Abstract (central claim)"},{"comment":"The claimed reductions to Reissner-Nordström and Schwarzschild limits are plausible but cannot be checked. In particular, the assumed metric must be shown to solve the Rastall field equations with a properly defined quintessence energy-momentum tensor. The abstract does not explain how Nq arises from the Rastall coupling constants or how the quintessence background is constructed. Without this, all derived observables are conditional on an unverified background. The authors should provide the metric, the field equations, and the energy-momentum tensor in the manuscript.","section":"Full text (not supplied)"},{"comment":"The abstract states that the Lyapunov-exponent method gives the quasinormal modes in the eikonal limit and that a lower bound on the greybody factor is derived. In modified-gravity or non-Einstein settings, the usual null-geodesic correspondence can require verification; the abstract provides no details of the effective potential or the bounds used. This is not necessarily an error, but it is a necessary check that the paper should present explicitly.","section":"Eikonal correspondence/greybody bound"}],"minor_comments":[{"comment":"The symbol Nq is used without definition. If it is the quintessence state parameter, it should be named and its allowed range stated (e.g., physically customary ω values).","section":"Abstract notation"},{"comment":"The quantity '{\\lambda}c' (coordinate time Lyapunov exponent) is introduced without a clear definition. Please define it and distinguish it from proper-time Lyapunov exponents.","section":"Abstract notation"},{"comment":"The phrase 'gradually increase with increasing black hole mass m' is qualitative. For a quantitative claim, specify the regime (e.g., weak-field, small Nq) and perhaps the leading-order term.","section":"Abstract wording"}],"recommendation":"uncertain","confidential_remarks":"The referee was provided only the abstract and no full text, so a definitive verdict is not possible. The sign-convention concern about the quintessence term is serious: the abstract's central directional claim may be reversed under the standard Kiselev sign convention. I recommend obtaining the full manuscript before a final decision, and asking the authors to state explicitly the metric form, the equation-of-state parameter, and the sign of Nq relative to the weak-field potential. If the deflection angle calculation indeed yields a decrease for positive Nq under the stated metric, the paper would need major revision rather than minor clarification."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Fair warning: I'm reading only the abstract, so this is a provisional take. What the paper does is straightforward and probably useful: it takes the Rastall-gravity charged black hole with quintessence, runs the usual machinery — weak deflection via Gauss-Bonnet, photon sphere/shadow, eikonal QNMs, greybody bound — and reports how observables vary with mass, charge, and the quintessence parameter. The limiting checks to Reissner-Nordstrom and Schwarzschild are good practice, and the claim that this specific combination hasn't been calculated before looks credible. No sign of fitting or circular reasoning.\n\nThe soft spot is the one you'd almost expect with this genre: the metric itself is assumed, and the abstract never states its sign convention for the quintessence term. The headline claim that positive Nq increases the deflection angle depends entirely on that convention. If the metric is the standard Kiselev-like form with g_tt = 1 - 2M/r + Q^2/r^2 - Nq r^{3ω+1}, then for ω ≈ -2/3 the term is -Nq r, which for positive Nq gives a repulsive contribution and should lower the deflection angle, not raise it. If the paper instead uses +Nq r, the source's energy density is negative and calling it quintessence is a stretch. The abstract doesn't tell us ω, the sign in the metric, or how Nq relates to the Rastall coupling, so the direction of the effect can't be checked. Since every observable is built from the same metric function, this is load-bearing, not cosmetic.\n\nThe secondary issue is that the eikonal Lyapunov correspondence is used without comment; that's standard but has known caveats for non-asymptotically flat or non-Einstein spacetimes. The referee should ask whether it holds here.\n\nBottom line: the paper is a credible new application of standard methods, and if the metric is right and the sign convention is stated properly, the results are a legitimate contribution to the modified-gravity black-hole literature. But the abstract alone doesn't let you verify the central directional claim. Send it to peer review — a good referee can check the metric against the Rastall field equations and fix the sign issue. It's not a desk reject.","headline":"Standard-application black-hole observables paper; direction of the quintessence effect is unverifiable from the abstract and may be sign-flipped.","tokens_in":1513,"tokens_out":2408,"would_cite":false,"duration_ms":26882,"reading_group":"maybe","serious_thinker":"unclear","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.70.-s"],"model":"deepseek-v4-flash","headline":"A quintessence field around a charged Rastall-gravity black hole raises the weak-field deflection angle above the Schwarzschild and Reissner–Nordström values, and all results reduce to those limits when the quintessence parameter vanishes.","keywords":["Rastall gravity","quintessence","black hole shadow","deflection angle","quasinormal modes","Lyapunov exponents","greybody factor","Gauss-Bonnet method"],"falsifier":"Take the metric the authors assume and substitute it directly into Rastall's field equations with the quintessence stress-energy tensor; if the field equations are not satisfied identically, the observable predictions are void. A purely observational check would be a lensing or shadow measurement of a black hole with independently known mass and distance that finds a deflection angle smaller than the Schwarzschild value, which would contradict the claimed increase for positive Nq.","tokens_in":790,"feed_emoji":"🕳️","tokens_out":8938,"duration_ms":96801,"temperature":0.7,"pith_summary":"This paper aims to show that a charged black hole immersed in a quintessence field, described by Rastall's modified gravity, leaves observable fingerprints in four independent channels: the bending of light in the weak-field limit, the size of the photon shadow, the quasinormal ringing frequencies, and the strength of Hawking radiation transmission. The authors report that deflection angles decrease with impact parameter and charge, increase with mass, and are larger than in Schwarzschild or Reissner–Nordström spacetimes when the quintessence parameter Nq is positive. They also report that the shadow shrinks with charge, expands with mass, and that the quasinormal modes can be obtained from the Lyapunov exponent of the unstable null circular geodesic in the eikonal limit. The lower bound on the greybody factor goes down with charge and up with mass. All four sets of expressions reduce exactly to Reissner–Nordström for Nq = 0 and to Schwarzschild for Nq = Q = 0. If these claims hold, the model gives concrete, separable predictions for testing modified gravity around black holes with existing lensing and ringdown observatories.","feed_headline":"Quintessence boosts black hole bending of light","feed_subtitle":"How charge, mass, and quintessence reshape shadow, ringdown, and lensing in Rastall-gravity black holes.","key_machinery":"The engine of the analysis is an assumed static, spherically symmetric, charged black hole solution of Rastall's field equations with a quintessence energy-momentum tensor as the source—this is the metric from which every observable is derived, although the abstract does not display it. Four standard tools are then applied to that metric: the Gauss–Bonnet theorem to integrate the photon trajectory in the weak-field regime, the null-geodesic condition to locate the photon sphere and hence the shadow radius, the eikonal correspondence that identifies the real part of quasinormal frequencies with the angular velocity of the unstable null circular geodesic and the imaginary part with its Lyapuno","core_discovery":"The central claim is that the quintessence background in Rastall gravity does not merely decorate the spacetime; it changes measurable gravitational observables in a systematic, parameter-dependent way. Specifically, for the charged Rastall–quintessence black hole, the weak-field deflection angle computed by the Gauss–Bonnet method is larger than the corresponding angle for Schwarzschild or Reissner–Nordström black holes when the quintessence parameter Nq is positive, and it falls off with impact parameter b and charge Q while rising with mass m. The photon sphere and shadow radius shrink with Q and grow with m; the quasinormal mode frequency in the eikonal limit is linked to the coordinate-","pith_inferences":["If the four observables are measured independently for the same object, they overdetermine the three parameters (m, Q, Nq); a consistent inversion would strengthen the model, and any inconsistency would falsify the metric at the level of its observable predictions.","The abstract does not give numerical magnitudes for the quintessence effect, so astrophysical detectability remains open; bounding Nq with current lensing or shadow data would settle whether the predicted boost in deflection is observable with existing instruments.","The natural next step, left implicit here, is a rotating generalization: spin would break shadow circularity and make the quintessence signature even sharper than the static case treated in the paper.","Because the whole chain hangs on a single assumed metric, an independent check that the metric satisfies the Rastall field equations rather than merely reproducing known limits is the cheapest way to validate the computation."],"forward_implications":["Measurements of gravitational lensing around a black hole whose mass and distance are known could distinguish this Rastall–quintessence model from Schwarzschild or Reissner–Nordström, because positive Nq raises the deflection angle above the GR values.","Shadow imaging would see a smaller shadow for larger charge and a larger shadow for larger mass; matching both trends fixes Q and m jointly.","Ringdown observations could test the eikonal relation: the quasinormal frequency and damping time should be exactly the angular frequency and Lyapunov timescale of the null circular orbit.","The greybody-factor bound controls how much Hawking radiation escapes, so the predicted decrease with Q and increase with m feeds into evaporation-rate estimates for this class of black holes.","The recovery of Reissner–Nordström and Schwarzschild limits at Nq=0 and Nq=Q=0 means the model is calibrated against known spacetimes, making the new quintessence terms cleanly identifiable."],"supporting_citations":[],"fun_headline_variants":["Quintessence outbends Schwarzschild in Rastall black holes","Charged quintessence black holes boost light deflection","Rastall gravity: quintessence amplifies gravitational lensing","Black hole bending amplified by quintessence in Rastall gravity"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The entire set of predictions rests on the unstated premise that the charged, quintessence-surrounded metric used at the start is a genuine solution of Rastall's field equations; if that metric does not satisfy the field equations, every derived deflection, shadow, quasinormal-mode, and greybody result collapses.","fun_headline_variants_meta":{"raw":{"variants":["Quintessence outbends Schwarzschild in Rastall black holes","Charged quintessence black holes boost light deflection","Rastall gravity: quintessence amplifies gravitational lensing","Black hole bending amplified by quintessence in Rastall gravity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000638,"raw_usage":{"total_tokens":2815,"prompt_tokens":822,"completion_tokens":1993,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":566,"completion_tokens_details":{"reasoning_tokens":1919}},"tokens_in":566,"tokens_out":1993,"duration_ms":23127,"temperature":1.0,"reasoning_tokens":1919,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T21:30:17.778062+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the metric the authors assume and substitute it directly into Rastall's field equations with the quintessence stress-energy tensor; if the field equations are not satisfied identically, the observable predictions are void. A purely observational check would be a lensing or shadow measurement of a black hole with independently known mass and distance that finds a deflection angle smaller than the Schwarzschild value, which would contradict the claimed increase for positive Nq.","supporting_citations":[],"review_version":1}