{"id":"f87e3b20-6b6d-4250-9d38-e57d4dded982","arxiv_id":"2505.12577","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The paper derives weak- and strong-field light deflection angles and relativistic image observables for an acoustic black-bounce spacetime, recovering Schwarzschild, Ellis-Bronnikov, and acoustic black hole limits.","lead":"Using a known technique for calculating how gravity bends light, this paper computes the bending angle and lensing observables for a black-bounce spacetime, a regularized analogue of a black hole often studied in fluid models. It shows how these predictions differ from ordinary Schwarzschild black holes, which matters for interpreting future high-precision lensing observations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table I is internally inconsistent with Eq. (50) and Fig. 3: the advertised s/θ∞ values near a/√q→1 require Δϕ_R≈4.6–7.7, whereas Fig. 3 shows Δϕ_R≈1–1.5.","rationale":"The reader's weakest assumption about unquantified higher-order terms in the Bozza expansion is plausible but secondary; the expansion is standard, and the ABH and q→0 limits in Eqs. (16), (27), (35), and (36) are recovered, which supports the leading strong-field structure. The sharper problem is that the paper's own numerical output contains an arithmetic contradiction. Equation (58) exponentiates (¯b−2π)/¯a, and Eq. (50) links ¯b directly to Δϕ_R. Fig. 3 places Δϕ_R in a narrow band around 1–1.5, but reproducing Table I requires Δϕ_R≈4.6 at a/√q=0.90 and ≈7.7 at 0.99. This is not a question of neglected higher-order terms; it is an internal inconsistency among displayed formulas, a displayed figure, and a displayed table. The paper does not describe the numerical evaluation of Δϕ_R, so a reader cannot tell which item is wrong, but the advertised detection improvement near a/√q→1 is exactly what depends on the disputed rows. The proposed recomputation is inexpensive and would definitively settle whether the central claim survives.","tokens_in":17207,"tokens_out":27334,"duration_ms":241817,"concrete_test":"Recompute Δϕ_R from Eq. (47) by numerical quadrature for a/√q=0.90 and 0.99 (set |q|=1), regularizing the integrand difference near z=0, then insert the result into Eq. (50) and Eq. (58) to obtain s/θ∞. If the computed values differ from Table I by more than a factor of 2 for either row, the inconsistency is confirmed and the central claim should be revised or withdrawn.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's headline claim—that strong-field lensing can distinguish the ABB from Schwarzschild because s/θ∞ grows to ~10^-3–10^-1 near a/√q→1—rests entirely on Table I. But Table I is not compatible with the paper's own definitions. From Eq. (58), s/θ∞ = exp[2(¯b−2π)/¯a]; from Eq. (50), ¯b = −¯a log[√3|q|/(2(3|q|−√3 a^2))] + Δϕ_R − π. Fig. 3 shows Δϕ_R in the range 1.0–1.5. Using Δϕ_R≈1.4 at a/√q=0.90 gives ¯a≈1.37, a log-term 0.84, hence ¯b≈0.84+1.4−π≈−0.90, so s/θ∞≈exp[2(−0.90−2π)/1.37]≈3×10^-5, about two orders of magnitude below the tabulated 3.1×10^-3. For a/√q=0.99 (¯a≈1.53), the tabulated 2.4×10^-1 requires ¯b≈5.2 and therefore Δϕ_R≈7.7, far outside Fig. 3. Thus Eq. (58), Eq. (50), Fig. 3, and Table I cannot simultaneously be correct. Since the observable enhancement is the basis of the distinguishability claim, that claim is unsupported unless the discrepancy is resolved.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes the deflection of light and gravitational lensing observables for two spherically symmetric metrics: the acoustic black hole (ABH) and the acoustic black-bounce (ABB). In the weak-field limit it obtains a series expansion for the deflection angle, Eq. (35), which reduces to the ABH result (Eq. (16)) for a→0 and to the Ellis-Bronnikov result (Eq. (36)) for q→0. In the strong-field limit it applies the Bozza–Tsukamoto method, deriving an analytic divergent part, Eq. (46), and a numerically evaluated regular part, Eq. (47). It then constructs lensing observables: the angular separation s between the outermost relativistic image and the asymptotic image position θ∞, and the flux ratio ˜r. The central claim is that for a/√q near 1 the observable ratio s/θ∞ reaches 10^-3 to 10^-1, exceeding the Schwarzschild value (~10^-3) and therefore making the ABB potentially distinguishable from Schwarzschild.","tokens_in":17502,"tokens_out":50552,"duration_ms":413304,"significance":"The formalism used is standard and the weak-field expansion is carefully derived and cross-checked against known limits. The paper's strong-field divergent part is obtained in closed form, which is a useful addition. If the observable predictions were correct, they would provide a concrete way to differentiate the acoustic black-bounce from Schwarzschild in strong-field lensing. The main strength is that the derivations are analytical and do not rely on numerical fitting. However, as detailed in the major comment, the key observable table is inconsistent with the paper's own equations, and the headline claim is therefore not supported by the manuscript as written.","major_comments":[{"comment":"Table I is internally inconsistent with the paper's own formulas. Combining Eq. (58) with Eqs. (50) and (51) and using the values of Δϕ_R shown in Fig. 3 (Δϕ_R ≈ 1.4 at a/√q = 0.90 and ≈ 1.5 at a/√q = 0.99) yields s/θ∞ ≈ 3 × 10^−5 and ≈ 7 × 10^−5, respectively, whereas Table I lists 3.1 × 10^−3 and 2.42 × 10^−1. To reproduce the tabulated entries, Eq. (50) would require Δϕ_R ≈ 4.6 at a/√q = 0.90 and Δϕ_R ≈ 7.7 at a/√q = 0.99, far outside the range of Fig. 3. The paper's conclusion in Sections V and VI that the ABB angular separation can exceed the Schwarzschild value (~10^−3) rests entirely on this table and is therefore unsupported. With the correct Δϕ_R, the ABB s/θ∞ remains below ~10^−4 for all a/√q < 1, i.e., smaller than the Schwarzschild value.","section":"V. LENS EQUATION AND OBSERVABLES, Table I and Fig. 7"}],"minor_comments":[{"comment":"The axis label in Fig. 1 reads 'q /β' but the text correctly refers to the ratio p|q|/β; the square-root notation should be used consistently in both the figure and the text.","section":"Fig. 1 and text"},{"comment":"There is a typographical error: 'Bozaa's point of view' should read 'Bozza's point of view'.","section":"Section V, text near Eq. (58)"},{"comment":"The strong-field observation is based on the truncation G(z,ρ0) ≃ Λ1 z + Λ2 z^2. The authors do not quantify the neglected higher-order terms or discuss the accuracy of this truncation as a/√q approaches 1; a brief comment on the validity of the expansion would be useful.","section":"Eqs. (19) and (39)"},{"comment":"The definition of ¯b in Eq. (50) is algebraically equivalent to the constant term in Eq. (46), but the equivalence is not transparent. A short explanatory sentence would improve readability.","section":"Eq. (50)"},{"comment":"The y-axis label '(s/θ∞)×10^-2' is difficult to interpret; a logarithmic scale would make the comparison between SBH, ABH, and ABB much clearer.","section":"Fig. 7"}],"recommendation":"major_revision","confidential_remarks":"The manuscript contains a high number of self-citations (e.g., Refs. [38,41,44,45,105]), but the core derivations are standard and do not appear to depend circularly on the authors' prior results. The main issue is the inconsistent observable table, which should be fixed before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a standard Bozza/Tsukamoto lensing calculation applied to the acoustic black-bounce metric. The analytic parts are mostly consistent, but the advertised strong-field enhancement rests on a table that does not agree with the paper's own equations. The conditional verdict is right, and I would put more weight on the Table I inconsistency than on the missing derivation details.\n\nWhat's actually new: explicit weak-field series (Eq. 35) and strong-field divergent term (Eq. 46) for the ABB, plus the Bozza observables. The a→0 limit recovers the ABH result and q→0 recovers Ellis-Bronnikov, which is a real check. Eq. (50) follows algebraically from Eq. (46); I found no separate problem with the divergent coefficient. This is competent use of a standard formalism, with no fitting and no circularity.\n\nSoft spots. First and most important: Table I cannot be reconciled with Eq. (50) and Fig. 3. Using Eq. (58) and Eq. (50) with Δφ_R ≈ 1.4 at a/√q = 0.90 gives s/θ∞ ≈ 3×10⁻⁵, about a hundred times smaller than the tabulated 3.1×10⁻³; the tabulated value would require Δφ_R ≈ 4.6. At a/√q = 0.99 the table implies Δφ_R ≈ 7.7, while Fig. 3 shows values around 1.5. So the claim that ABB lensing is distinguishable from Schwarzschild by large image separations is unsupported. The authors need to recompute Table I, or withdraw the claim. This is load-bearing, not cosmetic.\n\nSecond, Eq. (35) is asserted without derivation. The expansion mixes two small parameters (a and q), and the ordering of terms is not obvious; they should provide the series or a clear reference. Moderate.\n\nThird, the regular part Eq. (47) is evaluated only numerically, with no method, error control, or convergence check, and the Bozza quadratic truncation G ≈ Λ₁z + Λ₂z² is not tested near a/√q → 1. Minor to moderate.\n\nFinally, there is likely overlap with Ref. [105] from the same group; the paper should state what is new relative to that earlier work. Self-citation is not the issue; unacknowledged overlap is.\n\nWho it's for: people working on black-bounce lensing or analog-gravity observables. The analytic formulas are probably worth having, but not until the table is fixed.\n\nRecommendation: I would send this to peer review, asking the referee specifically to recompute Table I and check the weak-field expansion. If the table cannot be fixed, the observational claims fail and the paper reduces to a routine formula paper. Major revision before acceptance.","headline":"The analytic lensing formulas for the acoustic black-bounce are mostly consistent and the limits check out, but Table I—which carries the paper's main observational claim—contradicts the paper's own equations.","tokens_in":18112,"tokens_out":9049,"would_cite":false,"duration_ms":90238,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper derives analytic light-deflection formulas for the acoustic black-bounce spacetime and shows that its strong-field image separation can reach 0.24 of the shadow boundary, far above Schwarzschild's 0.001.","keywords":["acoustic black-bounce","gravitational lensing","light deflection","strong-field limit","photon sphere","relativistic images","Einstein ring"],"falsifier":"Numerically integrate the full deflection integral around Eq. (37) without replacing $G(z,\\rho_0)$ by $\\Lambda_1 z+\\Lambda_2 z^2$ for the Table I values, particularly $a/\\sqrt{q}=0.99$; if the exact deflection and the resulting $s/\\theta_\\infty$ disagree with Eq. (46) plus the regular part, the predicted enhancement is an artifact of the truncation rather than a property of the acoustic black-bounce metric.","tokens_in":16988,"feed_emoji":"🔭","tokens_out":10380,"duration_ms":92173,"temperature":0.7,"pith_summary":"The paper sets out to show that the acoustic black-bounce spacetime, a Simpson-Visser regularized version of an acoustic black hole, has a distinctive gravitational-lensing signature. It derives analytic formulas for the deflection of light in the weak-field limit and a logarithmic strong-field deflection near the photon sphere, then converts them into standard observables: the angular separation of relativistic images, the relative magnification of those images, and the Einstein ring radius. The paper's central quantitative claim is that when the throat radius $a$ is close to $\\sqrt{|q|}$, the normalized separation $s/\\theta_\\infty$ reaches about 0.24, orders of magnitude above the Schwarzschild value of roughly $10^{-3}$. The formulas reduce to the acoustic black hole when $a\\to0$ and to the Ellis-Bronnikov wormhole when $q\\to0$, which the authors use as consistency checks.","feed_headline":"Black-bounce parameter near 1 boosts lens image split to 0.24","feed_subtitle":"As throat radius a approaches √q, predicted image separation jumps from 10^-7 to 0.24, a testable signature.","key_machinery":"The carrying mechanism is the Bozza-Tsukamoto strong-field expansion of the deflection integral. Writing $z=1-\\rho_0/\\rho$, the integral's integrand $G(z,\\rho_0)$ is expanded near $z=0$ as $G(z,\\rho_0)\\simeq \\Lambda_1(\\rho_0)z+\\Lambda_2(\\rho_0)z^2$. The vanishing of $\\Lambda_1$ at the photon sphere forces a logarithmic divergence, and the coefficient $\\Lambda_2(\\rho_m)=4\\sqrt{3|q|}+4a^4/\\sqrt{3|q|}-8a^2$ controls the prefactor in Eq. (46). This expansion is the bridge from the metric functions to the observables $s$ and $\\tilde{r}$, and it is also what makes the $a\\to0$ limit reproduce the acoustic black hole.","core_discovery":"The central claim is that the acoustic black-bounce metric with $f(\\rho)=1-q^2/(\\rho^2+a^2)^2$ and $\\Sigma^2(\\rho)=\\rho^2+a^2$ produces a strong-field deflection whose divergent part near the photon sphere is $$\\$\\Delta$\\phi_D = -\\frac12\\sqrt{\\frac{\\sqrt{3}|q|}{\\sqrt{3}|q|-$a^{2}$}}\\,\\log\\left(\\frac{\\$\\beta$}{$3^{{3/4}}$\\sqrt{|q|/2}}-1\\right)+\\mathrm{const},$$ with a prefactor that grows as $a/\\sqrt{q}\\to1$. Together with a numerically evaluated regular part and the Bozza observable construction, this gives a normalized image separation $s/\\theta_\\infty$ that rises from $7.59\\times10^{-7}$ at $a/\\sqrt{q}=0.10$ to $2.42\\times10^{-1}$ at $a/\\sqrt{q}=0.99$, while the Schwarzschild value is about $10^{-3}$. In the weak-field regime the paper obtains $\\delta\\phi \\simeq \\pi a^2/(4\\beta^2) + 15\\pi q^2/(16\\beta^4) + 9\\pi a^4/(64\\beta^4) + 19\\pi a^2 q^2/(64\\beta^6) + 1545\\pi q^4/(1024\\beta^8)$, reducing to the Ellis-Bronnikov wormhole when $q\\to0$ and to the acoustic black hole when $a\\to0$. The conclusion is that strong-field lensing could distinguish the acoustic black-bounce spacetime from Schwarzschild, whereas the acoustic black hole alone would be far harder to resolve.","pith_inferences":["If the predicted jump near $a/\\sqrt{q}\\simeq0.9$ is real, then a single resolved relativistic-image separation above about $10^{-2}$ times the shadow radius would already disfavor both Schwarzschild and the acoustic black hole, assuming the lens mass and distances are known.","A direct numerical evaluation of the full deflection integral, without replacing $G(z,\\rho_0)$ by $\\Lambda_1 z+\\Lambda_2 z^2$, would settle whether the sharp enhancement at $a/\\sqrt{q}\\to1$ survives; the paper does not report that comparison.","The same observable pipeline could in principle be applied to a rotating or time-dependent acoustic black bounce or to other regularized metrics, an extension the paper leaves open."],"forward_implications":["If the acoustic black-bounce formulas are right, the normalized image separation $s/\\theta_\\infty$ spans about $7.6\\times10^{-7}$ to $2.4\\times10^{-1}$ as $a/\\sqrt{q}$ runs from 0.10 to 0.99, so the throat parameter is in principle measurable from strong-field lensing.","The acoustic black hole alone gives $s/\\theta_\\infty\\sim10^{-7}$, roughly four orders of magnitude below Schwarzschild, which means its relativistic images would be considerably harder to resolve.","In the $q\\to0$ limit the weak-field deflection becomes the Ellis-Bronnikov wormhole result, and in the $a\\to0$ limit it becomes the acoustic black hole result, so the paper's formulas interpolate between known limits.","The weak-field Einstein ring radius depends only on the throat radius $a$ and the distance ratios, not on the magnetic charge $q$, so measuring the ring would give a direct estimate of $a$."],"supporting_citations":[{"why":"Supplies the strong-field deflection expansion and the definitions of the observables $s$ and $\\tilde{r}$ that the paper applies to the acoustic black-bounce metric.","marker":"[52]"},{"why":"Improves the strong-field expansion method that the paper uses to obtain the logarithmic divergence near the photon sphere.","marker":"[53]"},{"why":"Gives the acoustic black-bounce metric as a solution of Einstein's equations supported by a phantom scalar field and nonlinear electrodynamics.","marker":"[29]"},{"why":"Introduces the Simpson-Visser regularization that converts the acoustic black hole into the acoustic black bounce.","marker":"[22]"},{"why":"Provides the exact Einstein-scalar-Gauss-Bonnet solution whose metric is the acoustic black hole used as the $a\\to0$ comparison.","marker":"[123]"},{"why":"Defines the canonical acoustic black hole metric used in Section III.","marker":"[108]"},{"why":"Establishes that acoustic perturbations in a fluid propagate like a scalar field in curved spacetime, the physical basis for acoustic black holes.","marker":"[107]"},{"why":"Gives the Ellis-Bronnikov wormhole result recovered in the $q\\to0$ weak-field limit.","marker":"[124]"}],"fun_headline_variants":["Acoustic black-bounce boosts lens image split to 0.24","Strong-field lensing distinguishes acoustic black-bounce from Schwarzschild","Lens image separation jumps 7 orders to 0.24 in acoustic black-bounce","Acoustic black-bounce lensing: strong-field splits reach 0.24","Acoustic black-bounce: lens split leaps to 0.24"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The strong-field predictions stand on the assumption that the light-bending function $G(z,\\rho_0)$ is faithfully represented by its first two Taylor terms near the photon sphere, and the paper does not quantify the error from dropping the remainder, especially as $a/\\sqrt{q}\\to1$.","fun_headline_variants_meta":{"raw":{"variants":["Acoustic black-bounce boosts lens image split to 0.24","Strong-field lensing distinguishes acoustic black-bounce from Schwarzschild","Lens image separation jumps 7 orders to 0.24 in acoustic black-bounce","Acoustic black-bounce lensing: strong-field splits reach 0.24","Acoustic black-bounce: lens split leaps to 0.24"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000879,"raw_usage":{"total_tokens":3855,"prompt_tokens":1054,"completion_tokens":2801,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":670,"completion_tokens_details":{"reasoning_tokens":2701}},"tokens_in":670,"tokens_out":2801,"duration_ms":19545,"temperature":1.0,"reasoning_tokens":2701,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:32:25.924088+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerically integrate the full deflection integral around Eq. (37) without replacing $G(z,\\rho_0)$ by $\\Lambda_1 z+\\Lambda_2 z^2$ for the Table I values, particularly $a/\\sqrt{q}=0.99$; if the exact deflection and the resulting $s/\\theta_\\infty$ disagree with Eq. (46) plus the regular part, the predicted enhancement is an artifact of the truncation rather than a property of the acoustic black-bounce metric.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the exact Einstein-scalar-Gauss-Bonnet solution whose metric is the acoustic black hole used as the $a\\to0$ comparison."},{"cited_title":"Gravitational lensing by $k-n$ generalized black-bounce space-times","cited_arxiv_id":"2504.19920","evidence_quote":"Establishes that acoustic perturbations in a fluid propagate like a scalar field in curved spacetime, the physical basis for acoustic black holes."},{"cited_title":"Ca˜ nate, J","cited_arxiv_id":null,"evidence_quote":"Gives the Ellis-Bronnikov wormhole result recovered in the $q\\to0$ weak-field limit."}],"review_version":1}