{"id":"3e9cdd63-c26c-48eb-9f76-94427bfeb41a","arxiv_id":"2505.07420","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"The authors derive strong- and weak-field lensing observables for the conical EiBI wormhole and find the cosmic string parameter increases image angular separation while decreasing brightness ratio.","lead":"This paper studies how a cosmic string piercing a wormhole in Eddington-inspired Born-Infeld gravity changes the bending of light and the resulting images, focusing on the strong-field limit. It claims the string increases image separation and decreases brightness ratio compared to the string-free Ellis-Bronnikov wormhole.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Impact parameter relation (Eq. 20 vs Eq. 21) is internally inconsistent, so the strong-field lens equation and the observables s and R are not derived from a single physical geometry; the quantitative results require re-derivation.","rationale":"The reader's weakest assumption identifies the same inconsistency between Eq. (20) and Eq. (21), and I agree that this is the load-bearing defect: every strong-field observable is derived after this step, and the weak-field Einstein radii use Eq. (20) directly. Independently, Eq. (28) also has the wrong distance/ψ scaling: from Eq. (26), dθ/dψ = 8aλ D_OS/(D_LS D_OL e^{(2n+1)aπ}), so μ_n should scale as D_OS/(D_LS ψ), not as (D_LS/D_OS)ψ as printed. These are internal algebraic inconsistencies rather than disagreements with consensus, and they invalidate the numerical tables and the claimed observability thresholds. The central deflection coefficient 1/a in Eq. (17) is derived correctly, so a corrected version might restore the qualitative conclusion; but for the present manuscript the reader's REJECT verdict should stand.","tokens_in":15677,"tokens_out":28714,"duration_ms":274072,"concrete_test":"Choose a concrete geometry (e.g., D_OL = 8.5 kpc, D_LS = 1 kpc) and derive the closest-approach radius r0 of a photon that reaches the observer with image angle θ from metric (3), including the conical factor a; this gives b/a = r0 ≈ D_OL θ (up to the conical angular factor). Substitute this relation into Eq. (17) and check whether it reproduces Eq. (21), then recompute θ0_n, s, and μ_n. Repeat using r0 ≈ D_LS θ. If the two computations disagree, the paper must state which relation is physical and regenerate Eqs. (24)–(34) and Tables 1–3 accordingly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The quantitative claims all pass through the relation between the impact parameter b and the image angle θ. Eq. (20) states b ≃ a D_LS θ, but the strong-field deflection angle in Eq. (21) contains log(D_OL θ/λ − 1), which corresponds to b ≃ a D_OL θ rather than to Eq. (20). Appendix A, which derives the D_LS version by setting u = 1/D_LS, does not describe the lens-plane geometry of Fig. 4. If the correct relation is the D_OL version, then Eq. (20) and Appendix A are wrong; if the D_LS version is intended, then θ0_n, s, and the image positions in Eqs. (24)–(26) are mis-scaled by D_LS/D_OL and all numerical tables are invalid. Because Eq. (30) for s and Eq. (31) for R are built on θ0_n and on the magnification ratio from Eq. (26), the headline a-dependence is not presently derived from any single consistent geometry. The weak-field lens equation (34) and the Einstein radii in Tables 2–3 also use Eq. (20), so they inherit the same ambiguity. The qualitative effect of a smaller a enhancing deflection may be plausible, but the paper's quantitative predictions are unsupported as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies gravitational lensing by a traversable wormhole in Eddington-inspired Born-Infeld (EiBI) gravity threaded by a cosmic string, using the metric of Eq. (3). It derives the deflection angle in both weak and strong field limits, constructs the strong-field lens equation, obtains image positions and magnifications, and defines the angular separation s and brightness ratio R. It then applies the formalism to Sagittarius A* and to bulge/LMC microlensing-like configurations, producing tables of Einstein angles and radii. The central claims are that the cosmic string parameter a increases the deflection relative to the Ellis-Bronnikov wormhole, that s grows and R decreases as a decreases, and that these observables are independent of the throat radius.","tokens_in":15930,"tokens_out":19577,"duration_ms":185421,"significance":"If the results were correct, the paper would provide a concrete, analytically tractable extension of strong-field lensing to a wormhole with a cosmic string, with parameters that are independently bounded: the EiBI parameter is constrained by GW170817/GRB170817A to |ε| ≤ 10^37 m^2, and the string tension is taken at the GUT scale, Gµ ∼ 10^-6. The derivation is analytic throughout and does not fit any free parameter to lensing data, and the paper checks the a → 1 limit against the Ellis-Bronnikov results. These are genuine strengths. The significance is currently conditional, however, because the quantitative predictions are built on an internally inconsistent set of distance relations and on a magnification formula that has the wrong scaling.","major_comments":[{"comment":"The impact-parameter relation is not consistent across the strong-field derivation. Eq. (20) states b ≃ a D_LS θ and Appendix A derives b = D_LS sin(aθ) by setting u = 1/D_LS in the conical-spacetime trajectory, but Eq. (21) uses Λ(θ) = -(1/a) log(D_OL θ/λ - 1) + (3/a) log 2 - π, which follows from Eq. (17) only if b/(aλ) = D_OL θ/λ, i.e. b = a D_OL θ. The lens-plane geometry of Fig. 4 places the observer at D_OL, not D_LS, so the Appendix A construction does not describe the angle θ seen by the observer. Because Eq. (24) for θ0_n, Eq. (25) for ΔΛ_n, Eq. (26) for image positions, Eq. (28) for magnifications, and Table 1 all carry D_OL, the strong-field observables are not derived from a single physical geometry. If the intended relation is b = a D_OL θ, then Eq. (20) and Appendix A are wrong; if b = a D_LS θ is intended, then θ∞ = λ/D_LS and the numerical values in Table 1 are mis-scaled. This must be resolved and all subsequent equations and tables re-derived consistently.","section":"§3, Eq. (28)"}],"minor_comments":[{"comment":"The sentence 'the magnification of n-th image increases exponentially with increasing n' is the opposite of what Eq. (28) implies: e^{(2n+1)aπ} appears in the denominator, so μ_n decreases as n grows. The following sentence, stating that the first image has the highest magnification, confirms the intended behavior; the wording should be corrected.","section":"§3, after Eq. (28)"},{"comment":"The conclusion states that the angular separation 'increase[s] as cosmic string parameter increases', but Eq. (30) gives s ∝ 8θ∞/e^{3aπ}, so s decreases as a increases (equivalently, increases as a decreases). This is also inconsistent with the body text after Eq. (30) and with the abstract's claim; the conclusion sentence should be corrected.","section":"§5, Conclusion"},{"comment":"The symbol L is used first for the Lagrangian in Eq. (4) and then for the conserved angular momentum in Eq. (6); the statement 'For the null geodesic, it is well known that L = 0' is confusing, since it is the Lagrangian that vanishes for null curves, not the angular momentum used in Eq. (7). Please use separate symbols.","section":"§2.2, around Eqs. (4)–(6)"},{"comment":"There are several typographical and wording errors, including 'Eills-Bronnikov' in the abstract, 'Bozzaa' for Bozza, 'ins-pired' in the title line, and 'deflection angel' in Section 2.2. A careful proofread is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper is a straightforward extension of Refs. [84,85,89,90] to strong-field lensing observables; the incremental novelty is modest but acceptable if the calculation is correct. The stress-test concern about the b–θ relation is confirmed on reading: Eq. (20) and Appendix A are not consistent with Eq. (21), and Eq. (34) does not follow from the stated relations. These are fixable in principle by re-deriving the lens equation with a single distance convention and recomputing the tables, so I do not recommend outright rejection, but the quantitative claims cannot be trusted in the present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a standard Bozza-formalism exercise applied to a known Ellis-Bronnikov-type metric with a cosmic string. The strong-field expansion and the s/R observables for this specific spacetime are not in the cited Ahmed papers, so the novelty, though modest, is real. The authors are honest about where the metric comes from, and the model parameters come from independent bounds, not fitted to data.\n\nWhat is good: the exact deflection angle is taken from prior work and the elliptic-integral expansion to Eq. (17) is standard and checks out. The idea that the string parameter changes the image separation and brightness ratio is plausible.\n\nThe problems are in the lensing geometry and the numerics. Eq. (20) sets b = a D_LS θ and Appendix A derives it, but Eq. (21) and everything after it use b = a D_OL θ, with D_OL appearing in the log. These are not interchangeable. If D_OL is right, Eq. (20) and Appendix A are wrong; if D_LS is right, then θ0_n, the image positions in Eq. (26), and the tables are all scaled by D_LS/D_OL and are wrong. The paper never chooses a single geometry.\n\nEq. (28) is also suspect. Differentiating the lens equation with Eq. (25) gives magnifications scaling as (1/ψ)(D_OS/D_LS), not as ψ D_LS/D_OS as printed. That error propagates into Figs. 5-6 and into the brightness ratio R. There is also a concrete numerical error in Table 1: for λ=10^9 km and D_OL=8.5 kpc, θ∞ should be about 786 microarcsec, not 0.786—a factor of 1000. The weak-field lens equation (34) does not follow from (19), (20), and (33) either; the constant term has the wrong distance combination.\n\nNone of this kills the qualitative claim that a<1 enhances strong deflection relative to a=1. But the quantitative predictions, including the distinguishability statements, are not supported as written. A corrected derivation and recomputed tables might make this a publishable routine extension. I would not cite it until that happens.\n\nRecommendation: send to a referee, because the errors are identifiable and fixable, but the current version should be rejected or returned for major revision rather than accepted.","headline":"A routine Bozza-formalism extension of a known conical EiBI wormhole whose quantitative results are undercut by inconsistent distance relations, a mis-scaled magnification, and a factor-1000 table error.","tokens_in":16487,"tokens_out":11568,"would_cite":false,"duration_ms":107928,"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":"A cosmic string threading an EiBI wormhole changes strong-field lensing observables: the first image's angular separation grows and its relative brightness falls as the string parameter a decreases.","keywords":["gravitational lensing","wormhole","cosmic string","Eddington-inspired Born-Infeld gravity","strong-field limit","deflection angle","relativistic images","Ellis-Bronnikov wormhole"],"falsifier":"Measure the angular separation $s$ and brightness ratio $R$ of the first two relativistic images around a candidate wormhole at sub-microarcsecond resolution. If the observed pair does not satisfy $R = (e^{-3a\\pi}+8e^{-6a\\pi})/(e^{-5a\\pi}+8e^{-10a\\pi})$ with the same $a$ that fits $s = 8\\theta_\\infty/e^{3a\\pi}$, the model's strong-field predictions fail.","tokens_in":15445,"feed_emoji":"🌌","tokens_out":11666,"duration_ms":99515,"temperature":0.7,"pith_summary":"The paper studies gravitational lensing by the simplest traversable wormhole in Eddington-inspired Born-Infeld (EiBI) gravity when a cosmic string passes through it. It aims to show that the string's conical deficit changes the strong-field deflection enough to be observable: for a fixed wormhole throat, a smaller string parameter $a$ (higher string tension) makes the first relativistic image sit farther from the others and makes the first image dimmer relative to the rest. These two observables, the angular separation $s$ and the brightness ratio $R$, come out independent of the wormhole throat radius, so measuring them would isolate the string's tension. The paper also computes Einstein radii for bulge and LMC lensing in the weak field, predicting larger image scales than the string-free EiBI wormhole. A sympathetic reader would care because this gives a concrete way to test both EiBI gravity and cosmic strings with strong lensing observations.","feed_headline":"Cosmic string boosts wormhole light bending","feed_subtitle":"Image spacing grows and brightness ratio shrinks with string tension, giving a clean lensing signature.","key_machinery":"The load-bearing object is the conical wormhole metric $ds^2 = -dt^2 + (1+\\varepsilon/r^2)^{-1}dr^2 + r^2(d\\theta^2+a^2\\sin^2\\theta\\,d\\phi^2)$, where $a=1-4G\\mu$ is the cosmic string parameter. The deflection angle is expressed through a complete elliptic integral of the first kind; in the strong-field limit $\\varepsilon=-\\lambda^2$ this collapses to the logarithmic form $\\Lambda(\\theta)=-(1/a)\\log(D_{OL}\\theta/\\lambda -1)+(3/a)\\log 2 -\\pi$. From that expansion the paper obtains the angular positions $\\theta_n$, magnifications $\\mu_n$, and the standard strong-lensing observables $s$ and $R$. The string parameter enters only through products like $a\\pi$ in exponentials, which is why $s$ and $R$ depend on $a$ alone.","core_discovery":"The central claim is that for the conical wormhole spacetime of EiBI gravity, the cosmic string parameter $a$ enters the strong-field lensing observables exponentially. With the throat radius $\\lambda$ and the deflection angle diverging logarithmically as the impact parameter approaches $a\\lambda$, the paper derives $s = 8\\theta_\\infty / e^{3a\\pi}$ and $R = (e^{-3a\\pi}+8e^{-6a\\pi})/(e^{-5a\\pi}+8e^{-10a\\pi})$. As $a$ decreases from 1, the angular separation $s$ grows and the brightness ratio $R$ falls, while both stay independent of the throat radius $\\lambda$. In the $a\\to 1$ limit the formulas reduce to the string-free wormhole case, and the authors argue the differences are large enough to distinguish the string-threaded EiBI wormhole from both the string-free wormhole and a Schwarzschild black hole using sub-microarcsecond observations.","pith_inferences":["If the string parameter is ignored, strong-lensing estimates of the wormhole throat radius from absolute image positions would be biased; ratios such as $R$ may be a more robust probe.","Measuring both $s$ and $R$ in the same lens system would over-determine $a$, because both are exponential functions of $a\\pi$; a mismatch between the two would reveal any error in how the impact parameter is related to image angle.","The same exponential scaling should appear in time delays between relativistic images, giving a complementary observable the paper does not compute.","Independent cosmic-string tension bounds from gravitational-wave backgrounds could be combined with these lensing predictions to accept or reject the EiBI wormhole interpretation."],"forward_implications":["In the strong-field limit, the angular separation $s$ grows exponentially as the string parameter $a$ drops, so higher-tension cosmic strings push the first relativistic image farther from the packed set of outer images.","The brightness ratio $R$ falls with the same parameter, so the first image becomes relatively fainter compared with the sum of all outer images.","Because $s$ and $R$ are independent of the wormhole throat radius, they provide a direct probe of string tension alone, without needing to know the throat size.","For throat radii around $10^{10}$-$10^{11}\\;\\mathrm{km}$ modeled on Sagittarius A*, the predicted angular separation is of the same order as the Schwarzschild strong-lensing separation, so high-resolution observations can distinguish the string-threaded EiBI wormhole from a Schwarzschild black hole.","In the weak-field limit the model predicts a single image whose magnification decreases as $a$ increases, with Einstein radii for bulge and LMC lensing larger than those of the string-free EiBI wormhole."],"supporting_citations":[{"why":"It supplies the EiBI wormhole-with-cosmic-string metric and the elliptic-integral deflection angle from which the strong-field analysis starts.","marker":"[89]"},{"why":"It introduces the strong-field lensing expansion and the s and R observables used to characterize the relativistic images.","marker":"[37]"},{"why":"It provides the string-free wormhole strong-deflection limit to which the a=1 case is compared.","marker":"[38]"},{"why":"It gives the logarithmic divergence form of the deflection angle used in Eq. (17).","marker":"[93]"},{"why":"It sets up the lens equation geometry and supplies the Schwarzschild observables used as a comparison baseline.","marker":"[94]"},{"why":"It presents an earlier strong-lensing computation in an EiBI spacetime with topological charge, used to benchmark the new results.","marker":"[84]"},{"why":"It imposes the GW170817 bound on the EiBI parameter that sets the wormhole throat radius scale.","marker":"[95]"},{"why":"It provides the bulge and LMC lensing parameter choices used for the weak-field Einstein radius estimates.","marker":"[96]"}],"fun_headline_variants":["Cosmic string widens wormhole image spacing","String tension shrinks wormhole brightness ratio","EiBI wormhole lensing reveals string-induced shifts","Wormhole deflection amplified by cosmic string"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predictions assume that the distance from the wormhole to the source, not the distance from the wormhole to the observer, controls how the cosmic string shrinks the apparent image angle; if that choice is wrong, the predicted image positions and magnifications are off by the ratio of those distances.","fun_headline_variants_meta":{"raw":{"variants":["Cosmic string widens wormhole image spacing","String tension shrinks wormhole brightness ratio","EiBI wormhole lensing reveals string-induced shifts","Wormhole deflection amplified by cosmic string"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000272,"raw_usage":{"total_tokens":1601,"prompt_tokens":884,"completion_tokens":717,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":500,"completion_tokens_details":{"reasoning_tokens":659}},"tokens_in":500,"tokens_out":717,"duration_ms":6993,"temperature":1.0,"reasoning_tokens":659,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:20:06.563532+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the angular separation $s$ and brightness ratio $R$ of the first two relativistic images around a candidate wormhole at sub-microarcsecond resolution. If the observed pair does not satisfy $R = (e^{-3a\\pi}+8e^{-6a\\pi})/(e^{-5a\\pi}+8e^{-10a\\pi})$ with the same $a$ that fits $s = 8\\theta_\\infty/e^{3a\\pi}$, the model's strong-field predictions fail.","supporting_citations":[{"cited_title":"Ahmed, Geodesics motion of test parti- cles around Schwarzschild-Klinkhamer worm- hole with topological defects and gravitational lensing, JCAP 11 (2023) 010","cited_arxiv_id":null,"evidence_quote":"It supplies the EiBI wormhole-with-cosmic-string metric and the elliptic-integral deflection angle from which the strong-field analysis starts."},{"cited_title":"Bozza, S","cited_arxiv_id":null,"evidence_quote":"It introduces the strong-field lensing expansion and the s and R observables used to characterize the relativistic images."},{"cited_title":"Tsukamoto, Strong deflection limit analysis and gravitational lensing of an Ellis wormhole, Phys","cited_arxiv_id":null,"evidence_quote":"It provides the string-free wormhole strong-deflection limit to which the a=1 case is compared."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It gives the logarithmic divergence form of the deflection angle used in Eq. (17)."},{"cited_title":"Furtado, J","cited_arxiv_id":null,"evidence_quote":"It presents an earlier strong-lensing computation in an EiBI spacetime with topological charge, used to benchmark the new results."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It imposes the GW170817 bound on the EiBI parameter that sets the wormhole throat radius scale."},{"cited_title":"Abe, Gravitational Microlensing by the Ellis Wormhole, Astrophys","cited_arxiv_id":null,"evidence_quote":"It provides the bulge and LMC lensing parameter choices used for the weak-field Einstein radius estimates."}],"review_version":1}