{"id":"a1b86258-2569-4394-ad78-ccfcca1d8045","arxiv_id":"2504.19282","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":10,"one_line_summary":"New f(Q) wormhole solutions are presented, but the claimed quasinormal-mode and grey-body signatures rest on an incorrect V''=0 assumption and produce an undefined grey-body factor.","lead":"This paper constructs two families of traversable wormhole solutions in f(Q) gravity with nonconstant redshift functions and studies their energy conditions, shadows, and ringing modes. It claims that negative non-metricity enlarges wormhole shadows and lowers quasinormal-mode frequencies, giving a possible observational signature of the modified gravity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim Im(ω0)=0 and the grey-body signature rest on V''00=0; direct differentiation gives V''00≠0, so the advertised non-metricity QNM signature is unsupported.","rationale":"The reader's weakest-assumption analysis and mine converge on the same load-bearing defect: the entire quasinormal-mode and grey-body-signature conclusion for both wormhole families is derived from V''00=0. Direct differentiation shows the second derivative is nonzero, so Im(ω0)=0 is not a consequence of the WKB equations; the damping rate is finite, and the grey-body formula (61) is being used in a regime where its denominator contains Im(ω0)=0. This is an internal inconsistency, not merely a disagreement with the broader literature: it invalidates the paper's central advertised claim that non-metricity imprints a distinct no-damping QNM signature. The algebraic construction of the wormhole solutions and the shadow computation may survive revision, but the QNM/grey-body result, which is featured in the abstract and concluding remarks, does not. The manuscript also itself notes that the potential for WH2 cannot be expressed in tortoise coordinates, yet QNMs are still assigned to WH2; this is secondary but reinforces the conclusion that the QNM section is not reliable. The verdict should remain as the reader stated: reject the preprint in its current form, with the understanding that the solution families could be salvaged after a corrected QNM treatment.","tokens_in":20649,"tokens_out":6629,"duration_ms":68328,"concrete_test":"Recompute the eikonal QNM for WH1 at (c1,c2)=(1,2), l=1, using the WKB formula (51) with V0=e^{2Φ}/r^2 and with V''00 computed as a second derivative with respect to the tortoise coordinate r*(r)=∫ e^{-Φ}(1-b/r)^{-1/2}dr at rph=sqrt(3/2). If Im(ω0) comes out negative and nonzero (about -0.4 in this sample) rather than zero, the paper's Im(ω0)=0 and the grey-body discussion are contradicted. A minimal algebraic cross-check is also decisive: at rph, the constraint (15) gives Φ''=-4/rph^2, hence d^2V0/dr^2=-6e^{2Φ}/rph^4≠0, so the asserted V''00=0 cannot hold.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The advertised new result is the Section 6 Remark that more negative Q gives larger shadow and smaller Re(ω0), with Im(ω0)=0 (no damping), used to claim stable wormhole QNMs and a distinct non-metricity signature. The load-bearing step is the sentence after Eq. (62): at the photon sphere rT=rph, V02=V''00=0. This is false. For V0(r)=e^{2Φ(r)}/r^2, V0'=2e^{2Φ}r^{-3}(rΦ'-1), so rΦ'=1 is a stationary point, but V0'' is not forced to vanish. For WH1, Φ=ln(c2-c1/r^2), b=1/r^3, rph=sqrt(3c1/c2), and Eq. (15) gives Φ''=-4/rph^2 at rph. Then d^2V0/dr^2 = 2e^{2Φ}r^{-3}(Φ'+rΦ'') = -6e^{2Φ}/rph^4 ≠ 0; with respect to the tortoise coordinate this is multiplied by (1-b/rph) ≠ 0, so V''00<0. For example (c1,c2)=(1,2) gives V00≈1.185 and V''00≈-1.48. Therefore Eqs. (51)-(59) do not yield Im(ω0)=0; they give a finite damping rate. Consequently Eq. (61) is not evaluated at Im(ω0)=0; the grey-body limit argument is based on a singular or zero-damping expression, and the interpretation of frequencies above the threshold as 'infinite transmission' misreads the formula. The QNM and grey-body section therefore does not support the advertised non-metricity signature. The shadow analysis is a separate claim and could survive a corrected QNM treatment.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript constructs two static spherically symmetric traversable-wormhole solutions in f(Q)=alpha Q^n gravity with nonconstant redshift functions (Eqs. (16)-(19) and (21)-(24)), checks the throat, flaring-out, asymptotic-flatness, and energy conditions in Section 3, computes photon-sphere shadows in Section 4, and then applies WKB eikonal methods to obtain quasinormal-mode frequencies and grey-body factors in Sections 5-6. The advertised result is that negative non-metricity Q enlarges the shadow and lowers Re(omega0), while Im(omega0)=0, so the wormholes are stable and undamped, giving a distinct observational signature of non-metricity. The paper itself flags restrictions: Q is singular at r=sqrt(c1/c2) for WH1, and the power-law f(Q) diverges as Q approaches 0 for n<1, so integer n>=1 is used.","tokens_in":21031,"tokens_out":13381,"duration_ms":124261,"significance":"The paper has useful elements: explicit wormhole solutions with checked flaring-out and asymptotic-flatness conditions, a clear energy-condition analysis, and an explicit admission that for WH1 the non-metricity scalar is singular at r=sqrt(c1/c2) and that the power-law model diverges as Q approaches 0 for n<1. If a fully corrected QNM computation were supplied, the shadow analysis could serve as a starting point for comparing f(Q) wormholes with EHT observations. However, the central result of Section 6 is built on a false curvature condition; after correcting it, Im(omega0) is nonzero and the advertised undamped, stable QNM signature disappears. The circular substitution of integration constants in terms of Re(omega0) means that Figs. 9-10 do not demonstrate a physical effect, and the grey-body interpretation is incorrect. The shadow claim additionally assumes the black-hole photon-sphere formula without a wormhole-specific derivation and uses parameter choices with a photon sphere inside the throat or a singular Q at the throat. The paper's principal advertised conclusion is therefore not established.","major_comments":[{"comment":"The statement immediately after Eq. (62) that at the photon sphere V02=V00''=0 is false. For V0(r)=exp(2Phi(r))/r^2, the photon-sphere condition rPhi'(r)=1 makes V0'(rph)=0, but V0''(rph) is not forced to vanish. For WH1 with Phi(r)=ln(c2-c1/r^2), direct differentiation gives V0''(rph)=-6 exp(2Phi(rph))/rph^4, and in the tortoise coordinate the second derivative is multiplied by exp(-2Phi(rph))(1-b(rph)/rph), which is nonzero. For (c1,c2)=(1,2) one obtains rph approximately 1.225 and V_{rT}'' approximately -1.48. Consequently Eqs. (58)-(59) yield Im(omega0)=-1/2 sqrt(-V02/(2V00)) not equal to zero, rather than Eq. (64); the advertised Im(omega0)=0, the stability statement, and the grey-body discussion built on Eq. (61) are not supported.","section":"Section 6, Eqs. (62)-(64)"},{"comment":"The analysis presented as an effect of non-metricity is circular. Eq. (65) is inverted to express c2 in terms of Re(omega0), rph, and c1, and Eq. (66) is inverted to express Phi0 in terms of Re(omega0) and rph; these values are then inserted into Q(r) and plotted against chosen values of Re(omega0). The resulting monotonic relation between Q and Re(omega0) is therefore constructed by definition rather than derived from the dynamics, so Figs. 9-10 provide no independent evidence that non-metricity lowers the quasinormal frequency.","section":"Section 6, Eqs. (65)-(67) and Figs. 9-10"},{"comment":"The grey-body interpretation misreads the WKB transmission formula. Eq. (61) is derived under the assumption Im(omega0) is nonzero; if Im(omega0)=0 the expression is singular. Taking the limit Im(omega0) approaching 0 from above gives Gamma_l(Omega) approaching 1 for Omega<Re(omega0) and Gamma_l(Omega) approaching 0 for Omega>Re(omega0), not an infinite transmission for frequencies above the threshold. The statement in the paragraph after Eq. (61) that a frequency above Omega0 gives infinite transmission is therefore incorrect, and the claimed threshold behavior does not follow.","section":"Section 6, Eq. (61) and following paragraph"},{"comment":"The shadow radius is taken as rsh=rph exp(-Phi(rph)), which is the standard black-hole photon-sphere result, but no justification is given for applying this formula to a traversable wormhole with two asymptotic regions. In a wormhole, a photon with impact parameter below the critical value can pass through the throat rather than being captured, so the definition of the shadow and the relation between rph and the observed boundary must be derived for the two-sided geometry. Without this, the quantitative claim that negative Q enlarges the shadow is not established.","section":"Section 4, Eq. (40)"},{"comment":"The parameter choices used in the shadow plots are inconsistent with the stated domain r>=r0=1. For (c1,c2)=(0.2,2), the photon-sphere equation rPhi'(r)=1 gives rph=sqrt(3c1/c2)=0.548, which is smaller than r0, so the photon sphere lies inside the throat and Eq. (40) cannot be used. For (c1,c2)=(1,1), the non-metricity scalar in Eq. (20) is singular at the throat r=1, a regime that Section 7 explicitly says is avoided. Only the set (c1,c2)=(1,2) appears to lie in the admissible exterior region.","section":"Section 4.3, Figs. 4-5"}],"minor_comments":[{"comment":"Eq. (20) appears to be algebraically inconsistent with Eq. (11) and the redshift function in Eq. (16): combining 2Phi'(r)+1/r gives a numerator 3c1+c2r^2, not c1+c2r^2, before division by c2-c1/r^2; please verify the display.","section":"Section 3.1, Eq. (20)"},{"comment":"The displayed expression for Re(omega0) in Eq. (65) and the substitution c2=Re(omega0)*rph/l+c1/rph^2 are inconsistent with Eq. (63), which contains a square root; the correct inversion is c2=(rph Re(omega0)/l)^2+c1/rph^2.","section":"Section 6, Eq. (65)"},{"comment":"The stability condition is written as 'Im(omega0 <= 0)' in the Remark; this should be stated as Im(omega0) <= 0.","section":"Section 6, Remark"},{"comment":"The notation V0 is used both for the l-independent coefficient in the expansion (55) and for the maximum of the full potential in Eq. (51); V00 and V02 are introduced without explicit definitions in terms of V0(rph) and its second tortoise-coordinate derivative, which makes the eikonal formulas unnecessarily hard to follow.","section":"Section 5, Eqs. (55)-(59)"},{"comment":"The discussion of the Raychaudhuri equation is internally inconsistent: it says NEC violation leads to geodesic focusing or convergence, while the following sentences correctly state that R_mu nu k^mu k^nu<0, i.e., NEC violation, is the criterion for defocusing; please reconcile these statements.","section":"Section 2.2, Eq. (10)"},{"comment":"Reference [8] is incomplete as printed ('Phys. Dark Univ. 47(8):101793' with no year), and a few references are cited in duplicated or ambiguous forms; please standardize the bibliography.","section":"References"}],"recommendation":"reject","confidential_remarks":"The central advertised result of the paper, Im(omega0)=0 and the associated non-metricity signature, is founded on a false assertion about the second derivative of the eikonal potential at the photon sphere. The subsequent grey-body and stability discussion inherits this error, and the parameter plots in Section 6 are circular. I do not see a way to preserve the manuscript's main conclusion within the current scope; a substantially rewritten QNM analysis would be needed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What should you know about this paper? The two wormhole families are new and the algebra up to the shadow section is mostly sound, but the quasinormal-mode section has a load-bearing error: the claim that V''00=0 at the photon sphere is false for WH1, so Im(ω0)=0 and the grey-body conclusions do not follow. The advertised non-metricity signature in QNMs is unsupported.\n\nThe genuinely new piece is Section 3: two traversable wormhole solutions in f(Q) gravity with nonconstant redshift—one with b=1/r^3 and Φ=ln(c2−c1/r^2), one with an exponential shape function—both checked for asymptotic flatness, flaring-out, and energy conditions. That part appears internally consistent; the field equations are solved correctly as far as I checked, and the parameter choices are reasonable. The shadow analysis is standard eikonal applied to these metrics, and the qualitative claim that more negative Q gives a larger shadow is plausible, though it rests on the unstated assumption that the usual r_sh=r_ph e^{−Φ(r_ph)} formula carries over to a two-sided wormhole geometry. That deserves at least a sentence of justification.\n\nThe soft spot is Section 6, and it is not minor. After Eq. (62) they assert V02=V''00=0 at the photon sphere. Direct differentiation of V0=e^{2Φ}/r^2 gives V''0=2e^{2Φ}r^{−4}(1+r^2Φ''). For WH1 at rΦ'=1, Φ''=−4/r^2, so V''00=−6e^{2Φ}/r^4 ≠ 0. Consequently the WKB formula gives a finite (negative) Im(ω0), not zero, and the grey-body factor in Eq. (61) is evaluated in a singular limit. The subsequent discussion of 'infinite transmission' above the threshold misreads the formula. On top of that, Eqs. (65)–(67) and Figures 9–10 re-express the integration constants in terms of Re(ω0) and then plot Q(r) as if this were an independent prediction; it is a reparameterization.\n\nThe shadow and energy-condition results could survive a corrected treatment; the QNM claims are the centerpiece of the abstract and cannot. I would not advise citing this as a source for QNM behaviour in f(Q) wormholes, but the solution families might be of interest to people constructing wormhole spacetimes in modified gravity.\n\nFor peer review: it deserves a serious referee—the solution construction is careful enough, and the QNM mistake is exactly the kind of thing a referee should catch. But as is, I would recommend reject, with a clear path to resubmission if the QNM section is reworked or removed.","headline":"New f(Q) wormhole solutions, but the advertised QNM signature rests on a false V''00=0 and the grey-body argument is broken.","tokens_in":21621,"tokens_out":4767,"would_cite":false,"duration_ms":41991,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83C57","83C15"],"pacs":["04.50.Kd","04.70.Bw"],"model":"deepseek-v4-flash","headline":"In f(Q) gravity, negative non-metricity enlarges traversable-wormhole shadows and sets the quasinormal-mode imaginary frequency to zero, a signature that could separate wormholes from black holes.","keywords":["traversable wormholes","f(Q) gravity","non-metricity scalar","photon shadow","quasinormal modes","grey body factors","energy conditions","Morris-Thorne metric"],"falsifier":"Evaluate V0''(r_T) from V0(r_T)=$e^{{2Φ(r_T)}}$/r_T² at the largest positive root of rΦ'(r)=1. For WH1, direct differentiation gives V0''(rph) = -$6e^{{2Φ(rph)}}$/$rph^{4}$ ≠ 0, so the eikonal formula would yield Im(ω0)≠0; checking this one derivative settles whether the no-damping and near-unity grey-body conclusions are correct.","tokens_in":20360,"feed_emoji":"🕳️","tokens_out":8764,"duration_ms":74765,"temperature":0.7,"pith_summary":"The paper constructs two traversable Morris–Thorne wormhole solutions in f(Q) gravity with a power-law model f(Q)=αQ^n, verifies their asymptotic flatness, flaring-out condition, and energy conditions, and then computes their photon shadows and quasinormal-mode spectra. Its central claim is that negative non-metricity Q acts like repulsive gravity: it is what allows a photon shadow to form, it enlarges the shadow radius as Q becomes more negative, and it lowers the real part of the fundamental quasinormal frequency while leaving the imaginary part zero, meaning the modes are undamped and the wormhole is stable. These signatures are presented as a distinct observational fingerprint of non-metricity, one that could in principle distinguish an f(Q) wormhole from a black hole through high-resolution imaging and gravitational-wave ringdown observations. The connection matters because wormhole candidates are otherwise very hard to tell apart from black holes in current telescope images.","feed_headline":"Wormhole shadows grow as non-metricity turns negative","feed_subtitle":"Power-law f(Q) gravity links repulsive non-metricity to larger shadows, softer oscillation tones, and undamped modes.","key_machinery":"The machinery is the eikonal (large-l) limit of the Schrödinger-like perturbation equation (d²/dr_T²+ω²-V)Ψ=0, with V(r)=$e^{{2Φ}}$[l(l+1)/r² - (rb'-b)/(2r³) + Φ'(r)(1-b/r)/r]. Its l² part is V0(r_T)=$e^{{2Φ(r_T)}}$/r_T², whose maximum fixes the photon sphere via rΦ'(r)=1; the shadow radius is then rsh=rph $e^{{-Φ(rph)}}$. The WKB eikonal formula gives Re(ω0)=l√V00 and Im(ω0)=-(1/2)√(-V0''/(2V00)), and the paper's Im(ω0)=0 follows from asserting V0''(rph)=0. The wormhole solutions are generated from the ansatz f(Q)=αQ^n combined with non-constant redshift functions and the shape functions b(r)=b0/r³ (WH1) and b(r)=-(4μ1/λ)$e^{{-λr}}$(1+3/(λr)+6/(λ²r²)+6/(λ³r³)) (WH2).","core_discovery":"The central claim is that in both wormhole solutions the observational quantities respond monotonically to the sign and magnitude of the non-metricity scalar: for Q<0 the effective potential develops a barrier that traps photons, the shadow radius rsh=rph $e^{{-Φ(rph)}}$ increases as Q becomes more negative, and the eikonal quasinormal frequency Re(ω0)=l $e^{{Φ(rph)}}$/rph decreases while Im(ω0)=0. The paper interprets the vanishing imaginary part as the absence of damping and therefore stability, and it reads the combination of a larger shadow, a softer oscillation tone, and near-total grey-body transmission below the threshold frequency as the signature that would separate this wormhole from a black hole. The final remark condenses the claim: 'more repulsive is the gravity, larger is the radius of the shadow and smaller will be the frequency of oscillation.'","pith_inferences":["If the shadow–QNM correspondence is robust, the product rsh × Re(ω0) equals the angular momentum number l, a parameter-free relation that could be tested whenever the same compact object is observed both by imaging and by ringdown analysis.","Extending the calculation to rotating wormholes, the spin-induced splitting of the quasinormal spectrum would provide a sharper discriminator between f(Q) wormholes and Kerr black holes than the spherically symmetric case.","The no-damping conclusion depends on a single second derivative of the eikonal potential; computing that derivative numerically for the exact perturbation equation would show whether Im(ω0)=0 is an artifact of the WKB shortcut."],"forward_implications":["A wormhole with f(Q)=αQ^n and negative non-metricity would appear to a distant observer with a photon shadow whose radius grows monotonically as Q becomes more negative, giving a concrete prediction for high-resolution imaging campaigns.","The real part of the fundamental quasinormal frequency decreases with more negative Q, so any ringdown-like signal from such a wormhole would be lower-pitched than the signal from a comparable black hole.","With Im(ω0)=0, the modes do not damp, so instead of the decaying 'ringdown' of a black hole the wormhole would show a long-lived oscillatory response.","The grey-body factor Γ_l(Ω) tends to unity for frequencies below the threshold Re(ω0), meaning low-frequency radiation passes through the throat with almost no reflection.","Because both the shadow radius and the oscillation frequency are controlled by the same factor e^{Φ(rph)}/rph, measuring one fixes the other within this model."],"supporting_citations":[{"why":"Supplies the null-geodesic derivation and the shadow-radius formula rsh=rph e^{-Φ(rph)} used for both wormholes.","marker":"[8]"},{"why":"Introduces the symmetric-teleparallel f(Q) action that defines the gravity theory being tested.","marker":"[10]"},{"why":"Provides the f(Q) field equations in the Morris–Thorne metric that determine the wormhole density and pressures.","marker":"[21]"},{"why":"Gives the Schrödinger-like perturbation equation and the quasinormal-mode/grey-body-factor correspondence invoked in the eikonal analysis.","marker":"[28]"},{"why":"Supplies the WKB treatment of quasinormal modes and the Im(ω)≤0 stability criterion used to read off the no-damping result.","marker":"[29]"},{"why":"Provides the field equations and non-metricity scalar expressions for the wormhole configurations.","marker":"[33]"},{"why":"Motivates the power-law f(Q)=αQ^n model that the two solutions are built on.","marker":"[34]"}],"fun_headline_variants":["Repulsive gravity enlarges wormhole shadows, lowers tone","Non-metricity negative: bigger shadows, softer quasinormal ring","Wormhole shadow grows as non-metricity turns repulsive","Quasinormal tone softens as wormhole shadow expands"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The no-damping conclusion rests on the assertion that the eikonal potential has vanishing second derivative at the photon sphere, V0''(rph)=0; if that derivative is nonzero, the imaginary part of the quasinormal frequency does not vanish and the modes would damp.","fun_headline_variants_meta":{"raw":{"variants":["Repulsive gravity enlarges wormhole shadows, lowers tone","Non-metricity negative: bigger shadows, softer quasinormal ring","Wormhole shadow grows as non-metricity turns repulsive","Quasinormal tone softens as wormhole shadow expands"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000241,"raw_usage":{"total_tokens":1471,"prompt_tokens":845,"completion_tokens":626,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":461,"completion_tokens_details":{"reasoning_tokens":554}},"tokens_in":461,"tokens_out":626,"duration_ms":5296,"temperature":1.0,"reasoning_tokens":554,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:56:30.532400+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate V0''(r_T) from V0(r_T)=$e^{{2Φ(r_T)}}$/r_T² at the largest positive root of rΦ'(r)=1. For WH1, direct differentiation gives V0''(rph) = -$6e^{{2Φ(rph)}}$/$rph^{4}$ ≠ 0, so the eikonal formula would yield Im(ω0)≠0; checking this one derivative settles whether the no-damping and near-unity grey-body conclusions are correct.","supporting_citations":[{"cited_title":"Dark Univ","cited_arxiv_id":null,"evidence_quote":"Supplies the null-geodesic derivation and the shadow-radius formula rsh=rph e^{-Φ(rph)} used for both wormholes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the symmetric-teleparallel f(Q) action that defines the gravity theory being tested."},{"cited_title":"Sahoo, Fortschr","cited_arxiv_id":null,"evidence_quote":"Provides the f(Q) field equations in the Morris–Thorne metric that determine the wormhole density and pressures."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the field equations and non-metricity scalar expressions for the wormhole configurations."},{"cited_title":"Chakraborty and S","cited_arxiv_id":null,"evidence_quote":"Motivates the power-law f(Q)=αQ^n model that the two solutions are built on."}],"review_version":1}