{"id":"8c6b4e47-2a5e-46b0-9998-25dff0669f4e","arxiv_id":"2505.04952","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"The thesis derives traversable wormhole solutions in f(Q) and f(Q,T) gravity for several matter models, all violating the null energy condition at the throat.","lead":"This PhD thesis constructs traversable wormhole solutions in modified theories of gravity called f(Q) and f(Q,T) gravity. It shows that certain linear models, combined with dark matter profiles or exotic matter equations of state, produce wormhole geometries that satisfy the necessary flare-out condition while violating the null energy condition at the throat.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The f(Q) dark-matter shape functions are not asymptotically flat, so the claimed 'viable wormholes' fail a stated Morris-Thorne condition.","rationale":"The reader's weakest assumption, the monopole energy-momentum simplification in Eq. (2.10), is plausible but not the sharpest point. The asymptotic-flatness failure is directly checkable from the thesis's own equations and affects the primary example classes in Chapter 2. The limit calculation is elementary: the leading term in b(r)/r is a constant set by eta and rho_s, not zero. This contradicts the figure captions and the conclusions, which repeatedly claim the asymptotic flatness condition is satisfied. A second, compounding issue is that the abstract's statement that 'the monopole charge eta driving NEC violation' is not supported by the thesis's own Eq. (2.28), where eta^2 enters with a positive sign in (rho + p_r) at the throat, so larger eta makes the radial NEC less negative; Sec. 2.7 itself concedes that monopole charges exert 'minimal influence.' These problems do not automatically invalidate Chapters 3-5, which are independent constructions in f(Q,T) gravity with MIT bag and noncommutative sources, so the overall CONDITIONAL verdict remains appropriate. However, the f(Q) dark-matter-halo claims in Chapter 2 need correction: either the wormholes should be presented as conical/global-monopole backgrounds, or a genuinely asymptotically flat shape function must be supplied.","tokens_in":64481,"tokens_out":16808,"duration_ms":167055,"concrete_test":"Evaluate lim_{r->inf} b(r)/r symbolically for the shape functions in Eqs. (2.23) and (2.38) with the parameter values used in Figs. 2.1 and 2.6. If the limit is nonzero, as the algebra indicates, then the asymptotic-flatness claims in Fig. 2.1, Fig. 2.6, and the Chapter 2 conclusions are false; a valid wormhole would require b(r)/r -> 0, or the solutions should be explicitly reclassified as conical global-monopole backgrounds rather than asymptotically flat wormholes.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Chapter 2's central existence claim rests on shape functions b(r) that are said to satisfy asymptotic flatness, but the exact limits contradict this. For the Pseudo-Isothermal profile, Eq. (2.23) gives lim_{r->inf} b(r)/r = 8*pi*(eta^2 + rho_s r_s^2)/alpha, and for the NFW profile, Eq. (2.38) gives lim_{r->inf} b(r)/r = 8*pi*eta^2/alpha. Both limits are nonzero for the parameter values used in Figs. 2.1 and 2.6 (alpha = -5, rho_s = 0.02, r_s = 0.5, eta = 0.15). A nonzero limit means the metric is not asymptotically flat; it is asymptotically conical, so the Morris-Thorne condition (3) stated in Sec. 1.2.2 is not met. The figures only plot r up to about 4, where b/r is still falling, giving the misleading impression that the limit is zero. Because the flare-out condition alone is insufficient for a traversable wormhole, the f(Q) dark-matter-halo solutions of Secs. 2.4.1 and 2.4.2 do not establish the claimed 'viable WHs.'","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The thesis studies static, spherically symmetric Morris-Thorne wormholes in symmetric teleparallel gravity and its f(Q,T) extension. Chapter 2 derives f(Q) wormhole solutions supported by pseudo-isothermal and Navarro-Frenk-White dark matter profiles with a global monopole charge, for linear and nonlinear f(Q) models. Chapter 3 studies f(Q,T) gravity with barotropic and anisotropic equations of state; Chapter 4 uses the MIT bag model with two assumed shape functions; Chapter 5 considers noncommutative Gaussian and Lorentzian sources. The recurring claims are that the shape functions satisfy the flare-out, throat, and asymptotic flatness conditions, that the null energy condition is violated at the throat, and that the solutions are stable under the Tolman-Oppenheimer-Volkoff analysis.","tokens_in":64713,"tokens_out":6776,"duration_ms":66660,"significance":"The thesis provides systematic derivations of wormhole field equations in f(Q) and f(Q,T) gravity, explicit shape functions for several matter models, parameter-range tables, volume-integral estimates, and TOV force-balance checks. The later chapters, especially Chapter 3 and Chapter 4, use power-law or asymptotically constant shape functions that do satisfy the stated Morris-Thorne conditions for the chosen parameters, and the parameter tables in Chapter 3 are a useful organizational contribution. However, the central existence claim of Chapter 2 is not correct for the stated parameter choices: the dark-matter-supported shape functions of Sections 2.4.1 and 2.4.2 are not asymptotically flat, and the alleged role of the monopole charge in driving NEC violation is contradicted by the explicit throat expressions. Because the abstract and the chapter conclusions rest on these solutions, the main claim of the thesis is not established.","major_comments":[{"comment":"The pseudo-isothermal shape function is not asymptotically flat. Directly from Eq. (2.23), lim_{r→∞} b(r)/r = 8π(η^2 + ρ_s r_s^2)/α, which is nonzero for the parameter values used in Figs. 2.1-2.5 (α = -5, ρ_s = 0.02, r_s = 0.5). For these values the limit is negative and b(r) itself becomes negative for sufficiently large r, so the metric does not approach Minkowski space and the Morris-Thorne condition (3) stated in Sec. 1.2.2 is violated. Figures 2.1-2.5 only extend to r ≈ 4, which hides the wrong asymptotic behavior. The conclusion in Sec. 2.7 that these are viable wormhole solutions is therefore not supported.","section":"Sec. 2.4.1, Eq. (2.23)"},{"comment":"The NFW-profile shape function has the same defect: lim_{r→∞} b(r)/r = 8πη^2/α, which is nonzero for the monopole parameters used throughout the chapter. In addition, the ρ_s term contributes a logarithmic growth in b(r), so b(r)/r decreases only logarithmically. The only way to obtain b(r)/r → 0 is η = 0, but then the claimed role of the monopole charge as the source of NEC violation is removed. Thus the NFW solutions of Sec. 2.4.2 fail the stated asymptotic flatness criterion for every case in which the monopole is active.","section":"Sec. 2.4.2, Eq. (2.38)"},{"comment":"The reduction of the monopole energy-momentum tensor to T^t_t = T^r_r = -η^2/r^2 truncates the gradient and self-interaction terms of Eqs. (2.7)-(2.9) without solving the Euler-Lagrange equation (2.5) or bounding the neglected terms. Near the throat, where b(r)/r → 1, the coefficient (1 - b/r) multiplying (F')^2 changes character, so the approximation cannot be assumed to be uniform. Since this reduction underlies all f(Q) results of Chapter 2, the derived shape functions and energy conditions are not established.","section":"Sec. 2.2, Eq. (2.10)"},{"comment":"The abstract's statement that the monopole parameter η drives NEC violation is contradicted by the explicit throat expressions. For α = -5, r0 = 1, ρ_s = 0.02, r_s = 0.5, Eq. (2.28) gives ρ + p_r at the throat equal to α/(8π) + η^2 + 0.004 (in the units used there), which becomes less negative as η increases. The violation is dominated by the negative α, not by η. This reverses the claimed physical mechanism and should be corrected or removed.","section":"Sec. 2.4.1, Eqs. (2.28), (2.32), (2.36)"},{"comment":"The parameter values α = -5, ρ_s = 0.02, r_s = 0.5 are chosen by hand to produce the displayed plots, and no observational constraints or error estimates are provided. Statements such as \"physically viable in the framework of f(Q) gravity\" in Sec. 2.7 therefore overstate the results, which at most demonstrate formal existence for a tuned, dimensionless parameter set.","section":"Sec. 2.4.3, Tables 2.1-2.2"}],"minor_comments":[{"comment":"The surrounding text labels G_μν as the \"Einstein tenor\"; this should be \"Einstein tensor\".","section":"Sec. 1.7, Eq. (1.12)"},{"comment":"The captions contain typographical errors: \"valus\" should be \"values\" in Fig. 4.2, and \"wih\" should be \"with\" in Fig. 5.5.","section":"Captions of Figs. 4.2 and 5.5"},{"comment":"Several displayed formulas have unbalanced parentheses or awkward line breaks that make independent verification difficult; please re-typeset these expressions carefully.","section":"Eqs. (2.53)-(2.55) and (3.7)-(3.9)"},{"comment":"The use of Birkhoff's theorem for f(Q,T) gravity is presented as a conjecture supported by references [201,202]; this should be explicitly stated as an assumption throughout the construction, since the cited results concern teleparallel and generalized teleparallel settings rather than f(Q,T) gravity directly.","section":"Sec. 4.2"},{"comment":"The tables of permissible parameter ranges should state explicitly whether they are derived only from the asymptotic-flatness requirement b(r)/r → 0 or also from positivity of the energy density and other physical conditions.","section":"Secs. 3.3 and 2.6"}],"recommendation":"reject","confidential_remarks":"The manuscript is a compilation of published papers, and the referee's main concern is a correctness issue in the central Chapter 2 claim rather than a presentation issue. The asymptotic flatness failure of Eqs. (2.23) and (2.38) is checkable in a few lines and cannot be repaired by a parameter choice while preserving the claimed monopole-driven NEC violation. The later chapters may contain useful material, but as submitted the abstract's headline claim is false; a major reworking of Chapter 2, or its removal and a corresponding revision of the claims, would be needed before the thesis could be considered sound."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thesis is a compilation of five papers that are already in the literature (EPJ Plus, CPC, PD Universe). The genuinely new material is the introductory chapter and the packaging; the results themselves are not new relative to the cited work. That said, the derivations are careful, the energy-condition tables are useful, and the TOV/VIQ/lensing sections show the author can execute standard wormhole machinery competently.\n\nThe main problem is in Chapter 2. The paper claims the PI and NFW shape functions satisfy the Morris-Thorne asymptotic flatness condition, but the exact limits contradict that. For Eq. (2.23), b(r)/r tends to 8π(η^2 + ρ_s r_s^2)/α; for Eq. (2.38) it tends to 8πη^2/α. For the parameters plotted in the figures (α = −5, η = 0.15, ρ_s = 0.02, r_s = 0.5), those limits are about −0.14 and −0.11, not zero. The figures only go to r = 4, where b/r is still falling, so they give a misleading impression. The geometry is asymptotically conical, not flat. That directly undercuts the \"viable WH\" claim in the abstract for the dark-matter examples. The other chapters' shape functions do tend to zero, so the issue is localized, but it is load-bearing in the chapter that motivates the thesis.\n\nA second soft spot is the monopole approximation. Setting the gradient and self-interaction terms to zero to get \\bar T^t_t = \\bar T^r_r = −η^2/r^2 is a strong assumption; the paper hand-waves it with \"it is difficult to get a precise analytical solution.\" Near the throat, where F(r) is not constant, this could change the shape functions and energy conditions.\n\nThe NEC violation itself is generic: any traversable wormhole with flare-out violates NEC at the throat. Attributing the violation to the monopole charge is therefore an overstatement. The hand-chosen parameters with no observational constraints are a minor issue in this subfield.\n\nI would send this to a serious referee. The math is checkable and mostly right, but the Chapter 2 asymptotic-flatness error needs to be caught and the claims tempered. If this is a PhD thesis, the committee should ask for that correction; if it is a journal submission, it is a derivative compilation and I would only accept it as a review or extended version.","headline":"A careful compilation of five published wormhole papers; Chapter 2's dark-matter solutions are not asymptotically flat, which undercuts the headline viability claim.","tokens_in":65306,"tokens_out":3757,"would_cite":false,"duration_ms":37410,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83C15"],"pacs":["04.50.Kd","04.20.Jb"],"model":"deepseek-v4-flash","headline":"The study claims traversable wormhole solutions satisfying the flare-out condition exist in linear f(Q) and f(Q,T) gravity, with the null energy condition violated at the throat, for dark matter, MIT bag, and noncommutative matter models.","keywords":["traversable wormholes","f(Q) gravity","f(Q,T) gravity","symmetric teleparallel gravity","null energy condition","dark matter halos","MIT bag model","noncommutative geometry"],"falsifier":"Numerically solve the full monopole field equation (Eq. 2.5) without the gradient/self-interaction simplification, feed the resulting energy-momentum tensor into the f(Q) field equations, and check whether $b'(r_0)<1$ and $\\rho+p_r<0$ still hold at the throat.","tokens_in":64218,"feed_emoji":"🕳️","tokens_out":7859,"duration_ms":75041,"temperature":0.7,"pith_summary":"Traversable wormholes are impossible in general relativity without exotic matter, so the study asks whether modified symmetric teleparallel gravity, where the connection carries no curvature or torsion and non-metricity drives gravity, can bypass that obstruction. It argues yes for linear f(Q) and f(Q,T) models, deriving shape functions that satisfy the Morris-Thorne flare-out and asymptotic-flatness conditions while the null energy condition is violated at the throat. The supporting matter models are concrete: pseudo-isothermal and NFW dark matter halos with magnetic monopole charge, the MIT bag equation of state for strange quark matter, and Gaussian or Lorentzian smeared noncommutative sources. The volume integral quantifier indicates only minimal exotic matter is needed in the linear f(Q) case, and Tolman-Oppenheimer-Volkoff analysis indicates equilibrium for the f(Q,T) solutions. The study also claims nonlinear models such as f(Q)=Q+mQ^n are incompatible with wormhole geometry.","feed_headline":"Traversable wormholes can exist in modified teleparallel gravity","feed_subtitle":"Flare-out solutions pass energy and stability tests across dark matter, bag, and noncommutative models.","key_machinery":"The central working objects are the Morris-Thorne metric with shape function $b(r)$ and redshift function $\\phi(r)$, the flare-out condition $b'(r_0)<1$, and the non-metricity scalar $Q$ of symmetric teleparallel gravity, with the actions for $f(Q)$ and $f(Q,T)$. On the matter side, the monopole energy-momentum tensor is reduced to $\\bar{T}^{t}_{t} = \\bar{T}^{r}_{r} = -\\eta^2/r^2$, dark matter enters through the pseudo-isothermal and NFW density profiles, strange matter through the MIT bag equation of state $p=(\\rho-4B)/3$, and noncommutative geometry through Gaussian and Lorentzian smeared densities. The volume integral quantifier measures the amount of exotic matter, and the TOV equation supplies the equilibrium condition for stability.","core_discovery":"The central claim is that the geometry-matter coupling in symmetric teleparallel extensions shifts the burden of sustaining a throat from exotic matter to the gravitational sector, so traversable wormholes can satisfy all kinematic conditions with otherwise ordinary sources. For linear f(Q)=alpha Q with monopole charge, the monopole parameter eta drives null-energy-condition violation while the pseudo-isothermal or NFW profile fixes the shape function. For linear f(Q,T)=alpha Q+beta T, power-law shape functions satisfy the flare-out condition under barotropic and anisotropic equations of state, and the same linear model supports throats when the matter is MIT bag strange matter or a noncommutative Gaussian/Lorentzian smeared fluid. The study further claims these f(Q,T) wormholes are stable according to the TOV equation, and that gravitational lensing of the noncommutative models produces a divergent deflection angle at the throat, offering an observational handle to distinguish them from black holes. Nonlinear f(Q) models are found not to support wormhole solutions.","pith_inferences":["The monopole approximation in Chapter 2 is the step most worth testing: solving the full scalar field equation near the throat would show whether the clean eta^2/r^2 form is reliable.","The NEC violation in f(Q,T) models can be read as a transfer of the energy-condition failure from matter to the geometry-matter coupling, which gives modified gravity a concrete signature to be checked by observations.","Rotating or time-dependent generalizations of these static solutions would be required before the lensing signature can be compared with real black-hole shadow data.","A testable extension is to compute the Shapiro time delay and tidal forces for the noncommutative wormhole models, turning the traversability claim into measurable predictions."],"forward_implications":["If the linear f(Q) results hold, wormholes embedded in galactic dark matter halos can be sustained with only a minimal amount of exotic matter, as measured by the volume integral quantifier.","If the f(Q,T) results hold, traversable wormholes can be built from barotropic or anisotropic fluids, from MIT bag strange matter, and from noncommutative smeared sources, all with TOV equilibrium.","If the claim that f(Q)=Q+mQ^n fails is correct, the existence of traversable wormhole solutions can be used to constrain the nonlinear part of f(Q).","If the deflection angle diverges at the throat, gravitational lensing observations of compact objects could reveal wormhole throats without resolving them directly."],"supporting_citations":[{"why":"Supplies the Morris-Thorne wormhole metric, traversability conditions, and energy-condition framework used throughout.","marker":"[7]"},{"why":"Introduces f(Q) gravity with the non-metricity scalar and gives the field equations used in Chapter 2.","marker":"[124]"},{"why":"Introduces f(Q,T) gravity with the matter-geometry coupling used in Chapters 3-5.","marker":"[129]"},{"why":"Provides the Volume Integral Quantifier method used to measure the amount of exotic matter.","marker":"[169]"},{"why":"Provides the Navarro-Frenk-White dark matter halo density profile.","marker":"[71]"},{"why":"Provides the pseudo-isothermal dark matter halo density profile.","marker":"[77]"},{"why":"Provides the Gaussian smeared energy density for noncommutative geometry.","marker":"[98, 99]"},{"why":"Applies noncommutative geometry to wormhole solutions, the starting point for Chapter 5.","marker":"[106, 107]"},{"why":"Derives the MIT bag model equation of state used as the strange matter source in Chapter 4.","marker":"[85, 86]"},{"why":"Provides the generalized TOV equation used for equilibrium and stability analysis.","marker":"[186-188]"}],"fun_headline_variants":["Teleparallel gravity eases exotic matter needs for wormholes","Geometry-matter coupling reduces exotic matter for wormholes","Traversable wormholes in f(Q,T) gravity need only ordinary matter","Nonlinear f(Q) fails, linear f(Q,T) builds stable wormholes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the monopole's gradient and self-interaction terms can be dropped, leaving $\\bar{T}^{t}_{t} = \\bar{T}^{r}_{r} = -\\eta^2/r^2$; if that reduction fails near the throat, the derived shape functions and energy-condition violations would change.","fun_headline_variants_meta":{"raw":{"variants":["Teleparallel gravity eases exotic matter needs for wormholes","Geometry-matter coupling reduces exotic matter for wormholes","Traversable wormholes in f(Q,T) gravity need only ordinary matter","Nonlinear f(Q) fails, linear f(Q,T) builds stable wormholes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000809,"raw_usage":{"total_tokens":3642,"prompt_tokens":1128,"completion_tokens":2514,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":744,"completion_tokens_details":{"reasoning_tokens":2439}},"tokens_in":744,"tokens_out":2514,"duration_ms":19802,"temperature":1.0,"reasoning_tokens":2439,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:16:29.273499+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerically solve the full monopole field equation (Eq. 2.5) without the gradient/self-interaction simplification, feed the resulting energy-momentum tensor into the f(Q) field equations, and check whether $b'(r_0)<1$ and $\\rho+p_r<0$ still hold at the throat.","supporting_citations":[],"review_version":1}