{"id":"ca098991-e6e4-45f0-bee4-3dcf5511ed40","arxiv_id":"2507.16465","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"The authors find traversable wormhole solutions in f(R,L_m,T) gravity sourced by a Dehnen-type dark matter density profile, but the claim of no exotic matter conflicts with the displayed null energy condition violations.","lead":"Wormhole solutions are constructed in f(R,L_m,T) gravity using a Dehnen-type dark matter halo density profile. The paper's claim that the wormholes avoid exotic matter is contradicted by its own energy condition plots.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (30) does not satisfy the throat condition psi(r0)=r0 for the stated parameters, so the central wormhole construction is algebraically invalid.","rationale":"The reader's formal weakest assumption concerns the choice L_m = -rho. That choice is conventional, and the reduction of Eqs. (22)-(24) to Eqs. (25)-(27) can actually be justified from the field equations when rho + Pr + 2Pt = 0, so the L_m choice is not the most fragile point. The fatal point is Eq. (30): the paper claims this shape function was obtained by imposing the throat condition, but the displayed expression violates psi(r0) = r0 for every sigma in [0,3) with the stated parameters. This is not a matter of interpretation; the central object is not a Morris-Thorne wormhole at r0. The paper's headline conclusion rests directly on this equation, so the manuscript cannot be accepted as written. A corrected version might restore the throat condition by properly fixing the integration constant or by rescaling rho_s so that kappa*rho_s/(3-sigma) = 1, but doing so would alter all subsequent plots and energy-condition statements. Secondary issues, such as the exoticity parameter in Eq. (39) using rho - Pr rather than rho + Pr, reinforce the concern but are not needed for this conclusion.","tokens_in":13730,"tokens_out":7937,"duration_ms":75974,"concrete_test":"Recompute the shape function from psi' = kappa * rho * r^2 with the boundary condition psi(r0) = r0, using the stated parameters eta = 0.5, chi = 0.9, alpha = 1, beta = 4, rho_s = 0.15, r_s = 0.99, r0 = 0.35, sigma = 1.5, and compare the result term-by-term with Eq. (30). If Eq. (30) evaluated at r0 does not equal r0, the throat condition fails; equivalently, check whether the psi - r curves in Fig. 1 can be reproduced from Eq. (30) by direct numerical integration of Eq. (29).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing defect is the shape function itself, not the energy-condition interpretation. Substituting r=r0 into Eq. (30) cancels the two hypergeometric terms and leaves psi(r0) = -[rho_s kappa/(sigma-3)] r0 = [rho_s kappa/(3-sigma)] r0. For the paper's values (kappa = 8*pi + eta/2 + chi = 26.283, rho_s = 0.15, 0 <= sigma < 3), this is not r0: at sigma = 1.5, psi(r0) is approximately 2.63*r0. Thus r0 is not a throat, and for r just above r0, 1 - psi/r < 0, so the metric has the wrong signature. The claim that the integration constant was fixed by psi(r0) = r0 is inconsistent with Eq. (30); the correct constant would be C = r0 - [rho_s kappa/(3-sigma)] * r0^(3-sigma) * 2F1(r0), which does not appear. Since the displayed solution is the basis for all subsequent plots and energy-condition claims, this algebraic failure invalidates the central claim of an asymptotically flat traversable wormhole.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript constructs Morris-Thorne wormholes in f(R,L_m,T) gravity with f=R+ηL_m+χT, adopting the matter Lagrangian L_m=-ρ, an anisotropic fluid, and a Dehnen double power-law density profile. After deriving the field equations and simplifying them under an implicit trace constraint, it integrates the shape function, computes the radial and transverse pressures, and analyzes energy conditions, TOV equilibrium, exoticity, and anisotropy. The paper claims asymptotically flat traversable wormholes that avoid exotic matter.","tokens_in":14005,"tokens_out":10154,"duration_ms":104831,"significance":"Taken at face value, the main claim--wormhole solutions supported by a Dehnen-type dark matter halo without exotic matter in modified gravity--would be notable. The paper's transparent derivation of the field equations for the chosen Lagrangian and its parameter scans are useful features. However, the load-bearing shape-function solution fails the throat condition, and the paper's own energy-condition plots contradict its 'no exotic matter' conclusion. These problems are not cosmetic; they undermine the central result.","major_comments":[{"comment":"Substituting r=r0 into Eq. (30) gives ψ(r0)=ρ_s κ r0/(3-σ), not r0, because the two hypergeometric terms cancel and the remaining +r0 inside the bracket is multiplied by the prefactor -ρ_sκ/(σ-3). For the stated parameters (η=0.5, χ=0.9, ρ_s=0.15, σ=1.5) this yields ψ(r0)≈2.63 r0. Hence r0 is not a throat, and 1-ψ/r is negative for r just above r0, giving the metric the wrong signature. The claim that the integration constant was fixed by ψ(r0)=r0 is inconsistent with the displayed expression. This error propagates to the pressures in Eqs. (32)-(33) and to all subsequent figures and conclusions.","section":"Specific solutions related to a double power-law profile, Eq. (30)"},{"comment":"Figure 2 shows ρ+P_r<0 for 0<σ<1.44 at the throat, which is a violation of the radial null energy condition and hence the presence of exotic matter by the paper's own criteria. The concluding statement that the negative trend of Ω at the throat 'suggests that there is no exotic matter' is not supported: with ρ>0, Ω=(P_r-ρ)/|ρ|, and the NEC-violating regime P_r<-ρ corresponds to negative Ω, not positive. The sign of Ω as defined is therefore not a valid indicator of the absence of exotic matter.","section":"Exotic matter, exoticity parameter, and anisotropy parameter's influence, Eq. (39) and concluding remarks"},{"comment":"The identity ρ+P_r+2P_t=0 follows from the simplified field equations (25)-(27), but the SEC stated in the same section requires both ρ+P_k≥0 for k=r,t and ρ+P_r+2P_t≥0. Since ρ+P_r<0 for part of the parameter range, the SEC is violated; the sentence 'ρ+P_r+2P_t=0 indicates that the SEC is satisfied' does not follow.","section":"Exotic matter, exoticity parameter, and anisotropy parameter's influence, Eq. (41)"},{"comment":"The reduction from Eqs. (22)-(24) to (25)-(27) is only possible under the trace constraint ρ+P_r+2P_t=0, which is imposed by the assumed matter Lagrangian L_m=-ρ with ρ independent of metric derivatives. This constraint is an input, not a prediction. The manuscript's general claim that exotic matter is absent 'in the context of f(R,L_m,T) gravity' overreaches, because the construction depends on this specific L_m and the additional constraint; a different matter Lagrangian changes Θ_μν in Eq. (5) and invalidates the simplified equations.","section":"The f(R,L_m,T) gravity, Eqs. (5)-(9) and (22)-(27)"},{"comment":"The metric (17) contains a redshift function Φ, but the field equations (22)-(24) and all subsequent expressions are written for Φ=0; this restriction is never stated. For a nonconstant Φ, additional terms involving Φ' and Φ'' would enter the field equations, so the constructed solutions are not the general static wormholes described by (17). The later TOV analysis does assume a constant redshift, but this assumption should have been stated before the field equations.","section":"Metric (17) and field equations (22)-(24)"}],"minor_comments":[{"comment":"The signs inside the absolute values appear inconsistent. Since Pr(r0)=-1/(κr0^2) from Eq. (26), one would expect ρ-|Pr| = ρ - 1/(κr0^2), but Eq. (42) displays a minus sign outside the 1/(r0^2κ) term, which would give ρ + 1/(κr0^2). A similar sign issue affects Eq. (43).","section":"Eqs. (42)-(43)"},{"comment":"Reference [10] appears in the bibliography but is never cited in the body; also, reference [14] is printed as 'Lázquez-Salcedo' but the paper is by Blázquez-Salcedo et al.","section":"References"},{"comment":"The colorbar labels in Figs. 2 and 3 contain apparent rendering artifacts (for example '3.65.4' and isolated '0.' entries) that should be cleaned up before publication.","section":"Figures"}],"recommendation":"reject","confidential_remarks":"The recommendation is reject because the central shape function in Eq. (30) fails the throat condition, and the paper's own Fig. 2 contradicts the abstract's claim of no exotic matter. Correcting the integration constant would require redoing the entire analysis and would very likely change the conclusions; the current manuscript cannot be repaired by local edits. I also note that the 'solutions' are generated by imposing a density profile and then solving for pressures, so the energy-condition results are consequences of the input rather than independent predictions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper doesn't work as written. The shape function in Eq. (30) does not satisfy psi(r0)=r0 for any sigma<3; the two hypergeometric terms cancel at r=r0 and leave psi(r0)=rho_s kappa/(3-sigma) r0, which is not r0 for the parameters used. So r0 is not a throat and the metric has the wrong signature nearby. This is not a cosmetic typo—it is the basis for every plot and conclusion that follows.\n\nWhat is worth keeping: the field equations for the linear f(R,L_m,T) model with L_m=-rho are derived cleanly, and the reduction to equations (25)-(27) is consistent and agrees with Moraes et al. The idea of seeding a wormhole shape function from a Dehnen double power-law profile is a reasonable exercise, and the hypergeometric integration is carried out carefully. If the integration constant were fixed properly, psi(r0)=r0 could be imposed; that part is fixable in principle.\n\nThe bigger problem is the no-exotic-matter claim. Their own Fig. 2 shows rho+Pr < 0 for 0 r_0$, the flare-out condition and traversability fail. These are direct numerical checks on the paper's own formulas.","tokens_in":13587,"feed_emoji":"🕳️","tokens_out":7919,"duration_ms":78119,"temperature":0.7,"pith_summary":"The paper sets out to show that a traversable wormhole need not rest on exotic matter or on artificial constructions such as a mass shell at the throat. It builds static, spherically symmetric wormhole solutions in $f(\\mathcal{R}, \\mathcal{L}_m, \\mathcal{T})$ gravity whose density follows the Dehnen double power-law profile used for dark matter halos. The authors report that the resulting spacetime is smooth, asymmetric, and asymptotically flat, and that the flaring-out condition, energy conditions, TOV equilibrium, and a negative exoticity parameter can all be met. If correct, the main consequence is that the same dark matter profiles invoked by galactic observations could, within this modified-gravity theory, keep a wormhole throat open.","feed_headline":"Dehnen dark halo profile builds traversable wormholes without exotic matter","feed_subtitle":"Double power-law density satisfies flaring-out and energy conditions at once, opening a path to realistic wormholes.","key_machinery":"The load-bearing object is the Morris-Thorne wormhole metric with redshift function $\\Phi$ and shape function $\\hat{\\psi}$. The construction works by matching the simplified field equation $\\hat{\\psi}' = \\kappa r^2 \\rho$ to the Dehnen double power-law density $\\rho = \\rho_s (r/r_s)^{-\\sigma}[(r/r_s)^\\alpha + 1]^{(\\sigma-\\beta)/\\alpha}$, which produces the shape function (30) containing a hypergeometric function ${}_2F_1$. The argument then leans on the Morris-Thorne traversability conditions $\\hat{\\psi}(r_0) = r_0$, $\\hat{\\psi}'(r_0) \\le 1$, $\\hat{\\psi}' < \\hat{\\psi}/r < 1$; on the TOV force balance $F_a + F_h = 0$; and on the exoticity parameter $\\Omega_{\\rm exoticity} = -(\\rho - P_r)/|\\rho|$ and anisotropy $\\Delta = (P_t - P_r)/\\rho$, which together are used to conclude that no exotic matter is present.","core_discovery":"The central claim is that the $f(\\mathcal{R}, \\mathcal{L}_m, \\mathcal{T})$ field equations, for the linear Lagrangian $f = R + \\eta \\mathcal{L}_m + \\chi T$ with matter Lagrangian $\\mathcal{L}_m = -\\rho$, admit a new family of traversable wormhole solutions when the energy density is the Dehnen double power-law profile. Integrating the simplified equation $\\hat{\\psi}' = \\kappa r^2 \\rho$ yields a shape function written in terms of a hypergeometric function, and the paper shows that this shape function satisfies the throat and flare-out conditions and approaches flat spacetime at infinity. The paper further claims that, for the chosen parameters, the radial null energy condition fails only in a narrow range of the slope parameter $\\sigma$, the tangential null energy condition holds, the strong energy condition holds as the identity $\\rho + P_r + 2P_t = 0$, and the exoticity parameter is negative near the throat, so no exotic matter is needed. The result is characterized as an asymmetric, asymptotically flat, traversable wormhole supported entirely by the dark-matter-like density distribution.","pith_inferences":["A natural test of the construction's robustness would be to rebuild the same wormhole with a matter Lagrangian other than $\\mathcal{L}_m = -\\rho$; the simplified equations (25)-(27) would change, and it remains open whether any Dehnen-type solution survives.","The same double power-law seeding could be applied to the Navarro-Frenk-White or Burkert halo profiles mentioned in the paper, and comparing the resulting shape functions would show which observed halo shapes permit traversability.","If wormholes of this kind exist, the ringdown and shadow diagnostics discussed in the closing section could be used to tell them from black holes, since the throat leaves a distinct imprint at late times."],"forward_implications":["If these solutions are valid, a wormhole throat can be held open by a dark-matter-like density profile inside $f(\\mathcal{R}, \\mathcal{L}_m, \\mathcal{T})$ gravity, without phantom matter.","The explicit shape function and pressure components give a concrete spacetime on which lensing, shadow, and ringdown computations can be carried out and compared with black hole observations.","Because the spacetime is asymptotically flat and the metric is smooth, the solutions avoid the mass-shell and differentiability pathologies noted for earlier fermion-supported wormholes.","The parameter $\\sigma$ of the Dehnen profile controls energy-condition behavior: for $1.44 < \\sigma < 3$ the radial NEC holds at the throat, so the halo slope alone can regulate the presence of exotic matter."],"supporting_citations":[{"why":"Supplies the Morris-Thorne wormhole metric and the throat and flare-out conditions that define traversability.","marker":"[60]"},{"why":"Gives the double power-law Dehnen-type density profile whose parameters $\\alpha$, $\\beta$, $\\sigma$ seed the shape function.","marker":"[29]"},{"why":"Introduces the $f(\\mathcal{R}, \\mathcal{L}_m, \\mathcal{T})$ action and field equations that the wormhole solutions are built on.","marker":"[30]"},{"why":"Original Dehnen profile used to model dark matter halo cusps and cores; the paper's density ansatz is its generalization.","marker":"[19]"},{"why":"Provides the comparable simplified field-equation forms that the paper checks its results against.","marker":"[61]"},{"why":"Defines the exoticity parameter used to infer the absence of exotic matter at the throat.","marker":"[67]"},{"why":"Supplies the TOV equation used for the equilibrium analysis of the wormhole.","marker":"[63]"}],"fun_headline_variants":["Dehnen halo yields wormholes without exotic matter","Dark matter halo shapes wormholes without exotic fluids","Non-exotic wormholes from Dehnen density in f(R,L,T)","Double power-law halo opens wormhole throat safely","Wormholes freed from exotic matter via Dehnen profile"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole construction rests on the choice of matter Lagrangian $\\mathcal{L}_m = -\\rho$ with $\\rho$ independent of metric derivatives, which cancels the second-derivative term and reduces the field equations to the simple forms used in the integration; if that choice is changed, the simplified equations no longer hold and the wormhole family is not guaranteed.","fun_headline_variants_meta":{"raw":{"variants":["Dehnen halo yields wormholes without exotic matter","Dark matter halo shapes wormholes without exotic fluids","Non-exotic wormholes from Dehnen density in f(R,L,T)","Double power-law halo opens wormhole throat safely","Wormholes freed from exotic matter via Dehnen profile"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00034,"raw_usage":{"total_tokens":1870,"prompt_tokens":932,"completion_tokens":938,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":548,"completion_tokens_details":{"reasoning_tokens":857}},"tokens_in":548,"tokens_out":938,"duration_ms":7819,"temperature":1.0,"reasoning_tokens":857,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:10:10.871248+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For the stated parameters, evaluate the exact shape function (30) and pressures (32)-(33) at the throat: if $\\rho + P_r$ is negative for any $\\sigma$ in the claimed range $1.44 < \\sigma < 3$, the radial NEC claim fails; similarly, if $\\hat{\\psi} - \\hat{\\psi}' r$ is not positive for all $r > r_0$, the flare-out condition and traversability fail. These are direct numerical checks on the paper's own formulas.","supporting_citations":[{"cited_title":"Gorini et al., Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the TOV equation used for the equilibrium analysis of the wormhole."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the exoticity parameter used to infer the absence of exotic matter at the throat."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the double power-law Dehnen-type density profile whose parameters $\\alpha$, $\\beta$, $\\sigma$ seed the shape function."},{"cited_title":"Haghani and T","cited_arxiv_id":null,"evidence_quote":"Introduces the $f(\\mathcal{R}, \\mathcal{L}_m, \\mathcal{T})$ action and field equations that the wormhole solutions are built on."},{"cited_title":"Dehnen, Mon","cited_arxiv_id":null,"evidence_quote":"Original Dehnen profile used to model dark matter halo cusps and cores; the paper's density ansatz is its generalization."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the comparable simplified field-equation forms that the paper checks its results against."}],"review_version":1}