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REVIEW 5 major objections 3 minor 82 references

Dehnen-type dark matter wormholes in the $f(\mathcal{R},\mathcal{L}_m,\mathcal{T})$ action

T0 review · 5 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that the Dehnen dark matter halo profile can generate traversable wormholes in $f(\mathcal{R}, \mathcal{L}_m, \mathcal{T})$ gravity without exotic matter.

desk verdict The displayed shape function fails the throat condition and the no-exotic-matter claim contradicts the paper's own figures; the construction is invalid as written. read the letter →

arxiv 2507.16465 v1 pith:DSJNGQED submitted 2025-07-22 gr-qc

A. Errehymy , O. Donmez , B. Turimov , K. Myrzakulov , N. Alessa , A.-H. Abdel-Aty This is my paper · ORCID
classification gr-qc MSC 83D0583C1583C2083C75 PACS 04.50.Kd04.20.Jb
keywords traversablewormholesf(RL_mT)gravityDehnendarkmatterhalodoublepower-lawdensityMorris-Thornemetricenergyconditionsexoticanisotropicfluid
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 3 minor

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.

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 (5)
  1. [Specific solutions related to a double power-law profile, Eq. (30)] 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.
  2. [Exotic matter, exoticity parameter, and anisotropy parameter's influence, Eq. (39) and concluding remarks] 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.
  3. [Exotic matter, exoticity parameter, and anisotropy parameter's influence, Eq. (41)] 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.
  4. [The f(R,L_m,T) gravity, Eqs. (5)-(9) and (22)-(27)] 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.
  5. [Metric (17) and field equations (22)-(24)] 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.
minor comments (3)
  1. [Eqs. (42)-(43)] 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).
  2. [References] 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.
  3. [Figures] 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.

Circularity Check

1 steps flagged · score 6.0 of 10

The SEC and hydrostatic-force results are algebraic identities of the simplified equations, so part of the energy-condition claim reduces to its own input ansatz.

  1. self definitional [Eqs. (25)-(27) and Eq. (41); Section 'Specific solutions related to a double power-law profile' and the energy-conditions discussion]
    "As a result, we can simplify our system of equations (22)-(24) to the following forms: ψ′ = κr2ρ , (25) − ψ = κr3Pr , (26) ψ − ψ′r = 2κr3Pt . (27) ... By carefully analyzing Eqs. (25)-(27), we can derive the SEC, which is closely related to the NEC ρ + Pr + 2Pt = 0. (41)"

    Solving (25)-(27) for the fluid variables gives ρ = ψ′/(κr²), Pr = −ψ/(κr³), Pt = (ψ − ψ′r)/(2κr³). Substituting into ρ + Pr + 2Pt yields [rψ′ − ψ + ψ − rψ′]/(κr³) = 0 identically, so Eq. (41) is an algebraic identity of the simplified equations, not a consequence of the original system (22)-(24) unless the same trace condition is imposed to effect the simplification. The paper then uses Eq. (41) to set F_m = 0 in the TOV analysis and to declare the SEC satisfied, making those stability statements tautological restatements of the input ansatz rather than independent predictions.

full rationale

Aside from the tautological SEC/stability step, the paper is a standard solution-generating construction: the Dehnen density profile (28) is inserted into Eq. (25) and integrated to give the shape function, with pressures obtained from (26)-(27). Positivity of the assumed density is therefore an input property, not a prediction; however the paper does not present the energy conditions as tests against external data, so the main scientific content is the geometry and parameter survey rather than a fitted prediction. No load-bearing self-citation appears: references to the authors' earlier works are contextual, and no uniqueness theorem is imported. The separate algebraic failure of the throat condition in Eq. (30) is a correctness defect, not a circularity, and is not scored here. The circularity score is set by the one case where a claimed result (SEC, F_m=0) is literally built into the simplified equations that produced it. That partial reduction of the central energy-condition claim warrants a score of 6 rather than 0-2.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central construction depends on a linear f(R,L_m,T) model plus a hand-chosen Dehnen density profile with eight free parameters. No new particles or forces are introduced, but the theory and the Lagrangian choice are postulates.

free parameters (8)
  • η = 0.5
    Coupling constant in f(R,L_m,T) chosen by hand; results depend on its value.
  • χ = 0.9
    Coupling constant chosen by hand.
  • ρ_s = 0.15
    Central density of the Dehnen profile, chosen for the plots.
  • r_s = 0.99
    Scale radius of the halo, chosen.
  • r0 = 0.35
    Throat radius, chosen; must satisfy the throat condition.
  • σ = varied in [0,3]
    Slope parameter of the Dehnen profile; the paper scans it to find allowed ranges.
  • α = 1
    Inner profile exponent, fixed in the numerical examples.
  • β = 4
    Outer profile exponent, fixed in the numerical examples.
assumptions (5)
  • domain assumption The f(R,L_m,T) action (Eq. 1) with f = R + ηL_m + χT is the correct gravitational theory.
    The entire paper works in this theory; no independent evidence for it is given.
  • domain assumption The matter Lagrangian is L_m = -ρ.
    Invoked in Section 2 to derive Θ_μν = -2T_μν - ρg_μν, which leads to the field equations used throughout.
  • domain assumption The wormhole metric is static and spherically symmetric (Eq. 17).
    Standard Morris-Thorne ansatz adopted without derivation.
  • domain assumption The redshift function is constant.
    In the TOV analysis the paper states 'Considering a constant redshift, F_g becomes vanishing'; this removes the gravitational force term.
  • domain assumption The matter density depends only on the metric and not its derivatives.
    Assumed to drop the second-order term in Eq. (4).

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Cite this review

Pith. "Pith review of Dehnen-type dark matter wormholes in the $f(\mathcal{R},\mathcal{L}_m,\mathcal{T})$ action." pith.science (2026). https://pith.science/paper/DSJNGQED

@misc{pith2026250716465,
  author       = {Pith},
  title        = {Pith review of: Dehnen-type dark matter wormholes in the $f(\mathcalR,\mathcalL_m,\mathcalT)$ action},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DSJNGQED}},
  note         = {Machine review of arXiv:2507.16465}
}
read the original abstract

We are exploring the possibility of traversable wormholes existing in a more realistic context. Specifically, we are looking at scenarios that don't rely on exotic factors, like having a mass shell at the throat or allowing particles and antiparticles to coexist without annihilation. To do this, we are constructing wormholes with double power-law density distributions, drawing inspiration from the Dehnen-type dark matter halo in the framework of generalized geometry-matter coupling gravity. Our investigation carefully considers the challenges of traversability and stability, as well as the roles of exotic matter, the exoticity parameter, and the anisotropy parameter. We have discovered solutions that describe asymmetric, asymptotically flat traversable wormholes, supported by a smooth metric and double power-law density distributions. These solutions successfully avoid the problems, giving us hope that such wormholes could actually exist in nature.

Figures

Figures reproduced from arXiv: 2507.16465 by the authors.

Figure 1
Figure 1. FIG. 1. The matter density and the conditions for the shape function of Dehnen-type dark matter wormholes are defined by the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The energy conditions for Dehnen-type dark matter wormholes are defined by the following key parameters: [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The anisotropic and hydrostatic forces, along with the exoticity and anisotropy parameters for Dehnen-type dark matter [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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