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REVIEW 3 major objections 6 minor 36 references

Traversable Wormholes Sourced by Dark Matter in Loop Quantum Cosmology

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that cold dark matter density profiles, combined with loop-quantum-cosmology effective corrections, produce regular traversable wormhole spacetimes that satisfy the Morris-Thorne conditions, and that the NFW-model shadow…

desk verdict Useful explicit LQC wormhole solutions for three dark matter profiles, but the M87 shadow fit rests on an unjustified photon-sphere assumption and the asymptotic-flatness claim is self-contradictory. read the letter →

arxiv 2411.12063 v3 pith:ABA3VY52 submitted 2024-11-18 gr-qc

Marcos V. de S. Silva , G. Alencar , R. N. Costa Filho , R. M. P. Neves , Celio R. Muniz This is my paper · ORCID
classification gr-qc
keywords traversablewormholesloopquantumcosmologydarkmatterdensityprofilesMorris-ThornemetricenergyconditionsexoticwormholeshadowM87observation
topics Dark Matter
open problems Dark MatterQuantum Gravity
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 traversable wormholes—hypothetical shortcuts through spacetime—can be supported by ordinary cold dark matter once loop-quantum-cosmology corrections are included. The authors take three standard dark-matter density profiles (NFW, pseudo-isothermal, and perfect-fluid), couple them to the LQC-modified field equations with a linear equation of state $p=\omega\rho$, and solve for the wormhole shape and redshift functions. Each solution satisfies the Morris-Thorne geometric conditions and is regular (finite Kretschmann scalar) under an upper bound on the central density $\rho_0$. They quantify the exotic matter required and find that lowering the LQC critical density $\rho_c$ reduces it. For the NFW profile, the computed shadow radius matches the M87 shadow observation for $\omega\approx0.025$, so the wormhole would be indistinguishable from a black hole by shadow size alone.

What carries the argument

The load-bearing machinery is the LQC effective-fluid mapping: $\rho_e(r)=\rho(r)(1-\rho(r)/\rho_c)$ and $p_e(r)=p(r)-\rho(r)(2p(r)+\rho(r))/\rho_c$, with $\rho_c$ the LQC critical density. This maps a normal dark-matter fluid with $p=\omega\rho$ into an effective stress-energy tensor whose radial pressure can go negative near the throat, providing the null-energy-condition violation that Morris-Thorne wormholes need. Feeding $\rho_e$ and $p_e$ into the Einstein equations for the Morris-Thorne metric and imposing the conservation equation, both the shape function $b(r)$ and the redshift function $\Phi(r)$ follow from the chosen density profile. The combination is what turns each dark-matter profile into a complete wormhole solution rather than just a rescaled general-relativistic source.

What would settle it

A direct calculation of the effective Hamiltonian constraint for a static, spherically symmetric spacetime in loop quantum cosmology—checking whether it reproduces Eqs. (8)-(9)—would settle whether these geometries are genuinely LQC wormholes, and a precise M87 shadow measurement that excludes $0<\omega\lesssim0.025$ would rule out the NFW shadow prediction.

Watch

Extended reading notes

Core claim

The paper's central claim is that isotropic dark matter described by the NFW, pseudo-isothermal and perfect-fluid profiles can serve as the source of traversable Morris-Thorne wormholes when LQC quantum-geometry corrections are encoded in effective fluid quantities $\rho_e = \rho(1-\rho/\rho_c)$ and $p_e = p-\rho(2p+\rho)/\rho_c$. Solving the LQC-modified Einstein equations together with the conservation equation, the authors obtain explicit shape functions $b(r)$ and redshift functions $\Phi(r)$ for each profile. Each solution obeys $b(r_0)=r_0$, $b(r)/r<1$, $b'(r_0)<1$, and the flaring-out condition $b-rb'>0$; Kretschmann scalars are finite provided $\rho_0$ stays below a model-dependent bound. Energy-condition analysis shows the effective source can violate the null energy condition in the throat region (identically satisfied at $\omega=-1$), and the volume integral quantifier decreases as $\rho_c$ decreases. Under the NFW profile, the photon-sphere approximation gives a shadow radius consistent with the M87 observation for $0<\omega\lesssim0.025$.

Load-bearing premise

The construction assumes, without derivation, that the LQC modified Friedmann equation can be translated locally and statically into the effective stress-energy formulas $\rho_e=\rho(1-\rho/\rho_c)$ and $p_e=p-\rho(2p+\rho)/\rho_c$; if that mapping is not what loop quantum gravity says around a compact object, the geometries are ordinary general-relativistic wormholes with a rescaled source rather than LQC wormholes.

Editorial extensions

If this is right

  • If the central claim holds, no bespoke exotic fluid is needed: standard cold-dark-matter profiles, with LQC corrections, can satisfy all Morris-Thorne traversability conditions.
  • Each profile comes with a quantitative regularity bound on the central density $\rho_0$; exceeding it produces singularities, so observations of central dark-matter densities can in principle test the construction.
  • Lowering the LQC critical density $\rho_c$ reduces the amount of exotic matter required, most strongly for the perfect-fluid model, while near the throat the perfect-fluid model demands the most exotic matter and the NFW model the least.
  • At $\omega\approx0.025$ the NFW-model shadow matches the M87 shadow observation, so shadow size alone cannot distinguish this wormhole from a black hole.

Reading between the lines

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

  • A testable extension the paper leaves implicit: adding rotation or a surrounding plasma to the NFW wormhole would shift the shadow and could break the degeneracy with a black hole that holds in the vacuum, static case.
  • The same effective-fluid recipe could be applied to other smooth dark-matter halo profiles whose densities appear as rational functions; the paper's mechanism suggests they would yield wormhole solutions with analogous regularity bounds.
  • If the LQC effective mapping is later found not to follow from full loop-quantum dynamics in static spherical symmetry, the conservative reading is that these are regular general-relativistic wormholes with rescaled sources—still a geometric result, but not a quantum-gravity one.
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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

3 major / 6 minor

Summary. The paper constructs static, spherically symmetric Morris-Thorne wormhole spacetimes sourced by three dark matter density profiles (NFW, pseudo-isothermal, and perfect fluid) within an LQC-inspired effective stress-energy framework. The authors solve the modified Einstein equations for the shape function b(r) and the conservation equation for the redshift function Phi(r), verify the standard geometric wormhole conditions, compute the Kretschmann scalar to argue regularity, study energy conditions and the volume integral quantifier, and finally compare the shadow of the NFW model with EHT observations of M87. The central construction is algebraic and the paper contains many closed-form results, but the asymptotic structure and the shadow/photon-sphere analysis contain load-bearing problems.

Significance. If correct, the paper would provide explicit traversable wormhole solutions supported by ordinary dark matter with LQC-type corrections, with a surprising observational match to the M87 shadow. The strengths are the closed-form expressions for b(r) and Phi(r), the explicit verification of flare-out and throat conditions, the Kretschmann regularity check, and the quantitative VIQ comparison across three profiles. However, the claimed M87 shadow compatibility is currently an artifact of an unjustified identification of the photon sphere with the throat, and the spacetimes are not asymptotically flat for the fitted value of omega. These issues undermine the paper's most striking observational claim, though the underlying construction machinery may still be salvageable after revision.

major comments (3)
  1. [Section VIII, Eqs. (58)-(59)] The photon-sphere radius is not derived; the paper simply sets rph = r0. For the metric (10), the condition d(gamma^2)/dr = 0 at r is equivalent to Phi'(r)=1/r. Substituting the NFW Phi'(r) from Eq. (19) with the M87 parameters of Fig. 20 (where rho0 Rs^3/(rho_c r0^3) ~ 1.8e-8) gives Phi'(r0) ~ omega/[(1+omega) r0], which equals 1/r0 only for omega very large, not for omega ~ 0.025. Therefore Eq. (59) is not the physical shadow radius of this spacetime, and the claimed EHT compatibility is not a consequence of the model.
  2. [Section III.B, Eq. (16) (and Eqs. (25), (29))] The redshift function is not asymptotically flat for omega != 0: for the NFW profile e^{2Phi} ~ r^{6 omega/(1+omega)} as r -> infinity, with analogous power-law behavior for the PI and PF profiles. The text acknowledges the undesirable asymptotic behavior but then claims that the vanishing of curvature scalars (Fig. 4 and the discussion after Eq. (19)) establishes asymptotic flatness. This is incorrect: a vanishing Kretschmann scalar is necessary but not sufficient for asymptotic flatness; the metric coefficients must approach Minkowski values. Since the shadow calculation in Eq. (59) uses the bare metric at a distant observer coordinate Ro, and the wormhole interpretation normally requires asymptotic flatness or an explicit exterior matching, this issue is load-bearing.
  3. [Section II, Eqs. (8)-(9)] The effective density and pressure are obtained by transplanting the LQC modified Friedmann equation into a local, static, spherically symmetric setting, citing Refs. [10,11]. No derivation or justification is given for why these homogeneous cosmological corrections apply locally around a compact object. Because the shape functions, energy conditions, and shadow results all depend on this mapping, the claim that these are LQC wormholes requires either a derivation or an explicit statement that this is a phenomenological ansatz. As written, the model is 'LQC-inspired' rather than a derivation from loop quantum gravity.
minor comments (6)
  1. [Abstract and throughout] There are numerous typographical errors (e.g., 'with in', 'ana lyze', 'comp are', 'state parameter') and grammatical slips that should be corrected in a revised manuscript.
  2. [Section III.B] The phrase 'except when omega -> 0' should be 'except when omega = 0', since it is the value, not the limit, that makes the asymptotic exponent vanish.
  3. [Section VIII] The sentence 'Here we will consider rph = r0, since the calculation will be made in the approximation of a vacuum medium' is not physically meaningful: a vacuum exterior does not place the photon sphere at the throat. This justification should be removed or replaced with a proper photon-sphere calculation.
  4. [Section VII, Eqs. (44), (49), (54)] The volume integral quantifier diverges logarithmically for the NFW and PF models and linearly for the PI model as r -> infinity. The comparison in Fig. 19 is therefore cutoff-dependent; please state the integration cutoff and discuss the physical interpretation of an infinite amount of exotic matter.
  5. [Figure 20] The EHT observational constraint on the M87 shadow is quoted without error bars or a confidence interval; the compatibility claim should be stated relative to the reported 1-sigma range.
  6. [Figure 20 and Section II] The parameters in Fig. 20 are given in SI units (kg/m^3, m), while the field equations are written in natural units with 8 pi G = c = 1. Please state the conversion explicitly or confirm that the dimensionless ratios such as rho0/rho_c and rho0 Rs^3/(rho_c r0^3) are computed consistently in geometric units.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the wormhole geometries are constructed from chosen dark-matter profiles and LQC effective relations supported by an independent prior reference; the M87 shadow statement is a parameter-compatibility claim, not a forced prediction.

full rationale

The paper's derivation chain is constructive rather than predictive. The dark-matter density profiles are inputs fixed by Eq. (1) from known models, and the LQC effective density and pressure in Eqs. (8)-(9) are taken from Refs. [10,11], where Ref. [10] has no author overlap with the present paper. Thus the main input is not a self-citation chain and is not derived from the wormhole solutions themselves. The shape and redshift functions are genuine outputs of integrating the field equation (11) with b(r0)=r0 and the conservation equation (14), and the Morris-Thorne checks, Kretschmann regularity bounds, and VIQ values are consequences of those solved functions rather than restatements of the inputs. The shadow section is also not circular: Fig. 20 scans the free equation-of-state parameter omega and reports the interval (0.00, 0.025) for which the shadow size is compatible with EHT; this is a postdiction or compatibility statement, not a parameter-free prediction. The explicit assumption rph=r0 in Sec. VIII is an extra geometric identification that is not derived from Eq. (58), so the shadow result is conditional on that assumption; this is a model-validity or correctness concern, not a circular reduction. No equation in the paper is equivalent by construction to the claim it is used to support. The only mild self-citation issue is that Ref. [11] shares two authors and is cited for Eqs. (8)-(9), but the independent Ref. [10] is cited for the same expressions, so no load-bearing circularity results.

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

The construction depends on the assumed LQC effective stress-energy tensor, the Morris-Thorne metric ansatz, and several free parameters (rho_c, rho_0, R_s, r_0, omega). No new physical entities are introduced. The shadow comparison uses omega as a fitted parameter.

free parameters (5)
  • rho_c (LQC critical density) = chosen per plot (e.g., 1e-5 in Figs. 1-3; 1e10 kg/m^3 in Sec. VIII)
    Sets the quantum correction scale; not derived in the paper.
  • rho_0 (central dark matter density) = chosen per plot (e.g., 1e-6; 4.4e-21 kg/m^3 in Sec. VIII)
    Amplitude of the density profile.
  • R_s (scale radius) = 2 in plots; 6.17e20 m in Sec. VIII
    Sets the radial scale of the dark matter distribution.
  • r_0 (throat radius) = 1 in plots; 1.8e13 m in Sec. VIII
    Throat radius boundary condition b(r0)=r0.
  • omega (equation of state parameter) = 1 in Kretschmann plots, -1/2 in VIQ plot, 0.025 in M87 shadow fit
    Linear equation of state p=omega*rho; in Sec. VIII it is tuned to match the M87 shadow.
assumptions (5)
  • domain assumption Effective density and pressure are given by rho_e = rho(1 - rho/rho_c) and p_e = p - rho(2p+rho)/rho_c (Eqs. 8-9).
    Taken from Refs. [10,11] as the LQC modification; underpins all shape and redshift functions.
  • domain assumption The wormhole geometry is described by the Morris-Thorne metric Eq. (10).
    Standard static spherically symmetric ansatz; restricts to zero-tidal-force form.
  • ad hoc to paper Dark matter obeys a linear equation of state p = omega*rho.
    Introduced to close the system; no microphysical justification for the dark matter profiles.
  • domain assumption The three density profiles in Eqs. (1)-(4) describe dark matter in galaxies.
    Taken from astrophysical literature; their use around a wormhole throat is an extrapolation.
  • standard math The Einstein tensor is divergence-free, so the conservation equation Eq. (14) is automatic.
    Bianchi identity; used to derive the redshift function.

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Pith. "Pith review of Traversable Wormholes Sourced by Dark Matter in Loop Quantum Cosmology." pith.science (2026). https://pith.science/paper/ABA3VY52

@misc{pith2026241112063,
  author       = {Pith},
  title        = {Pith review of: Traversable Wormholes Sourced by Dark Matter in Loop Quantum Cosmology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ABA3VY52}},
  note         = {Machine review of arXiv:2411.12063}
}
read the original abstract

In this work, we investigate the existence of wormholes within the framework of Loop Quantum Cosmology, using isotropic dark matter as the source. We analyze three distinct density profiles and solve the modified gravity field equations alongside the stress-energy tensor conservation, applying appropriate boundary conditions to obtain traversable wormhole solutions. Each solution is shown to satisfy the geometric criteria for wormholes, and their regularity is verified by computing the Kretschmann scalar to ensure the absence of singularities under determined conditions. Additionally, we examine the stress-energy tensor to identify scenarios in which energy conditions are violated within this model. The wormhole geometry is further explored through embedding diagrams, and the amount of exotic matter required to sustain these structures is computed using the Volume Integral Quantifier. Finally, we study the shadow produced by our wormhole solution, considering one of the dark matter density profiles, and compare it with observations of the M87 galaxy.

Figures

Figures reproduced from arXiv: 2411.12063 by the authors.

Figure 1
Figure 1. Behavior of b(r)/r considering the model (15) in terms of the radial coordinate with r0 = 1, Rs = 2, ρc = 10−5 , and ρ0 = 10−6 . Changes in the densities ρc and ρ0 do not significantly alter the shape of the graph. where we have taken into account the boundary condition b(r0) = r0 in order to determine the integration constant. The condition b(r0) = r0 was used to integrate the field equation and obtain the form of … view at source ↗
Figure 2
Figure 2. Behavior of b ′ (r) considering the model (15) in terms of the radial coordinate with r0 = 1, Rs = 2, and ρc = 10−5 , for different values of ρ0. Changes in the density ρc do not significantly alter the shape of the graph. 0.99999 1.00000 1.00000 1.00001 1.00001 1.00002 1.00002 1.00003 1.00003 0 5 10 15 20 b(r)−rb’(r) r ρ0 =10−5 ρ0 =3x10−5 ρ0 =5x10−5 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Behavior of b(r) − rb′ (r) considering the model (15) in terms of the radial coordinate with r0 = 1, Rs = 2, and ρc = 10−5 , for different values of ρ0. Changes in the density ρc do not significantly alter the shape of the graph. ω → 0, thus requiring, in general, the imposition of junction conditions. However, the curvature scalars clearly indicate that asymptotic flatness is achieved. This can be seen in [PITH_FU… view at source ↗
Figures from the paper (17 more)
Figure 4
Figure 4. Figure 4: Behavior of the Kretschmann scalar for model ( [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Behavior of b(r)/r considering the model (24) in terms of the radial coordinate with r0 = 1, Rs = 2, ρc = 5 × 10−5 , and ρ0 = 10−6 . Changes in the densities ρc and ρ0 do not significantly alter the shape of the graph. 0 2×10−6 4×10−6 6×10−6 8×10−6 1×10−5 1.2×10−5 1.4×…
Figure 6
Figure 6. Figure 6: Behavior of b ′ (r) considering the model (24) in terms of the radial coordinate with r0 = 1, Rs = 2, and ρc = 5 × 10−5 , for different values of ρ0. Changes in the density ρc do not significantly alter the shape of the graph. B. Redshift function From Eq. (1), (3), (1…
Figure 7
Figure 7. Figure 7: Behavior of b(r) − rb′ (r) considering the model (24) in terms of the radial coordinate with r0 = 1, Rs = 2, and ρc = 5 × 10−5 , for different values of ρ0. Changes in the density ρc do not significantly alter the shape of the graph. expression is not clear. Φ ′ (r) = …
Figure 8
Figure 8. Figure 8: Behavior of the Kretschmann scalar for model ( [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Behavior of b(r)/r considering the model (28) in terms of the radial coordinate with r0 = 1, Rs = 2, ρc = 5 × 10−5 , and ρ0 = 10−7 . Changes in the densities ρc and ρ0 do not significantly alter the shape of the graph. the second condition for wormholes. In [PITH_FULL…
Figure 10
Figure 10. Figure 10: Behavior of b ′ (r) considering the model (28) in terms of the radial coordinate with r0 = 1 and Rs = 2. In the left panel, we fix ρ0 = 10−7 and vary ρc. In the right panel, we fix ρc = 5 × 10−5 and vary ρ0. 0.999998 0.999999 0.999999 1.000000 1.000000 1.000001 1.0000…
Figure 11
Figure 11. Figure 11: Behavior of b(r) − rb′ (r) considering the model (28) in terms of the radial coordinate with r0 = 1 and Rs = 2. In the left panel, we fix ρ0 = 10−7 and vary ρc. In the right panel, we fix ρc = 5 × 10−5 and vary ρ0. B. Redshift function From Eq. (1), (4), (14), and sta…
Figure 12
Figure 12. Figure 12: Behavior of the Kretschmann scalar for model ( [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: Behavior of z(r) considering the model (15) in terms of the radial coordinate with r0 = 1 and Rs = 2. In the left panel, we fix ρ0 = 0.01 and vary ρc. In the right panel, we fix ρc = 0.001 and vary ρ0. Now, we will embed this spacetime into another spacetime, which is…
Figure 14
Figure 14. Figure 14: Embedding diagrams considering the model ( [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: Behavior of z(r) considering the model (24) in terms of the radial coordinate with r0 = 1 and Rs = 2. In the left panel, we fix ρ0 = 0.001 and vary ρc. In the right panel, we fix ρc = 0.00005 and vary ρ0. model, where the higher the value of ρ0 or the lower the value …
Figure 16
Figure 16. Figure 16: Embedding diagrams considering the model ( [PITH_FULL_IMAGE:figures/full_fig_p019_16.png]
Figure 17
Figure 17. Figure 17: Behavior of z(r) considering the model (28) in terms of the radial coordinate with r0 = 1 and Rs = 2. In the left panel, we fix ρ0 = 0.001 and vary ρc. In the right panel, we fix ρc = 0.0005 and vary ρ0. VII. ENERGY CONDITIONS AND AMOUNT OF EXOTIC MATTER The energy co…
Figure 18
Figure 18. Figure 18: Embedding diagrams considering the model ( [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]
Figure 19
Figure 19. Figure 19: VIQ as a function of the radial coordinate, for the [PITH_FULL_IMAGE:figures/full_fig_p024_19.png]
Figure 20
Figure 20. Figure 20: Shadow radius, in meters, as a function of the stat [PITH_FULL_IMAGE:figures/full_fig_p025_20.png]

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Reviewed August 12, 2026 · model on record in the stance chip above.