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Study of Wormholes in Symmetric Teleparallel Theories of Gravity

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Pith's one-line read 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.

desk verdict A careful compilation of five published wormhole papers; Chapter 2's dark-matter solutions are not asymptotically flat, which undercuts the headline viability claim. read the letter →

arxiv 2505.04952 v1 pith:LILO5VKN submitted 2025-05-08 gr-qc

Moreshwar Tayde This is my paper · ORCID
classification gr-qc MSC 83D0583C15 PACS 04.50.Kd04.20.Jb
keywords traversablewormholesf(Q)gravityf(QT)symmetricteleparallelnullenergyconditiondarkmatterhalosMITbagmodelnoncommutativegeometry
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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 / 5 minor

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.

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 (5)
  1. [Sec. 2.4.1, Eq. (2.23)] 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.
  2. [Sec. 2.4.2, Eq. (2.38)] 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.
  3. [Sec. 2.2, Eq. (2.10)] 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.
  4. [Sec. 2.4.1, Eqs. (2.28), (2.32), (2.36)] 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.
  5. [Sec. 2.4.3, Tables 2.1-2.2] 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.
minor comments (5)
  1. [Sec. 1.7, Eq. (1.12)] The surrounding text labels G_μν as the "Einstein tenor"; this should be "Einstein tensor".
  2. [Captions of Figs. 4.2 and 5.5] The captions contain typographical errors: "valus" should be "values" in Fig. 4.2, and "wih" should be "with" in Fig. 5.5.
  3. [Eqs. (2.53)-(2.55) and (3.7)-(3.9)] Several displayed formulas have unbalanced parentheses or awkward line breaks that make independent verification difficult; please re-typeset these expressions carefully.
  4. [Sec. 4.2] 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.
  5. [Secs. 3.3 and 2.6] 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.

Circularity Check

1 steps flagged · score 6.0 of 10

The barotropic f(Q,T) chapter's NEC violation is built into the assumed phantom EoS; other chapters construct solutions from assumed profiles rather than predict them.

  1. self definitional [Chapter 3, Sec. 3.3.0.1, Eqs. (3.16) and (3.23)-(3.25), Fig. 3.3, Table 3.2]
    "In this study, we focus on WH solutions governed by the following form of EoS [155, 182] pr = ωρ . (3.16) ... Considering some specific values of ω and β from the derived range, we plotted the graph for the energy density in Fig. 3.2. ... the radial NEC, that is, ρ + pr, shows an increasing negative behavior in the vicinity of the throat."

    With pr = ωρ imposed as the input equation of state, the radial NEC is simply ρ + pr = (1 + ω)ρ. The paper selects the phantom value ω = -1.5 (Table 3.1 lists the allowed range ω ∈ (-∞,-1)) and shows ρ > 0 in Fig. 3.2. Therefore ρ + pr = -0.5ρ < 0 is an algebraic identity of the assumed EoS; it holds for any shape function and any gravity model, independent of the f(Q,T) field equations. The chapter's conclusion that the radial NEC is violated, and that this indicates effective matter-geometry coupling, restates the input EoS rather than deriving a dynamical effect. No field-equation output can change the sign of 1 + ω once this EoS and parameter value are chosen.

full rationale

The only step that reduces by construction is the barotropic NEC violation in Chapter 3. Elsewhere the thesis works constructively: in Chapter 2 the shape function is integrated from an assumed dark-matter energy density and then the energy conditions are evaluated; in Chapters 4 and 5 shape functions or smeared density profiles are assumed and the resulting field equations are solved. These are ansatz-based constructions rather than circular predictions, although their physical validity is weakened by other issues: for example, Eqs. (2.23) and (2.38) give nonzero limits for b(r)/r as r → ∞ for the plotted parameters, contradicting the claimed asymptotic flatness. That is a correctness problem, not a circularity. The Chapter 3 barotropic case is different because pr = ωρ with ω = -1.5 fixes ρ + pr = -0.5ρ, so the observed NEC violation is exactly the input EoS restated. Since the abstract presents NEC violation as a headline outcome of the f(Q,T) analysis, this is a partial but real circularity; the remaining chapters and the anisotropic f(Q,T) solutions retain independent computational content.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The thesis introduces no new particles, forces, or conserved quantities. The monopole charge is a standard field-theory concept, and the noncommutative profiles are taken from prior literature. The free parameters listed are the most influential choices made by hand in the constructions.

free parameters (6)
  • alpha (f(Q) or f(Q,T) model parameter) = -5 or 1
    Chosen by hand to satisfy shape function conditions and produce positive energy density plots; not constrained by observations (Secs. 2.4.3, 3.3).
  • beta (f(Q,T) coupling) = e.g., 1, 14, 38, 42
    Selected from the permissible ranges derived from asymptotic flatness; specific values are chosen for plots (Sec. 3.3, Table 3.1).
  • eta (monopole charge) = 0.05, 0.15, 0.25
    Varied to show its effect on NEC; no observational constraint (Sec. 2.4.3).
  • omega (barotropic EoS parameter) = -1.5, -0.5
    Chosen in the phantom or quintessence regions to satisfy conditions (Sec. 3.3).
  • r0 (throat radius) = 1
    Set to unity without loss of generality, but it sets the length scale for all plots (Secs. 2.4, 3.3).
  • Theta (noncommutativity parameter) = 2
    Chosen for plots; the physical value is unknown (Sec. 5.3).
assumptions (6)
  • domain assumption Morris-Thorne metric ansatz with static spherical symmetry (Eq. 1.13).
    All wormhole solutions in the thesis are built on this metric form.
  • domain assumption Flare-out condition b'(r0) < 1 and asymptotic flatness b(r)/r -> 0 as r -> infinity.
    These conditions define a traversable wormhole and are enforced in every construction.
  • domain assumption Field equations of f(Q) and f(Q,T) gravity as given in Secs. 1.10.1 and 1.10.2.
    The thesis relies on these modified gravity actions without deriving them from more fundamental principles.
  • domain assumption Pseudo-Isothermal and NFW dark matter density profiles from the literature (Eqs. 1.36, 1.37).
    These profiles are used as inputs to derive shape functions; their validity is taken from prior work.
  • domain assumption MIT bag model EoS pr = omega (rho - 4B) (Eq. 4.4).
    The bag model is assumed to describe quark matter in the wormhole throat.
  • domain assumption Noncommutative Gaussian and Lorentzian density profiles (Eqs. 1.52, 1.53).
    These profiles are taken from string theory inspired noncommutative geometry literature.

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Pith. "Pith review of Study of Wormholes in Symmetric Teleparallel Theories of Gravity." pith.science (2026). https://pith.science/paper/LILO5VKN

@misc{pith2026250504952,
  author       = {Pith},
  title        = {Pith review of: Study of Wormholes in Symmetric Teleparallel Theories of Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LILO5VKN}},
  note         = {Machine review of arXiv:2505.04952}
}
abstract

This thesis explores traversable wormhole (WH) solutions within symmetric teleparallel gravity and its extensions, including $f(Q)$ and $f(Q, T)$ gravity. Chapter I reviews WH geometry and properties, general relativity, and modified gravity's role in WH physics. Chapter II constructs WHs in $f(Q)$ gravity using dark matter profiles like Pseudo-Isothermal and Navarro-Frenk-White (NFW). For linear $f(Q)$ models, suitable redshift and shape functions satisfying the flare-out condition yield viable WHs, with the monopole charge $\eta$ driving Null Energy Condition (NEC) violation. The Volume Integral Quantifier (VIQ) method shows minimal exotic matter is needed. Nonlinear models like $f(Q) = Q + m Q^n$ fail to meet WH criteria. Chapter III studies $f(Q, T)$ gravity, where $Q$ and the trace $T$ of the energy-momentum tensor are coupled. WHs are examined under barotropic and anisotropic equations of state using forms like $f(Q, T) = \alpha Q + \beta T$ and $f(Q, T) = Q + \lambda_1 Q^2 + \eta_1 T$. NEC violations occur near the throat, indicating effective matter-geometry coupling. Tolman-Oppenheimer-Volkoff (TOV) analysis confirms equilibrium under suitable parameters. Chapter IV employs the MIT bag model in $f(Q, T)$ gravity, treating it as a source of exotic matter. Specific shape functions lead to WHs with NEC violation and TOV-based stability under radial perturbations. Chapter V considers WHs in $f(Q, T)$ gravity with noncommutative geometries inspired by string theory. Gaussian and Lorentzian smeared sources are used. Linear models yield analytical WH solutions, nonlinear ones are numerical. All satisfy the flare-out condition and exhibit NEC violation. Gravitational lensing analysis reveals distinguishable features from black holes. Chapter VI summarizes the results, emphasizing observational prospects in extended gravity frameworks.

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    2025

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.