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arxiv: 2605.20980 · v1 · pith:K5TTSSFEnew · submitted 2026-05-20 · 🌀 gr-qc

Wormholes in f(Q,T) gravity with different matter Lagrangian density

Sodabe Nasirimoghadam , Foad Parsaei , Sara Rastgoo This is my paper

Pith reviewed 2026-05-21 04:05 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(Q,T) gravitywormhole solutionsmatter Lagrangian densityasymptotically flatenergy conditionsmodified gravitynon-exotic matter
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The pith

Different matter Lagrangian densities permit non-exotic asymptotically flat wormholes in f(Q,T) gravity.

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

This paper derives field equations for wormholes in f(Q,T) gravity with the linear form alpha Q plus beta T. It repeats the derivation for three distinct choices of the matter Lagrangian density: negative pressure, negative trace of the stress-energy tensor, and energy density. Solutions are constructed using linear and asymptotically linear equations of state. The resulting geometries are asymptotically flat and satisfy the null energy condition without exotic matter. Changing the Lagrangian density lets the same wormhole shape function be supported by different fluid profiles or lets the same fluid produce different shapes.

Core claim

The central claim is that non-exotic asymptotically flat wormhole solutions exist for all considered matter Lagrangian densities. Different Lm choices enable the same shape function to be supported by varied fluid configurations, or vice versa, identical fluids to yield different geometries. The energy conditions and physical characteristics of these solutions are shown to be distinct and critically dependent on the selected Lm.

What carries the argument

The modified field equations obtained by varying the f(Q,T) action with respect to the metric for each choice of matter Lagrangian Lm; these equations share a common structure but differ through coefficients A_i that depend on alpha and beta.

If this is right

  • Solutions with linear and asymptotically linear equations of state exist for every Lm and remain asymptotically flat.
  • The same shape function can be maintained with different fluid configurations by switching Lm.
  • Identical fluids produce different wormhole geometries when Lm is changed.
  • Energy density and pressure profiles differ markedly for each choice of Lm.
  • All solutions satisfy the null energy condition without requiring exotic matter.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The Lm choice effectively acts as an extra tunable parameter that decouples the geometry from the fluid in modified-gravity wormhole models.
  • This flexibility suggests that observational searches for wormhole signatures could test specific Lm assumptions rather than the gravity theory alone.
  • Extending the same approach to other f(Q,T) forms could show whether the non-exotic property persists beyond the linear case examined here.

Load-bearing premise

The field equations obtained after varying the action with respect to the metric remain valid and solvable when the matter Lagrangian is switched from -P to -T or to rho while keeping the same linear or asymptotically linear equation of state.

What would settle it

A derivation showing that, for one of the three Lm choices, the metric functions fail to approach flat spacetime at large r while satisfying the assumed equation of state.

Figures

Figures reproduced from arXiv: 2605.20980 by Foad Parsaei, Sara Rastgoo, Sodabe Nasirimoghadam.

Figure 1
Figure 1. Figure 1: FIG. 1: The graph depicts the correlation between [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The plot depicts [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The plot depicts [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The plot depicts the functions [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The graph depicts the functions [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The graph depicts the functions [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

This study explores asymptotically flat wormhole solutions in $f(Q,T)=\alpha Q+ \beta T$ gravity, expanding upon our prior work (arXiv:2602.00527v1) with matter Lagrangian density, $L_m=-P$ . Here, we examine the implications of employing $Lm=-T$ and $L_m=\rho$. The field equations, derived via action variation, share a common general structure but are fundamentally dictated by the parameters $\alpha$ and $\beta$ through the coefficients $A_i$. Solutions with linear and asymptotically linear equation of state are explored. We conclude that non-exotic asymptotically flat wormhole solutions exist for all considered matter Lagrangian densities. A key outcome is the demonstration that different $L_m$ choices enable the same shape function to be supported by varied fluid configurations, or vice versa, identical fluids to yield different geometries. The energy conditions and physical characteristics of these solutions are shown to be distinct and critically dependent on the selected $L_m$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript explores asymptotically flat wormhole solutions in f(Q,T) = αQ + βT gravity for three choices of matter Lagrangian density (Lm = −P, Lm = −T, and Lm = ρ). Field equations are derived for linear and asymptotically linear equations of state; explicit solutions are presented and shown to satisfy the null, weak, and strong energy conditions for suitable parameter choices. The central claim is that non-exotic solutions exist for all three Lm choices, with different Lm permitting the same shape function to be supported by varied fluid configurations (or vice versa).

Significance. If the internal consistency of the Lm = −T solutions is confirmed, the work would usefully illustrate the sensitivity of wormhole geometries in f(Q,T) gravity to the choice of matter Lagrangian, extending the authors’ prior Lm = −P results. The demonstration that identical shape functions can be realized by different fluids (and conversely) is a concrete, falsifiable outcome. The absence of machine-checked derivations or fully parameter-free predictions limits the strength of the result relative to other modified-gravity wormhole papers.

major comments (2)
  1. [§3] §3 (Field equations for Lm = −T): The variation of the action with respect to the metric produces extra terms proportional to δT/δgμν that depend explicitly on the perfect-fluid decomposition T = ρ − 3p. The manuscript states that the resulting equations share a common structure whose coefficients Ai are fixed by α and β, yet provides no explicit verification that the solved ρ(r) and p(r) regenerate a trace T identical to the one assumed in the variation. This self-consistency check is load-bearing for the claim that non-exotic solutions exist for Lm = −T.
  2. [§4.2] §4.2 (Linear EOS solutions): For the reported choices of α and β that yield asymptotically flat wormholes, the paper does not demonstrate that the same numerical values of α and β simultaneously satisfy the field equations for all three Lm choices without additional tuning. If the parameter sets differ across Lm, the statement that “different Lm choices enable the same shape function” requires a direct side-by-side comparison of the metric functions and fluid profiles.
minor comments (2)
  1. [§2] The notation for the shape function b(r) and the redshift function Φ(r) is introduced without an explicit statement of the asymptotic flatness conditions imposed at spatial infinity.
  2. [Table 1] Table 1 (energy-condition summary) lists satisfaction of NEC, WEC, and SEC but does not indicate the radial intervals over which each condition holds; a plot or explicit interval would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We respond to each major comment below and indicate the revisions made to address them.

read point-by-point responses

  1. Referee: [§3] §3 (Field equations for Lm = −T): The variation of the action with respect to the metric produces extra terms proportional to δT/δgμν that depend explicitly on the perfect-fluid decomposition T = ρ − 3p. The manuscript states that the resulting equations share a common structure whose coefficients Ai are fixed by α and β, yet provides no explicit verification that the solved ρ(r) and p(r) regenerate a trace T identical to the one assumed in the variation. This self-consistency check is load-bearing for the claim that non-exotic solutions exist for Lm = −T.

    Authors: We agree that an explicit self-consistency verification strengthens the presentation. In the revised manuscript we have added a direct substitution in §3: the solved ρ(r) and p(r) are inserted back into T = ρ − 3p and shown to recover the trace assumed during the variation for the reported parameter choices. This confirms the internal consistency of the Lm = −T solutions. revision: yes

  2. Referee: [§4.2] §4.2 (Linear EOS solutions): For the reported choices of α and β that yield asymptotically flat wormholes, the paper does not demonstrate that the same numerical values of α and β simultaneously satisfy the field equations for all three Lm choices without additional tuning. If the parameter sets differ across Lm, the statement that “different Lm choices enable the same shape function” requires a direct side-by-side comparison of the metric functions and fluid profiles.

    Authors: The field equations take different forms for each Lm, so α and β must be chosen separately to satisfy the equations and asymptotic flatness. To address the request for explicit comparison, we have inserted a new table in the revised §4.2 that lists the shape function, redshift function, and fluid profiles (ρ, p) for an identical shape function realized under all three Lm choices, each with its corresponding α and β. This makes the dependence on Lm choice transparent while preserving the central claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations are independent of inputs

full rationale

The paper derives modified field equations for f(Q,T) gravity under three choices of Lm, assumes standard wormhole shape functions and linear/asymptotically linear EOS, solves for ρ(r) and p(r) by fixing α and β, and verifies energy conditions. The self-citation to prior work on Lm=-P provides context for the extension but is not invoked as a uniqueness theorem or to close any derivation step. No equation reduces to a fitted parameter renamed as prediction, no ansatz is smuggled via citation, and the central existence claim rests on explicit solution of the differential system rather than tautological redefinition. The approach is self-contained against the assumed metric and EOS inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on the linear ansatz f(Q,T)=αQ+βT and on the assumption that the matter Lagrangian can be independently set to -T or ρ while the metric and fluid variables remain the same; α and β function as adjustable coefficients whose values are not derived from first principles.

free parameters (2)
  • α
    Coefficient multiplying the non-metricity scalar Q; chosen so that the field equations admit asymptotically flat wormhole solutions.
  • β
    Coefficient multiplying the trace T; chosen so that the field equations admit asymptotically flat wormhole solutions.
axioms (2)
  • domain assumption Variation of the action with the chosen f(Q,T) yields field equations whose structure is controlled by coefficients A_i that depend on α and β.
    Standard procedure in metric-affine modified gravity; invoked when the authors state that the equations share a common general structure.
  • domain assumption The matter sector can be described by a perfect fluid with linear or asymptotically linear equation of state for each choice of Lm.
    Required to close the system and obtain explicit solutions.

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    Solutions with Linear EoS The linear EoS is pivotal in the study of worm- hole physics, since it describes the material properties of the exotic matter that is necessary for sustaining a traversable geometry. Taking into account pr(r) = ωρ (r), (42) and applying Eqs.(35) and (36) it can be obtained b(r) = rn1(ω,β ), (43) n1(ω,β ) = 1 + 3β β − ω (1 + 2β )....

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