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arxiv: 2308.10612 · v1 · submitted 2023-08-21 · 🌀 gr-qc

A Study of Morris-Thorne Wormhole in Einstein-Cartan Theory

Sagar V. Soni , A. C. Khunt , A. H. Hasmani This is my paper

Pith reviewed 2026-05-24 07:03 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Einstein-Cartan theoryMorris-Thorne wormholeWeyssenhoff fluidenergy conditionstetrad formalismspin densityred-shift functiontorsion
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The pith

The spin density of a Weyssenhoff fluid in a Morris-Thorne wormhole is derived from the red-shift function in Einstein-Cartan theory.

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

This paper applies Einstein-Cartan theory, which includes spacetime torsion, to the Morris-Thorne wormhole metric. Using the Newman-Penrose-Jogia-Griffiths tetrad formalism and a Weyssenhoff fluid with anisotropic matter, it derives the spin density in terms of the red-shift function. It then examines the energy conditions at the wormhole throat. A sympathetic reader would care because this shows how torsion from spin can influence the exotic matter requirements for wormholes, potentially offering new ways to stabilize them compared to standard general relativity.

Core claim

In the Einstein-Cartan theory with a Weyssenhoff fluid, the field equations for the Morris-Thorne wormhole are solved using tetrad methods, yielding an expression for the spin density directly in terms of the red-shift function, while the energy conditions are checked at the throat where the shape function meets its minimum.

What carries the argument

The Newman-Penrose-Jogia-Griffiths tetrad formalism applied to Einstein-Cartan field equations with Weyssenhoff fluid for the Morris-Thorne metric.

If this is right

  • The energy conditions at the throat are modified by the torsion term arising from the spin density.
  • Wormhole solutions exist when the spin density satisfies the relation to the red-shift function.
  • The anisotropic stress-energy of the Weyssenhoff fluid supports the throat geometry under torsion.
  • Torsion contributions can alter the usual violations of energy conditions seen in general relativity.

Where Pith is reading between the lines

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

  • This derivation suggests torsion could reduce the need for phantom energy in wormhole models.
  • The approach may extend to other metrics or dynamic wormholes in Einstein-Cartan theory.
  • Numerical simulations with specific red-shift functions could test the energy condition outcomes.

Load-bearing premise

That the Newman-Penrose-Jogia-Griffiths tetrad formalism and the Weyssenhoff fluid ansatz with anisotropic matter are sufficient to capture the torsion effects and yield consistent field equations for the wormhole metric.

What would settle it

A calculation showing that the spin density cannot be expressed solely in terms of the red-shift function while satisfying the Einstein-Cartan field equations for the given metric, or an observation where energy conditions at a hypothetical wormhole throat contradict the derived relations.

Figures

Figures reproduced from arXiv: 2308.10612 by A. C. Khunt, A. H. Hasmani, Sagar V. Soni.

Figure 1
Figure 1. Figure 1: Left Panel (a) Profile of shape functions b(r) and the red-shift function (Φ(r) = r0 rn , with r0 = 1, n = 3), Right Panel (b) The flare-out condition against the radial coordinate. The vertical grey band represent throat radius region, r0 ≤ 1 Employing this particular choice of SF, we investigate different cases. The fea￾tures of the shape function and the trend of the red-shift function are shown in Fig … view at source ↗
Figure 2
Figure 2. Figure 2: Variation of ρ, pr, pt and ∆ with radial coordinate r for particular choice of SF with n = 3 , r0 = 1 and C = 0.9. The vertical grey band represent throat radius region, r0 ≤ 1 [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Variation of energy conditions, NEC, SEC and DEC against radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The hydrostatic balance of the structure under different forces. [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
read the original abstract

This paper focuses on the Einstein-Cartan theory, an extension of general relativity that incorporates a torsion tensor into spacetime. The differential form technique is employed to analyze the Einstein-Cartan theory, which replaces tensors with tetrads. A tetrad formalism, specifically the Newmann-Penrose-Jogia-Griffiths formalism, is used to study the field equations. The energy-momentum tensor is also determined, considering a Weyssenhoff fluid with anisotropic matter. The spin density is derived in terms of the red-shift function. We also examine the energy conditions at the throat of a Morris-Thorne wormhole. The results shed light on the properties of wormholes in the context of the Einstein-Cartan theory, including the energy conditions at the throat.

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

1 major / 1 minor

Summary. The paper examines Morris-Thorne wormholes in Einstein-Cartan theory using the differential-form approach and the Newman-Penrose-Jogia-Griffiths tetrad formalism. It models the matter source as a Weyssenhoff fluid with anisotropic pressures, derives an expression for the spin density in terms of the redshift function, and evaluates the energy conditions at the wormhole throat.

Significance. If the central derivations hold without gaps in the tetrad decomposition or contorsion terms, the work would provide a concrete illustration of how torsion sourced by spin density can modify the effective stress-energy tensor and potentially relax the null-energy-condition violation at the throat of a Morris-Thorne wormhole.

major comments (1)
  1. [Field equations and energy-momentum tensor (abstract description)] The central claim that the NPJG formalism applied to the Morris-Thorne metric yields a spin-density expression depending only on the redshift function Φ(r) (with shape function b(r) remaining free) requires explicit verification that the spin coefficients, torsion 2-forms, and decomposition of the Weyssenhoff spin tensor into anisotropic fluid variables are consistent with the coordinate patch; any mismatch would propagate directly into the effective stress-energy and invalidate the energy-condition statements at the throat.
minor comments (1)
  1. [Abstract] Abstract: 'Newmann-Penrose' is a typographical error and should read 'Newman-Penrose'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the single major comment point by point below.

read point-by-point responses

  1. Referee: The central claim that the NPJG formalism applied to the Morris-Thorne metric yields a spin-density expression depending only on the redshift function Φ(r) (with shape function b(r) remaining free) requires explicit verification that the spin coefficients, torsion 2-forms, and decomposition of the Weyssenhoff spin tensor into anisotropic fluid variables are consistent with the coordinate patch; any mismatch would propagate directly into the effective stress-energy and invalidate the energy-condition statements at the throat.

    Authors: We agree that explicit verification of these intermediate steps is essential for rigor. Our derivations apply the NPJG tetrad formalism directly to the Morris-Thorne line element in the standard coordinate patch, with the Weyssenhoff spin tensor decomposed into anisotropic pressure components consistent with the contorsion contributions. The cancellation that leaves spin density dependent only on Φ(r) arises from the specific structure of the torsion 2-forms in this geometry. To address the concern transparently, we will add an appendix containing the full expressions for the spin coefficients, torsion 2-forms, and the decomposition verification in the revised manuscript. This addition will not alter the energy-condition results at the throat but will make the consistency explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of spin density or energy conditions

full rationale

The paper applies the NPJG tetrad formalism and Weyssenhoff fluid to the Morris-Thorne metric within Einstein-Cartan theory, deriving spin density from the field equations in terms of the redshift function and checking energy conditions at the throat. The abstract and description provide no equations or steps that reduce a claimed result to its own inputs by construction, no fitted parameters renamed as predictions, and no load-bearing self-citations. The derivation chain uses standard torsion extensions and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the derivation of spin density from the redshift function and the choice of fluid ansatz are the main unstated modeling choices.

pith-pipeline@v0.9.0 · 5661 in / 1043 out tokens · 21141 ms · 2026-05-24T07:03:57.143284+00:00 · methodology

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Reference graph

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