pith. sign in

arxiv: 1906.10323 · v1 · pith:MIR3HEZ7new · submitted 2019-06-25 · 🌀 gr-qc

Wormholes without exotic matter in nonminimal torsion-matter coupling f(T) gravity

Rui-Hui Lin , Zhen-Yuan Wu , Xiang-Hua Zhai This is my paper

Pith reviewed 2026-05-25 17:00 UTC · model grok-4.3

classification 🌀 gr-qc
keywords wormholesf(T) gravitynonminimal couplingtorsionnull energy conditionasymptotic flatnessexotic matter
0
0 comments X

The pith

Nonminimal torsion-matter coupling in f(T) gravity lets nonexotic matter thread finite wormholes.

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

The paper studies wormhole solutions in f(T) gravity modified by a nonminimal coupling between torsion and matter. It establishes that this coupling supplies the effective negative energy density required to keep the throat open even when the matter itself satisfies standard energy conditions. Geometric constraints then force the solutions to be finite in size: asymptotic flatness demands rapid density falloff at large radius, and without it the metric either changes signature or loses a valid embedding. A reader would care because the result removes the usual need for exotic matter while revealing a built-in limit on how far such a wormhole can extend.

Core claim

The central claim is that the nonminimal torsion-matter coupling can hold the wormhole open. However, for the wormhole to have asymptotic flatness, the coupling matter density must falloff rapidly at large radius, otherwise the physical wormhole must be finite due to either change of metric signature or lack of valid embedding. On the other hand, the matter source supporting the wormhole can satisfy the null energy condition only in the neighborhood of the throat of the wormhole. Therefore, the wormhole in the underlying model has finite sizes and cannot stretch to the entire spacetime.

What carries the argument

The nonminimal torsion-matter coupling function, which enters the gravitational action and modifies the effective energy-momentum tensor so that ordinary matter can support a wormhole throat.

If this is right

  • The matter source satisfies the null energy condition only near the throat.
  • Coupling matter density must falloff rapidly at large radius to allow asymptotic flatness.
  • Without rapid falloff the wormhole becomes finite because of metric signature change or lack of valid embedding.
  • The resulting wormholes cannot stretch to the entire spacetime.

Where Pith is reading between the lines

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

  • These solutions suggest that traversable wormholes in the model can connect only limited spacetime regions rather than distant parts of the universe.
  • One could look for gravitational lensing or redshift signatures that distinguish finite wormhole geometries from infinite ones.
  • A natural extension would be to derive the required coupling function from a more fundamental action instead of choosing it to fit the throat equations.

Load-bearing premise

The specific nonminimal coupling function is introduced by hand to supply the effective negative energy near the throat while the matter remains nonexotic, rather than being derived from first principles.

What would settle it

A explicit integration of the field equations showing either that the density fails to fall off rapidly enough for asymptotic flatness or that the metric signature changes at finite radius would confirm the finite-size conclusion.

read the original abstract

Wormholes are hypothetical tunnels that connect remote parts of spacetime. In General Relativity, wormholes are threaded by exotic matter that violates the energy conditions. In this work, we consider wormholes threaded by nonexotic matter in nonminimal torsion-matter coupling $f(T)$ gravity. We find that the nonminimal torsion-matter coupling can indeed hold the wormhole open. However, from geometric point of view, for the wormhole to have asymptotic flatness, the coupling matter density must falloff rapidly at large radius, otherwise the physical wormhole must be finite due to either change of metric signature or lack of valid embedding. On the other hand, the matter source supporting the wormhole can satisfy the null energy condition only in the neighborhood of the throat of the wormhole. Therefore, the wormhole in the underlying model has finite sizes and cannot stretch to the entire spacetime.

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 examines traversable wormholes in nonminimal torsion-matter coupling f(T) gravity using a Morris-Thorne-like metric. It claims that a suitably chosen nonminimal coupling allows the wormhole to be threaded by nonexotic matter that satisfies the null energy condition near the throat, while the coupling itself supplies the effective negative energy density required to keep the throat open; however, geometric constraints force the wormhole to be of finite size, with the matter density required to fall off rapidly for asymptotic flatness.

Significance. If the explicit solutions and field-equation checks hold, the work supplies a concrete existence proof that nonminimal f(T) gravity can support wormholes without exotic matter, extending earlier f(T) results. The geometric limitation to finite size and the restriction of NEC compliance to the throat region are clearly stated and constitute falsifiable predictions for the model class.

major comments (2)
  1. [Abstract and the section defining the nonminimal coupling] The specific nonminimal coupling function (introduced to close the modified field equations) is chosen by hand to produce the desired effective negative energy density near the throat while keeping the matter tensor nonexotic. No variational principle, symmetry argument, or limiting procedure from a more fundamental action is supplied to motivate this functional form; because the central claim rests on this choice, the result remains an existence proof rather than evidence that such couplings arise naturally.
  2. [Geometric analysis and asymptotic-flatness discussion] The geometric argument that rapid fall-off of the coupling matter density is required for asymptotic flatness (otherwise the wormhole is finite due to signature change or embedding failure) is stated but not accompanied by an explicit check that the derived metric functions and density profiles actually satisfy the asymptotic-flatness boundary conditions at large r while remaining consistent with the field equations.
minor comments (2)
  1. Notation for the torsion scalar T and the coupling function should be introduced with an explicit equation number on first use.
  2. [Abstract] The abstract would be clearer if it briefly indicated the explicit form adopted for the nonminimal coupling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and the section defining the nonminimal coupling] The specific nonminimal coupling function (introduced to close the modified field equations) is chosen by hand to produce the desired effective negative energy density near the throat while keeping the matter tensor nonexotic. No variational principle, symmetry argument, or limiting procedure from a more fundamental action is supplied to motivate this functional form; because the central claim rests on this choice, the result remains an existence proof rather than evidence that such couplings arise naturally.

    Authors: We agree that the nonminimal coupling is selected by hand to close the field equations and produce the required effective negative energy density while keeping the matter source nonexotic. The manuscript is presented explicitly as an existence proof that such couplings in nonminimal f(T) gravity can support wormholes threaded by nonexotic matter near the throat. No variational principle or fundamental derivation is supplied because the work explores the consequences within this class of models rather than deriving the coupling from a more basic action. We therefore do not intend to alter this aspect of the presentation. revision: no

  2. Referee: [Geometric analysis and asymptotic-flatness discussion] The geometric argument that rapid fall-off of the coupling matter density is required for asymptotic flatness (otherwise the wormhole is finite due to signature change or embedding failure) is stated but not accompanied by an explicit check that the derived metric functions and density profiles actually satisfy the asymptotic-flatness boundary conditions at large r while remaining consistent with the field equations.

    Authors: The geometric constraints on asymptotic flatness and embedding are derived in the manuscript from the Morris-Thorne-like metric and the requirement that the metric signature remain Lorentzian with a valid embedding. We acknowledge that an explicit verification applying the specific derived metric functions and density profiles to confirm the large-r boundary conditions and field-equation consistency would strengthen the argument. In the revised version we will add this explicit check. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces a nonminimal torsion-matter coupling in f(T) gravity and solves the modified field equations for a Morris-Thorne wormhole metric, finding that the coupling can support the throat with nonexotic matter satisfying NEC locally. The functional form of the coupling is selected to satisfy the equations rather than derived from a variational principle, but this is an explicit modeling assumption, not a self-definitional loop, fitted input renamed as prediction, or reduction via self-citation. No load-bearing uniqueness theorems or ansatze from the authors' prior work are invoked, and the geometric constraints on asymptotic flatness and finite size emerge directly from the metric and field equations without circularity. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed from abstract alone; the full paper would be expected to specify the exact f(T) form and coupling function, which typically introduce free parameters and domain assumptions about the metric.

axioms (1)
  • domain assumption The spacetime is described by a static, spherically symmetric metric of Morris-Thorne wormhole form.
    Standard ansatz invoked for wormhole studies; location implied by context of asymptotic flatness and throat.

pith-pipeline@v0.9.0 · 5685 in / 1261 out tokens · 26974 ms · 2026-05-25T17:00:45.001004+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    Morris, K.S

    M.S. Morris, K.S. Thorne, Am. J. Phys. 56(5), 395 (1988). DOI 10.1119/1.15620

    work page doi:10.1119/1.15620 1988

  2. [2]

    Visser, Lorentzian Wormholes: From Einstein to Hawking (AIP, 1995)

    M. Visser, Lorentzian Wormholes: From Einstein to Hawking (AIP, 1995)

    work page 1995

  3. [3]

    Sotiriou, V

    T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82(1), 451 (2010). DOI 10.1103/revmodphys.82.451

    work page doi:10.1103/revmodphys.82.451 2010

  4. [4]

    De Felice, S

    A. De Felice, S. Tsujikawa, Living Rev. Relativity 13, 3 (2010). DOI 10.12942/lrr-2010-3

    work page doi:10.12942/lrr-2010-3 2010

  5. [5]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov, Phys. Rep. 505(2), 59 (2011). DOI https://doi.org/10.1016/j.physrep.2011.04.001

    work page doi:10.1016/j.physrep.2011.04.001 2011

  6. [6]

    Lobo, M.A

    F.S.N. Lobo, M.A. Oliveira, Phys. Rev. D 80, 104012 (2009). DOI 10.1103/PhysRevD.80.104012

    work page doi:10.1103/physrevd.80.104012 2009

  7. [7]

    Pavlovic, M

    P. Pavlovic, M. Sossich, Eur. Phys. J. C 75(3), 117 (2015). DOI 10.1140/epjc/s10052-015-3331-y

    work page doi:10.1140/epjc/s10052-015-3331-y 2015

  8. [8]

    Bambi, A

    C. Bambi, A. Cardenas-Avendano, G.J. Olmo, D. Rubiera-Garcia, Phys. Rev. D 93, 064016 (2016). DOI 10.1103/PhysRevD.93.064016

    work page doi:10.1103/physrevd.93.064016 2016

  9. [9]

    Mazharimousavi, M

    S.H. Mazharimousavi, M. Halilsoy, Mod. Phys. Lett. A 31(37), 1650203 (2016). DOI 10.1142/S0217732316502035

    work page doi:10.1142/s0217732316502035 2016

  10. [10]

    Mazharimousavi, M

    S.H. Mazharimousavi, M. Halilsoy, Mod. Phys. Lett. A 31(34), 1650192 (2016). DOI 10.1142/S0217732316501923

    work page doi:10.1142/s0217732316501923 2016

  11. [11]

    Garcia, F.S.N

    N.M. Garcia, F.S.N. Lobo, Phys. Rev. D 82, 104018 (2010). DOI 10.1103/PhysRevD.82.104018

    work page doi:10.1103/physrevd.82.104018 2010

  12. [12]

    Garcia, F.S.N

    N.M. Garcia, F.S.N. Lobo, Class. Quantum Grav. 28(8), 085018 (2011). DOI 10.1088/0264-9381/28/8/085018

    work page doi:10.1088/0264-9381/28/8/085018 2011

  13. [13]

    Harko, F.S.N

    T. Harko, F.S.N. Lobo, M.K. Mak, S.V. Sushkov, Phys. Rev. D 87, 067504 (2013). DOI 10.1103/PhysRevD.87. 067504

    work page doi:10.1103/physrevd.87 2013

  14. [14]

    Zubair, M., Waheed, Saira, Ahmad, Yasir, Eur. Phys. J. C 76(8), 444 (2016). DOI 10.1140/epjc/ s10052-016-4288-1

    work page doi:10.1140/epjc/ 2016

  15. [15]

    Moraes, P.K

    P.H.R.S. Moraes, P.K. Sahoo, Phys. Rev. D 96, 044038 (2017). DOI 10.1103/PhysRevD.96.044038

    work page doi:10.1103/physrevd.96.044038 2017

  16. [16]

    Sahoo, P.H.R.S

    P.K. Sahoo, P.H.R.S. Moraes, P. Sahoo, Eur. Phys. J. C 78(1), 46 (2018). DOI 10.1140/epjc/s10052-018-5538-1

    work page doi:10.1140/epjc/s10052-018-5538-1 2018

  17. [17]

    Maeda, M

    H. Maeda, M. Nozawa, Phys. Rev. D 78, 024005 (2008). DOI 10.1103/PhysRevD.78.024005

    work page doi:10.1103/physrevd.78.024005 2008

  18. [18]

    Kanti, B

    P. Kanti, B. Kleihaus, J. Kunz, Phys. Rev. Lett. 107, 271101 (2011). DOI 10.1103/PhysRevLett.107.271101

    work page doi:10.1103/physrevlett.107.271101 2011

  19. [19]

    Hohmann, C

    M. Hohmann, C. Pfeifer, M. Raidal, H. Veerme, J. Cos- mol. Astropart. Phys. 2018(10), 003 (2018)

    work page 2018

  20. [20]

    Lobo, Class

    F.S.N. Lobo, Class. Quantum Grav. 25(17), 175006 (2008). DOI 10.1088/0264-9381/25/17/175006

    work page doi:10.1088/0264-9381/25/17/175006 2008

  21. [21]

    Shaikh, S

    R. Shaikh, S. Kar, Phys. Rev. D 94, 024011 (2016). DOI 10.1103/PhysRevD.94.024011

    work page doi:10.1103/physrevd.94.024011 2016

  22. [22]

    Shaikh, Phys

    R. Shaikh, Phys. Rev. D 98, 064033 (2018). DOI 10. 1103/PhysRevD.98.064033

    work page 2018

  23. [23]

    Jim´ enez, L

    J.B. Jim´ enez, L. Heisenberg, G.J. Olmo, D. Rubiera- Garcia, Phys. Rep. 727, 1 (2018). DOI https://doi.org/ 10.1016/j.physrep.2017.11.001

    work page doi:10.1016/j.physrep.2017.11.001 2018

  24. [24]

    Aldrovandi, J

    R. Aldrovandi, J. Pereira, Teleparallel Gravity: An In- troduction. Fundamental Theories of Physics (Springer Netherlands, 2012)

    work page 2012

  25. [25]

    Maluf, Ann

    J.W. Maluf, Ann. Phys. (Berlin) 525(5), 339 (2013). DOI 10.1002/andp.201200272

    work page doi:10.1002/andp.201200272 2013

  26. [26]

    Bengochea, R

    G.R. Bengochea, R. Ferraro, Phys. Rev. D 79(12), 124019 (2009). DOI 10.1103/physrevd.79.124019

    work page doi:10.1103/physrevd.79.124019 2009

  27. [27]

    Linder, Phys

    E.V. Linder, Phys. Rev. D 81(12), 127301 (2010). DOI 10.1103/physrevd.81.127301

    work page doi:10.1103/physrevd.81.127301 2010

  28. [28]

    Y.F. Cai, S. Capozziello, M. De Laurentis, E.N. Saridaki s, Rep. Prog. Phys. 79(10), 106901 (2016). DOI 10.1088/ 0034-4885/79/10/106901

    work page 2016

  29. [30]

    Feng, F.F

    C.J. Feng, F.F. Ge, X.Z. Li, R.H. Lin, X.H. Zhai, Phys. Rev. D 92(10), 104038 (2015). DOI 10.1103/physrevd. 92.104038

    work page doi:10.1103/physrevd 2015

  30. [31]

    Lin, X.H

    R.H. Lin, X.H. Zhai, X.Z. Li, Eur. Phys. J. C 77(8), 504 (2017). DOI 10.1140/epjc/s10052-017-5074-4

    work page doi:10.1140/epjc/s10052-017-5074-4 2017

  31. [32]

    B¨ ohmer, T

    C.G. B¨ ohmer, T. Harko, F.S.N. Lobo, Phys. Rev. D 85, 044033 (2012). DOI 10.1103/PhysRevD.85.044033

    work page doi:10.1103/physrevd.85.044033 2012

  32. [33]

    Sharif, S

    M. Sharif, S. Rani, Phys. Rev. D 88, 123501 (2013). DOI 10.1103/PhysRevD.88.123501

    work page doi:10.1103/physrevd.88.123501 2013

  33. [34]

    Bahamonde, U

    S. Bahamonde, U. Camci, S. Capozziello, M. Jamil, Phys. Rev. D 94, 084042 (2016). DOI 10.1103/PhysRevD.94. 084042

    work page doi:10.1103/physrevd.94 2016

  34. [35]

    Sharif, K

    M. Sharif, K. Nazir, Ann. Phys. 393, 145 (2018). DOI https://doi.org/10.1016/j.aop.2018.04.003

    work page doi:10.1016/j.aop.2018.04.003 2018

  35. [36]

    Krˇ sˇ s´ ak, E.N

    M. Krˇ sˇ s´ ak, E.N. Saridakis, Class. Quant. Grav.33(11), 115009 (2016). DOI 10.1088/0264-9381/33/11/115009

    work page doi:10.1088/0264-9381/33/11/115009 2016

  36. [37]

    Golovnev, T

    A. Golovnev, T. Koivisto, M. Sandstad, Class. Quantum Grav. 34(14), 145013 (2017). DOI 10.1088/1361-6382/ aa7830

    work page doi:10.1088/1361-6382/ 2017

  37. [38]

    Lucas, Y.N

    T.G. Lucas, Y.N. Obukhov, J.G. Pereira, Phys. Rev. D 80, 064043 (2009). DOI 10.1103/PhysRevD.80.064043

    work page doi:10.1103/physrevd.80.064043 2009

  38. [39]

    Lin, X.H

    R.H. Lin, X.H. Zhai, Phys. Rev. D 99, 024022 (2019). DOI 10.1103/PhysRevD.99.024022

    work page doi:10.1103/physrevd.99.024022 2019

  39. [40]

    Lin, X.H

    R.H. Lin, X.H. Zhai, X.Z. Li, Journal of Cosmology and Astroparticle Physics 2017(03), 040 (2017). DOI 10.1088/1475-7516/2017/03/040

    work page doi:10.1088/1475-7516/2017/03/040 2017

  40. [41]

    Minazzoli, T

    O. Minazzoli, T. Harko, Phys. Rev. D 86(8), 087502 (2012). DOI 10.1103/physrevd.86.087502

    work page doi:10.1103/physrevd.86.087502 2012

  41. [42]

    Rosa, J.P.S

    J.a.L. Rosa, J.P.S. Lemos, F.S.N. Lobo, Phys. Rev. D 98, 064054 (2018). DOI 10.1103/PhysRevD.98.064054

    work page doi:10.1103/physrevd.98.064054 2018

  42. [43]

    Cataldo, P

    M. Cataldo, P. Labra˜ na, S. del Campo, J. Crisostomo, P. Salgado, Phys. Rev. D 78, 104006 (2008). DOI 10. 1103/PhysRevD.78.104006

    work page 2008

  43. [44]

    B¨ ohmer, A

    C.G. B¨ ohmer, A. Mussa, N. Tamanini, Class. Quantum Grav. 28(24), 245020 (2011). DOI 10.1088/0264-9381/ 28/24/245020

    work page doi:10.1088/0264-9381/ 2011

  44. [45]

    Tamanini, C.G

    N. Tamanini, C.G. B¨ ohmer, Phys. Rev. D 86(4), 044009 (2012). DOI 10.1103/physrevd.86.044009

    work page doi:10.1103/physrevd.86.044009 2012

  45. [46]

    Ferraro, F

    R. Ferraro, F. Fiorini, Phys. Rev. D 84, 083518 (2011). DOI 10.1103/PhysRevD.84.083518

    work page doi:10.1103/physrevd.84.083518 2011