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arxiv: 2606.11261 · v1 · pith:CMLMR5PFnew · submitted 2026-06-09 · 🌀 gr-qc

Slowly rotating traversable wormholes supported by radially varying string-fluid matter: From regular geometries to photon trajectories

A. Errehymy , B. Turimov , M. A. Khan , S. Usanov , Z. Yasakov , Z. Avezmuratova This is my paper

Pith reviewed 2026-06-27 12:46 UTC · model grok-4.3

classification 🌀 gr-qc
keywords traversable wormholesstring fluidslow rotationphoton trajectoriesframe draggingasymptotically flatgeneral relativityanisotropic matter
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0 comments X

The pith

Radially varying string fluids support slowly rotating traversable wormholes that remain regular and asymptotically flat.

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

This paper establishes that string fluids whose properties vary with radial distance can serve as matter sources for slowly rotating traversable wormholes. Allowing the transverse pressure to depend on radius lets the fluid transition smoothly from a de Sitter-like core near the throat to a string-dominated region at larger distances. The resulting energy density and shape function stay well-behaved, satisfy the Einstein equations, and produce a regular, horizon-free, asymptotically flat spacetime. Modest rotation introduces frame-dragging that twists photon paths differently for co-rotating and counter-rotating cases, with the differences most pronounced near the throat. Distinct radial profiles for the string fluid generate different photon-ring patterns that could act as observational signatures.

Core claim

The central claim is that a string fluid with radially dependent transverse pressure supplies a consistent source for slowly rotating traversable wormholes. This choice keeps the energy density and shape function regular, satisfies the field equations, and yields geometries without horizons that are asymptotically flat. Slow rotation adds frame-dragging effects that separate co-rotating and counter-rotating photon trajectories most strongly near the throat, while static potentials dominate at large distances. Different radial profiles of the fluid produce distinctive photon-sphere structures.

What carries the argument

The radially dependent transverse pressure in the string fluid, chosen so the energy density and shape function remain well-behaved and satisfy the Einstein equations for a regular asymptotically flat geometry.

If this is right

  • The spacetime stays regular and horizon-free when slow rotation is included.
  • Photon trajectories display frame-dragging differences strongest near the throat.
  • Different radial profiles of the string fluid yield distinctive photon-ring patterns.
  • At large distances the spacetime is governed by the static gravitational potentials.
  • Anisotropic matter influences both spacetime curvature and light propagation.

Where Pith is reading between the lines

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

  • These wormhole models could be tested by comparing predicted photon rings against observations of light around compact objects.
  • The radial-variation approach might extend to other anisotropic matter sources or to faster rotation regimes.
  • Photon trajectory differences could help distinguish wormholes from black holes in future imaging data.
  • Stability of the geometries against small perturbations remains an open question for these matter profiles.

Load-bearing premise

The transverse pressure can be chosen to depend on radius so that the energy density and shape function stay well-behaved, satisfy the Einstein equations, and produce a regular horizon-free asymptotically flat geometry.

What would settle it

A calculation showing that no radial dependence of the transverse pressure produces an energy density and shape function that remain positive and finite while satisfying the Einstein equations for an asymptotically flat rotating wormhole metric.

Figures

Figures reproduced from arXiv: 2606.11261 by A. Errehymy, B. Turimov, M. A. Khan, S. Usanov, Z. Avezmuratova, Z. Yasakov.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

This work investigates slowly rotating traversable wormholes supported by string fluids whose properties vary with distance from the throat. This radial variation allows the matter to transition smoothly from a de Sitter-like core near the center to a string-dominated environment further out, producing a regular, horizon-free, and asymptotically flat spacetime. By letting the transverse pressure depend on radius, the fluid naturally adapts to the surrounding geometry, resulting in a well-behaved energy density and shape function. Even modest rotation introduces frame-dragging effects that gently twist photon paths, creating subtle differences between co-rotating and counter-rotating trajectories. These effects are strongest near the throat, while at larger distances the spacetime is largely governed by the static gravitational potentials. Circular photon orbits reveal that the interplay of the redshift function, wormhole shape, and rotation shapes the photon-sphere structure. Different radial profiles of the string fluid generate distinctive photon-ring patterns, offering potential observational signatures of both the rotation and the internal matter distribution. Overall, radially varying string fluids provide a flexible and physically consistent source for traversable wormholes, bridging smoothly between vacuum-like and string-dominated regions while maintaining regularity and supporting slow rotation. This study highlights how anisotropic matter can influence both curvature and light propagation, providing a realistic framework for horizonless exotic spacetimes and suggesting new avenues to explore subtle observational effects around traversable wormholes.

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

0 major / 3 minor

Summary. The paper constructs slowly rotating traversable wormholes supported by string fluids with radially dependent properties. The transverse pressure is chosen as a function of radius to produce a smooth transition from a de Sitter-like core near the throat to a string-dominated regime at larger distances, yielding regular, horizon-free, asymptotically flat spacetimes that satisfy the Einstein equations. The analysis further examines frame-dragging effects on photon trajectories and the structure of circular photon orbits for different radial profiles of the string fluid, identifying potential observational signatures.

Significance. If the explicit solutions and photon-orbit calculations hold, the work supplies a concrete example of anisotropic matter sourcing slowly rotating wormholes while maintaining regularity and asymptotic flatness. It also quantifies how modest rotation modifies light propagation near the throat, which may be relevant for horizonless spacetime models and future observational searches for exotic compact objects.

minor comments (3)
  1. [§2] §2 (metric ansatz): the slow-rotation frame-dragging term is introduced but its explicit functional dependence on the radial coordinate and angular velocity parameter should be written out to make the perturbative order transparent.
  2. [§4] §4 (energy-momentum tensor): the chosen radial profiles for the string-fluid density and transverse pressure are stated to produce well-behaved quantities, yet the text does not tabulate the resulting energy conditions or null-energy-condition violation measure as a function of radius.
  3. [Figure 5] Figure 5 (photon rings): the caption does not label which curves correspond to co-rotating versus counter-rotating orbits, reducing clarity when comparing the reported differences in photon-sphere radii.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful summary and positive evaluation of the significance of our work on slowly rotating traversable wormholes sourced by radially varying string fluids. The recommendation of minor revision is noted. No specific major comments appear in the report, so we have no individual points requiring detailed rebuttal. We will implement appropriate minor revisions in the resubmitted version.

Circularity Check

0 steps flagged

No significant circularity; explicit ansatz construction

full rationale

The paper constructs wormhole solutions by explicitly choosing a radially dependent transverse pressure for the string fluid so that the Einstein equations produce regular, horizon-free, asymptotically flat metrics with slow rotation. This is presented as a model-building exercise rather than a first-principles derivation whose outputs reduce to the inputs by definition. No load-bearing self-citations, uniqueness theorems, or fitted parameters renamed as predictions appear in the provided material. The central results follow directly from the stated ansatz choices and are reported as such, making the derivation chain self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model relies on choosing specific functional forms for the matter profiles and metric functions to satisfy the wormhole conditions; no new entities are postulated.

free parameters (1)
  • radial profile parameters for string fluid density and pressure
    Specific functional dependence on radius is chosen to achieve the de Sitter-like core, string-dominated exterior, and regularity.
axioms (2)
  • standard math Einstein field equations
    The spacetime must satisfy the Einstein equations sourced by the string fluid.
  • domain assumption Slow rotation approximation to first order
    The metric includes frame-dragging terms linear in the rotation parameter.

pith-pipeline@v0.9.1-grok · 5804 in / 1298 out tokens · 25907 ms · 2026-06-27T12:46:33.614129+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

86 extracted references · 1 canonical work pages

  1. [1]

    M. S. Morris and K. S. Thorne, Am. J. Phys.56, 395 (1988)

    1988

  2. [2]

    H. G. Ellis, J. Math. Phys.14, 104 (1973)

    1973

  3. [3]

    K. A. Bronnikov, Acta Phys. Polon. B4, 251 (1973)

    1973

  4. [4]

    H. G. Ellis, Gen. Rel. Grav.10, 105 (1979)

    1979

  5. [5]

    Gurtas Dogan, A

    S. Gurtas Dogan, A. Guvendi, and O. Mustafa, Nucl. Phys. B1018, 117000 (2025)

    2025

  6. [6]

    Gurtas Dogan, A

    S. Gurtas Dogan, A. Guvendi, and O. Mustafa, Phys. Lett. B868, 139626 (2025)

    2025

  7. [7]

    Gurtas Dogan, A

    S. Gurtas Dogan, A. Guvendi, and O. Mustafa, Eur. Phys. J. C85, 896 (2025), arXiv:2504.10518 [physics.class-ph]

    arXiv 2025

  8. [8]

    Gurtas Dogan, A

    S. Gurtas Dogan, A. Guvendi, and O. Mustafa, Phys. Lett. B868, 139824 (2025), arXiv:2503.18967 [gr-qc]

    arXiv 2025

  9. [9]

    Guvendi, O

    A. Guvendi, O. Mustafa, and S. Gurtas Dogan, Phys. Lett. B862, 139313 (2025), arXiv:2503.12550 [gr-qc]

    arXiv 2025

  10. [10]

    Guvendi, S

    A. Guvendi, S. Gurtas Dogan, and R. L. L. Vitória, Eur. Phys. J. Plus139, 721 (2024), arXiv:2408.00356 [hep-th]

    arXiv 2024

  11. [11]

    Guvendi and S

    A. Guvendi and S. G. Dogan, Gen. Rel. Grav.56, 32 (2024), arXiv:2503.16564 [gr-qc]

    arXiv 2024

  12. [12]

    Guvendi and S

    A. Guvendi and S. Gurtas Dogan, Few Body Syst.64, 65 (2023)

    2023

  13. [13]

    Guvendi and H

    A. Guvendi and H. Hassanabadi, Phys. Lett. B843, 138045 (2023)

    2023

  14. [14]

    Guvendi and F

    A. Guvendi and F. Ahmed, Int. J. Mod. Phys. A38, 2350179 (2023), arXiv:2402.00088 [gr-qc]

    arXiv 2023

  15. [15]

    Ditta, I

    A. Ditta, I. Hussain, G. Mustafa, A. Errehymy, and M. Daoud, Eur. Phys. J. C81, 880 (2021)

    2021

  16. [16]

    Errehymy, S

    A. Errehymy, S. Hansraj, S. K. Maurya, C. Hansraj, and M. Daoud, Phys. Dark Univ.41, 101258 (2023)

    2023

  17. [17]

    Errehymy, S

    A. Errehymy, S. K. Maurya, S. Hansraj, M. Daoud, H. I. Alrebdi, and A.-H. Abdel-Aty, Annalen Phys.535, 2300178 (2023)

    2023

  18. [18]

    Errehymy, Phys

    A. Errehymy, Phys. Dark Univ.44, 101438 (2024)

    2024

  19. [19]

    Errehymy, S

    A. Errehymy, S. K. Maurya, S. Hansraj, M. Mahmoud, K. S. Nisar, and A.-H. Abdel-Aty, Chin. J. Phys.89, 56 (2024)

    2024

  20. [20]

    Mustafa, A

    G. Mustafa, A. Errehymy, F. Javed, S. K. Maurya, S. Hansraj, and S. Sadiq, JHEAp42, 1 (2024)

    2024

  21. [21]

    Errehymy, S

    A. Errehymy, S. K. Maurya, G.-E. Vîlcu, M. A. Khan, and M. Daoud, Astropart. Phys.160, 102972 (2024)

    2024

  22. [22]

    Errehymy, A

    A. Errehymy, A. Banerjee, S. Hansraj, O. Donmez, K. S. Nisar, and A.-H. Abdel-Aty, Eur. Phys. J. C84, 573 (2024)

    2024

  23. [23]

    Errehymy, Y

    A. Errehymy, Y. Khedif, O. Donmez, M. Daoud, K. Myrzakulov, and S. Bekov, Eur. Phys. J. C84, 908 (2024), arXiv:2408.07667 [gr-qc]

    arXiv 2024

  24. [24]

    Errehymy, A

    A. Errehymy, A. Banerjee, O. Donmez, M. Daoud, K. S. Nisar, and A.-H. Abdel-Aty, Gen. Rel. Grav.56, 76 (2024), arXiv:2406.04049 [gr-qc]

    arXiv 2024

  25. [25]

    Battista, S

    E. Battista, S. Capozziello, and A. Errehymy, Eur. Phys. J. C84, 1314 (2024), arXiv:2409.09750 [gr-qc]

    arXiv 2024

  26. [26]

    Errehymy, Y

    A. Errehymy, Y. Khedif, M. Daoud, K. Myrzakulov, A. H. Abdel-Aty, and K. S. Nisar, JHEAp47, 100370 (2025)

    2025

  27. [27]

    Errehymy, O

    A. Errehymy, O. Donmez, A. Syzdykova, K. Myrzakulov, S. Muminov, A. Dauletov, and J. Rayimbaev, Annals Phys.480, 170105 (2025), arXiv:2505.21081 [gr-qc]

    arXiv 2025

  28. [28]

    Errehymy, O

    A. Errehymy, O. Donmez, B. Turimov, K. Myrzakulov, N. Alessa, and A. H. Abdel-Aty, Annals Phys.481, 170164 (2025), arXiv:2507.16465 [gr-qc]

    arXiv 2025

  29. [29]

    Errehymy and S

    A. Errehymy and S. Hansraj, Annals Phys.482, 170200 (2025), arXiv:2508.17492 [gr-qc]

    arXiv 2025

  30. [30]

    Errehymy, B

    A. Errehymy, B. Turimov, A. Syzdykova, K. Myrzakulov, N. Alessa, and A. H. Abdel-Aty, Nucl. Phys. B1019, 117116 (2025)

    2025

  31. [31]

    R. Feng, Y. Yu, L. Wu, J. Wang, Q. Tan, and S. N. Burokur, Opt. Lett.50, 5161 (2025). 15

    2025

  32. [32]

    T. Xie, X. Ma, X. Yang, P. Cui, X. Ning, and J. Lü, IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.18, 27781 (2025)

    2025

  33. [33]

    W. Yu, Q. Wu, X. Chen, J. Huo, J. Li, J. Yang, and A. Zhang, Laser Photon. Rev. , e1816 (2025)

    2025

  34. [34]

    Y. Yang, Y. W. Ni, P. F. Chen, and X. S. Feng, Astro- phys. J.985, 104 (2025)

    2025

  35. [35]

    Fang and R

    Y. Fang and R. Cai, Mon. Not. Roy. Astron. Soc.542, 1172 (2025)

    2025

  36. [36]

    Zhang, W

    J. Zhang, W. Huang, Q. Wang, A. D. Shaw, M. I. Friswell, and K. Huang, Phys. Rev. Applied (2026), 10.1103/nxpg-92kv

    work page doi:10.1103/nxpg-92kv 2026

  37. [37]

    Xiang, Y

    Y. Xiang, Y. Ye, P. Feng, H. Li, X. Pang, X. Lan, and N. Zhang, Mon. Not. Roy. Astron. Soc.546, stag150 (2026)

    2026

  38. [38]

    H. Lin, C. Pan, Q. Zhang, S. Wang, Y. Zhang, S. Qiao, and J. Wang, IEEE Trans. Instrum. Meas.75, 1 (2026)

    2026

  39. [39]

    P. K. F. Kuhfittig, Phys. Rev. D67, 064015 (2003), arXiv:gr-qc/0401028

    Pith/arXiv arXiv 2003

  40. [40]

    P. E. Kashargin and S. V. Sushkov, Phys. Rev. D78, 064071 (2008), arXiv:0809.1923 [gr-qc]

    Pith/arXiv arXiv 2008

  41. [41]

    Kleihaus and J

    B. Kleihaus and J. Kunz, Phys. Rev. D90, 121503 (2014), arXiv:1409.1503 [gr-qc]

    Pith/arXiv arXiv 2014

  42. [42]

    Hoffmann, T

    C. Hoffmann, T. Ioannidou, S. Kahlen, B. Klei- haus, and J. Kunz, Phys. Rev. D97, 124019 (2018), arXiv:1803.11044 [gr-qc]

    Pith/arXiv arXiv 2018

  43. [43]

    X. Y. Chew, V. Dzhunushaliev, V. Folomeev, B. Klei- haus, and J. Kunz, Phys. Rev. D100, 044019 (2019), arXiv:1906.08742 [gr-qc]

    arXiv 2019

  44. [44]

    B. Azad, J. L. Blazquez-Salcedo, F. S. Khoo, and J. Kunz, Phys. Lett. B848, 138349 (2024), arXiv:2301.05243 [gr-qc]

    arXiv 2024

  45. [45]

    Clément and D

    G. Clément and D. Gal’tsov, Phys. Lett. B838, 137677 (2023), arXiv:2210.08913 [gr-qc]

    arXiv 2023

  46. [46]

    Cisterna, K

    A. Cisterna, K. Müller, K. Pallikaris, and A. Viganò, Phys. Rev. D108, 024066 (2023), arXiv:2306.14541 [gr- qc]

    arXiv 2023

  47. [47]

    Tangphati, B

    T. Tangphati, B. Chaihao, D. Samart, P. Channuie, and D. Momeni, Nucl. Phys. B999, 116446 (2024), arXiv:2307.13968 [gr-qc]

    arXiv 2024

  48. [48]

    Teo, Phys

    E. Teo, Phys. Rev. D58, 024014 (1998), arXiv:gr- qc/9803098

    arXiv 1998

  49. [49]

    Deligianni, B

    E. Deligianni, B. Kleihaus, J. Kunz, P. Nedkova, and S. Yazadjiev, Phys. Rev. D104, 064043 (2021), arXiv:2107.01421 [gr-qc]

    arXiv 2021

  50. [50]

    Deligianni, J

    E. Deligianni, J. Kunz, P. Nedkova, S. Yazadjiev, and R. Zheleva, Phys. Rev. D104, 024048 (2021), arXiv:2103.13504 [gr-qc]

    arXiv 2021

  51. [51]

    Errehymy, A

    A. Errehymy, A. Guvendi, S. Gurtas Dogan, and O. Mustafa, Phys. Lett. B869, 139847 (2025)

    2025

  52. [52]

    Errehymy, A

    A. Errehymy, A. Guvendi, S. G. Dogan, and O. Mustafa, Eur. Phys. J. C86, 124 (2026), arXiv:2509.16739 [gr-qc]

    arXiv 2026

  53. [53]

    Errehymy, S

    A. Errehymy, S. K. Maurya, M. Govender, K. N. Singh, J.Rayimbaev, B.Myrzakulova, andS.Murodov, (2026), arXiv:2604.18246 [gr-qc]

    Pith/arXiv arXiv 2026

  54. [54]

    Errehymy, M

    A. Errehymy, M. Govender, S. K. Maurya, K. N. Singh, B. Myrzakulova, J. Rayimbaev, and M. Vapayev, Phys. Lett. B876, 140435 (2026)

    2026

  55. [55]

    Errehymy, M

    A. Errehymy, M. Govender, O. Donmez, B. Myrzakulova, J. Rayimbaev, and M. Matyoqubov, Phys. Lett. B876, 140388 (2026)

    2026

  56. [56]

    R. P. Geroch, J. Math. Phys.11, 1955 (1970)

    1955

  57. [57]

    R. P. Geroch, J. Math. Phys.11, 2580 (1970)

    1970

  58. [58]

    R. O. Hansen, J. Math. Phys.15, 46 (1974)

    1974

  59. [59]

    K. S. Thorne, Rev. Mod. Phys.52, 299 (1980)

    1980

  60. [60]

    Gürsel, Gen

    Y. Gürsel, Gen. Rel. Grav.15, 737 (1983)

    1983

  61. [61]

    D. R. Mayerson, SciPost Phys.15, 154 (2023), arXiv:2210.05687 [gr-qc]

    arXiv 2023

  62. [62]

    R. R. Caldwell, R. Dave, and P. J. Steinhardt, Phys. Rev. Lett.80, 1582 (1998), arXiv:astro-ph/9708069

    Pith/arXiv arXiv 1998

  63. [63]

    P. J. E. Peebles and B. Ratra, Rev. Mod. Phys.75, 559 (2003), arXiv:astro-ph/0207347

    Pith/arXiv arXiv 2003

  64. [64]

    V. V. Kiselev, Class. Quant. Grav.20, 1187 (2003), arXiv:gr-qc/0210040

    Pith/arXiv arXiv 2003

  65. [65]

    Capozziello, V

    S. Capozziello, V. F. Cardone, G. Lambiase, and A.Troisi,Int.J.Mod.Phys.D15,69(2006),arXiv:astro- ph/0601266

    arXiv 2006

  66. [66]

    H. H. Soleng, Gen. Rel. Grav.27, 367 (1995), arXiv:gr- qc/9412053

    arXiv 1995

  67. [67]

    Sofue and V

    Y. Sofue and V. Rubin, Ann. Rev. Astron. Astrophys. 39, 137 (2001), arXiv:astro-ph/0010594

    Pith/arXiv arXiv 2001

  68. [68]

    Vilenkin, Phys

    A. Vilenkin, Phys. Rev. D24, 2082 (1981)

    2082

  69. [69]

    R. J. Nemiroff and B. Patla, Am. J. Phys.76, 265 (2008), arXiv:astro-ph/0703739

    Pith/arXiv arXiv 2008

  70. [70]

    Arshad and U

    S. Arshad and U. Sheikh, Int. J. Theor. Phys.63, 90 (2024)

    2024

  71. [71]

    L. C. Nunes dos Santos, Phys. Rev. D111, 064032 (2025), arXiv:2502.15846 [gr-qc]

    arXiv 2025

  72. [72]

    C. R. Muniz, M. S. Cunha, and L. C. N. Santos, (2025), arXiv:2505.07028 [gr-qc]

    arXiv 2025

  73. [73]

    Estrada, (2026), arXiv:2602.03050 [gr-qc]

    M. Estrada, (2026), arXiv:2602.03050 [gr-qc]

    Pith/arXiv arXiv 2026

  74. [74]

    P. S. Letelier, Phys. Rev. D20, 1294 (1979)

    1979

  75. [75]

    P. S. Letelier, Phys. Rev. D22, 807 (1980)

    1980

  76. [76]

    R. M. Wald,General Relativity(Chicago Univ. Pr., Chicago, USA, 1984)

    1984

  77. [77]

    J. B. Hartle, Astrophys. J.150, 1005 (1967)

    1967

  78. [78]

    J. B. Hartle and K. S. Thorne, Astrophys. J.153, 807 (1968)

    1968

  79. [79]

    K. S. Thorne, Rend. Scu. Int. Fis. Enrico Fermi 47: 237- 83 (1971). (1970)

    1971

  80. [80]

    Papapetrou, Ann

    A. Papapetrou, Ann. Inst. H. Poincare Phys. Theor. A 4, 83 (1966)

    1966

Showing first 80 references.