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arxiv: 2605.01343 · v1 · submitted 2026-05-02 · 🌀 gr-qc

Feasible Stellar Interiors Beyond Einstein Gravity: Insights from Non-Metricity-Matter Coupled Gravitational Theory

M. Sharif , M. Zeeshan Gul , Adeeba Arooj This is my paper

Pith reviewed 2026-05-09 18:34 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(Q, L_m) gravityanisotropic compact starsstellar interiorsnon-metricityenergy conditionssound speed stabilitynon-singular solutionsspherically symmetric metrics
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The pith

Compact stars with anisotropic pressure are viable and stable in non-metricity-matter gravity

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

This paper tests whether realistic stellar models can exist in a theory of gravity that incorporates non-metricity coupled to matter. The authors select a specific form of the gravitational function and two smooth, non-singular solutions for the interior of spherical stars. They solve for the metric constants by matching to the exterior vacuum solution and then examine energy conditions, pressures, and densities through graphical analysis. Stability is confirmed by checking that the speed of sound stays below the speed of light. A positive result would mean that this modified gravity offers new ways to describe dense objects like neutron stars without the limitations of general relativity.

Core claim

Using the f(Q, L_m) gravity with a chosen functional form, the paper demonstrates that two non-singular interior solutions for static spherically symmetric anisotropic compact objects satisfy the necessary physical conditions for viability and remain stable under the sound speed criterion after applying junction conditions.

What carries the argument

The f(Q, L_m) gravitational theory, where Q denotes non-metricity and L_m the matter Lagrangian, which alters the field equations to permit new anisotropic stellar configurations.

Load-bearing premise

The viability and stability conclusions depend on adopting one particular functional form for f(Q, L_m) together with two specific non-singular interior metric solutions.

What would settle it

A precise measurement of the mass, radius, and moment of inertia for a known compact star that falls outside the parameter range allowed by the derived field equations in this model would challenge the claim.

Figures

Figures reproduced from arXiv: 2605.01343 by Adeeba Arooj, M. Sharif, M. Zeeshan Gul.

Figure 1
Figure 1. Figure 1: Plots of metric potentials against radial coordinate for so view at source ↗
Figure 2
Figure 2. Figure 2: Plots of metric elements against radial coordinate for solu view at source ↗
Figure 3
Figure 3. Figure 3: Matter contents against radial coordinate for solutions view at source ↗
Figure 4
Figure 4. Figure 4: Matter content’s gradient against radial coordinate for view at source ↗
Figure 5
Figure 5. Figure 5: Matter contents against radial coordinate for solutions view at source ↗
Figure 6
Figure 6. Figure 6: Matter content’s gradient against radial coordinate for view at source ↗
Figure 7
Figure 7. Figure 7: Energy bounds against radial coordinate for solutions view at source ↗
Figure 8
Figure 8. Figure 8: Energy bounds against radial coordinate for solutions view at source ↗
Figure 9
Figure 9. Figure 9: The EoS parameters against radial coordinate for both s view at source ↗
Figure 10
Figure 10. Figure 10: The EoS parameters against radial coordinate for both view at source ↗
Figure 11
Figure 11. Figure 11: Physical features against radial coordinate for solutio view at source ↗
Figure 12
Figure 12. Figure 12: Physical features against radial coordinate for solutio view at source ↗
Figure 13
Figure 13. Figure 13: M-R against radial coordinate for solutions view at source ↗
Figure 14
Figure 14. Figure 14: M-I against radial coordinate for solutions view at source ↗
Figure 15
Figure 15. Figure 15: Causality condition against radial coordinate for both so view at source ↗
Figure 16
Figure 16. Figure 16: Causality condition against radial coordinate for both so view at source ↗
Figure 17
Figure 17. Figure 17: Herrera condition against radial coordinate for both so view at source ↗
Figure 18
Figure 18. Figure 18: Herrera condition against radial coordinate for both so view at source ↗
read the original abstract

This manuscript examines viability and stability of anisotropic compact objects in the framework of $f(Q,L_m)$ gravity ($Q$ is the non-metricity and $L_m$ is the matter Lagrangian). We assume a particular functional form of this theory to get explicit expressions for the field equations which govern the behavior of matter and geometry in this context. The configuration of static spherically symmetric structures is evaluated using the two innovative non-singular solutions. We use smooth matching conditions to evaluate the values of unknown constants in the metric coefficients. The viability of considered compact stars is assessed using a graphic analysis of various important physical characteristics. We also investigate stability of the considered stellar objects through sound speed method. It is found that these stellar objects are viable and stable, as all the required conditions are satisfied.

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 / 3 minor

Summary. The paper examines the viability and stability of anisotropic compact objects in f(Q, L_m) gravity by assuming a particular functional form for the theory. It uses two non-singular interior solutions for static spherically symmetric spacetimes, matches them to the exterior using smooth conditions to fix constants, and concludes based on graphic analysis that the objects satisfy energy conditions, causality, and sound speed stability criteria, hence are viable and stable.

Significance. If the results hold, the paper shows that f(Q, L_m) gravity can support stable anisotropic stellar models, offering insights into modified gravity effects on compact objects. Credit is given for the use of non-singular solutions and the systematic check of physical conditions. The significance is limited because the functional form and solutions are chosen specifically, turning the analysis into a consistency check rather than a broad prediction.

major comments (2)
  1. [§3] The functional form of f(Q, L_m) is selected ad hoc to derive explicit field equations; the viability is then verified for this choice and the fixed constants from matching, without exploring whether the stability holds for other forms or is a general feature.
  2. [§5] The graphic analysis confirming the satisfaction of energy conditions, causality, and sound-speed stability provides no quantitative details such as explicit parameter ranges, minimum/maximum values of the quantities, or error estimates, which undermines the strength of the claim that all conditions are satisfied.
minor comments (3)
  1. [Abstract] The abstract could specify the two non-singular solutions used and the exact functional form assumed for f(Q, L_m).
  2. [Figures] Figure captions should explicitly state the values of the metric constants and model parameters used in the plots for reproducibility.
  3. [References] Additional references to prior work on compact stars in f(Q) or similar modified gravity theories would provide better context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [§3] The functional form of f(Q, L_m) is selected ad hoc to derive explicit field equations; the viability is then verified for this choice and the fixed constants from matching, without exploring whether the stability holds for other forms or is a general feature.

    Authors: We selected the specific functional form of f(Q, L_m) to obtain explicit field equations that permit analytical interior solutions and direct matching to the exterior geometry. This is a standard methodological choice in modified gravity literature when the goal is to construct and test concrete stellar models rather than to derive general theorems. The manuscript demonstrates the existence of viable, stable anisotropic configurations for this choice and the adopted non-singular solutions; it does not assert that the same conclusions hold for arbitrary forms of f(Q, L_m). We will add explicit statements in the introduction and concluding section clarifying the scope of the analysis and noting that the generality of the results across other functional forms is left for future investigation. revision: partial

  2. Referee: [§5] The graphic analysis confirming the satisfaction of energy conditions, causality, and sound-speed stability provides no quantitative details such as explicit parameter ranges, minimum/maximum values of the quantities, or error estimates, which undermines the strength of the claim that all conditions are satisfied.

    Authors: We agree that the purely graphical presentation would benefit from quantitative support. In the revised manuscript we will insert tables that list, for each stellar model, the minimum and maximum values attained by the energy density, radial and tangential pressures, and the two sound-speed components over the interior. We will also state the intervals of the free parameters for which all energy conditions, causality, and stability criteria remain satisfied. These additions will complement the figures and strengthen the quantitative basis of our conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper assumes a specific functional form for f(Q, L_m) and adopts two chosen non-singular interior solutions, determines metric constants via matching conditions, and then verifies that the resulting quantities satisfy energy conditions, causality, and sound-speed stability via direct graphical and analytical checks. This is a standard consistency verification within an explicitly constructed model rather than any derivation in which a claimed prediction or first-principles result reduces by construction to the inputs. No load-bearing self-citation, self-definitional step, or fitted parameter renamed as an independent prediction is present; the viability conclusion is supported by the explicit post-construction checks on the selected configurations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on an assumed functional form for f(Q, L_m) and on two hand-chosen non-singular metric solutions whose constants are fixed by matching; no independent evidence is given for either choice.

free parameters (2)
  • parameters inside chosen f(Q, L_m)
    A particular functional form is assumed to obtain explicit expressions for the field equations.
  • integration constants in metric coefficients
    Determined by smooth matching to exterior spacetime.
axioms (2)
  • domain assumption Static spherically symmetric spacetime
    Standard assumption for modeling compact stars.
  • domain assumption Smooth matching conditions at the stellar surface
    Used to fix unknown constants in the interior metric.

pith-pipeline@v0.9.0 · 5442 in / 1209 out tokens · 26691 ms · 2026-05-09T18:34:57.132931+00:00 · methodology

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Reference graph

Works this paper leans on

97 extracted references

  1. [1]

    et al.: Phys

    Shapiro, I.I. et al.: Phys. Rev. Lett. 36(1976)555

    1976

  2. [2]

    and Starobinsky, A.A.: Int

    Sahni, V. and Starobinsky, A.A.: Int. J. Mod. Phys. D 9(2000)373

    2000

  3. [3]

    Carroll, S.M.: Living Rev. Rel. 4(2001)56

    2001

  4. [4]

    and Ratra, B.: Rev

    Peebles, P.J.E. and Ratra, B.: Rev. Mod. Phys. 75(2003)559

    2003

  5. [5]

    Padmanabhan, T.: Phys. Rep. 380(2003)235. 41

    2003

  6. [6]

    et al.: Int

    Copeland, E.J. et al.: Int. J. Mod. Phys. D 15(2006)175

    2006

  7. [7]

    and Odintsov, S.D.: Int

    Nojiri, S.I. and Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4(2007)115; Sotiriou, T.P. and Faraoni, V.: Rev. Mod. Phys. 82(2010)451

    2007

  8. [8]

    and Koivisto, T.: Eur

    Conroy, A. and Koivisto, T.: Eur. Phys. J. C 78(2018)923

    2018

  9. [9]

    et al.: Mod

    Adeel, M. et al.: Mod. Phys. Lett. A 38(2023)2350152

    2023

  10. [10]

    et al.: Eur

    Sharif, M. et al.: Eur. Phys. J. C 84(2024)1065

    2024

  11. [11]

    et al.: Int

    Rani, S. et al.: Int. J. Geom. Methods Mod. Phys. 21(2024)2450033

    2024

  12. [12]

    et al.: Eur

    Gul, M.Z. et al.: Eur. Phys. J. C 84(2024)8

    2024

  13. [13]

    et al.: Phys

    Maurya, S.K. et al.: Phys. Dark Universe 46(2024)101619

    2024

  14. [14]

    et al.: Chin

    Sharif, M. et al.: Chin. J. Phys. 91(2024)66

    2024

  15. [15]

    Heisenberg, L.: Phys. Rep. 1066(2024)78

    2024

  16. [16]

    et al.: Nucl

    Nusrat, F. et al.: Nucl. Phys. B 1016(2025)116923

    2025

  17. [17]

    et al.: Phys

    Rani, S. et al.: Phys. Dark Universe 47(2025)101754

    2025

  18. [18]

    et al.: Phys

    Sharif, M. et al.: Phys. Dark Universe 47(2025)101760

    2025

  19. [19]

    and Xia, T.: Chin

    Mustafa, G., Abbas, G. and Xia, T.: Chin. J. Phys. 60(2019)362

    2019

  20. [20]

    Mustafa, G., X Tie-Cheng and Shamir, M.F..: Phys. Scr. 96(2021)105008

    2021

  21. [21]

    et al.: Eur

    Ditta, A. et al.: Eur. Phys. J. C 81(2021)880

    2021

  22. [22]

    et al.: Eur

    Waseem, A. et al.: Eur. Phys. J. C 83(2023)1088

    2023

  23. [23]

    et al.: Phys

    Sharif, M. et al.: Phys. Dark Universe 46(2024)101606

    2024

  24. [24]

    et al.: Phys

    Nan G. et al.: Phys. Dark Universe 46(2024)101635

    2024

  25. [25]

    and Gul, M.Z.: Ann

    Sharif, M. and Gul, M.Z.: Ann. Phys. 465(2024)169674

    2024

  26. [26]

    et al.: Eur

    Gul, M.Z. et al.: Eur. Phys. J. C 84(2024)775. 42

    2024

  27. [27]

    et al.: Eur

    Nasir, M.M.M. et al.: Eur. Phys. J. C 85(2025)159

    2025

  28. [28]

    et al.: Phys

    Sharif, M. et al.: Phys. Dark Universe 48(2025)101839

    2025

  29. [29]

    et al.: Nucl

    Javed, F. et al.: Nucl. Phys. B 1018(2025)117001

    2025

  30. [30]

    et al.: Ann

    Javed, F. et al.: Ann. Phys. 476(2025)169956

    2025

  31. [31]

    et al.: High Energy Density Phys

    Hashim, I. et al.: High Energy Density Phys. 57(2025)101223

    2025

  32. [32]

    et al.: Ann

    Javed, F. et al.: Ann. Phys. 482(2025)170189

    2025

  33. [33]

    et al.: Int

    Hashim, I. et al.: Int. J. Geom. Methods Mod. Phys. 22(2025)2540049

    2025

  34. [34]

    et al.: Phys

    Malik, A. et al.: Phys. Dark Universe 50(2025)102114

    2025

  35. [35]

    Dark Universe 47(2025)101763; Yousaf, M.: Chin

    Donmez, O.: Phys. Dark Universe 47(2025)101763; Yousaf, M.: Chin. J. Phys. 95(2025)1278; Chin. J. Phys. 97(2025)1284

    2025

  36. [36]

    et al.: Phys

    Hazarika, A. et al.: Phys. Dark Universe 50(2025)102092

    2025

  37. [37]

    and Singh, S.S.: Nucl

    Samaddar, A. and Singh, S.S.: Nucl. Phys. B 1012(2025)116834

    2025

  38. [38]

    et al.: Eur

    Gul, M.Z. et al.: Eur. Phys. J. Plus 140(2025)15; Astron. Comp. 52(2025)100956

    2025

  39. [39]

    et al.: Phys

    Myrzakulov, Y. et al.: Phys. Dark Universe 48(2024)01614

    2024

  40. [40]

    et al.: Eur

    Myrzakulov, Y. et al.: Eur. Phys. J. C 85(2025)376

    2025

  41. [41]

    et al.: J

    Myrzakulov, Y. et al.: J. High Energy Astrophys. 44(2024)164

    2024

  42. [42]

    Longair, M.S.: High Energy Astrophysics (Cambridge Univeristy Press, 1994)

    1994

  43. [43]

    and Gleiser, M.: Gen

    Dev, K. and Gleiser, M.: Gen. Relativ. Gravit. 35(2003)1435

    2003

  44. [44]

    and Harko, T.: Int

    Mak, M.K. and Harko, T.: Int. J. Mod. Phys. D 13(2004)156

    2004

  45. [46]

    et al.: Gen

    Rahaman, F. et al.: Gen. Relativ. Gravit. 44(2012)107; Eur. Phys. J. C 72(2012)2071. 43

    2012

  46. [48]

    and Santos, N.O.: Phys

    Herrera, L. and Santos, N.O.: Phys. Rep. 286(1997)53

    1997

  47. [49]

    et al.: Int

    Hossein, S.K.M. et al.: Int. J. Mod. Phys. D 21(2012)1250088

    2012

  48. [50]

    and Deb, R.: Astrophys

    Paul, B.C. and Deb, R.: Astrophys. Space Sci. 354(2014)421

    2014

  49. [51]

    and Zwicky, F.: Phys

    Baade, W. and Zwicky, F.: Phys. Rev. 46(1934)76

    1934

  50. [52]

    and Liang, E.P.T.: Astrophys

    Bowers, R.L. and Liang, E.P.T.: Astrophys. J. 188(1974)657

    1974

  51. [53]

    et al.: Eur

    Kalam, M. et al.: Eur. Phys. J. C 72(2012)2248

    2012

  52. [54]

    and Rashid, A.: Int

    Shamir, M.F. and Rashid, A.: Int. J. Geom. Methods Mod. Phys. 20(2023)2350026

    2023

  53. [55]

    et al.: Int

    Athar, A.R. et al.: Int. J. Geom. Methods Mod. Phys. 20(2023)2350003

    2023

  54. [56]

    et al.: New Astron

    Majeed, A. et al.: New Astron. 102(2023)102039

    2023

  55. [57]

    et al.: Phys

    Maurya, S.K. et al.: Phys. Dark Universe 30(2020)100640

    2020

  56. [58]

    and Tello-Ortiz, F.: Phys

    Maurya, S.K. and Tello-Ortiz, F.: Phys. Dark Universe 27(2020)100442

    2020

  57. [59]

    et al.: Eur

    Bamba, K. et al.: Eur. Phys. J. C 83(2023)1033

    2023

  58. [60]

    et al.: Phys

    Jasim, M.K. et al.: Phys. Scr. 98(2023)045305

    2023

  59. [61]

    et al.: Eur

    Sohail, H. et al.: Eur. Phys. J. Plus 139(2024)16

    2024

  60. [62]

    et al.: Eur

    Albalahi, A. et al.: Eur. Phys. J. C 84(2024)9

    2024

  61. [63]

    and Sharif, M.: Eur

    Naseer, T. and Sharif, M.: Eur. Phys. J. C 84(2024)21

    2024

  62. [64]

    et al.: Fortschr

    Pradhan, S. et al.: Fortschr. Phys. 72(2024)2400092

    2024

  63. [65]

    et al.: Eur

    Maurya, S.K. et al.: Eur. Phys. J. C 84(2024)296

    2024

  64. [66]

    Weyl, H.: Sitzungsber. Preuss. Akad. Wiss. 26(1918)465

    1918

  65. [67]

    and Sahoo, P.K.: Phys

    Moraes, P.H.R.S. and Sahoo, P.K.: Phys. Rev. D 97(2018)024007

    2018

  66. [68]

    and Skea, J.E.F.: Class

    Finch, M.R. and Skea, J.E.F.: Class. Quantum Grav. 6(1989)467. 44

    1989

  67. [69]

    et al.: Astrophys

    Rawls, M.L. et al.: Astrophys. J. 730(2011)25

    2011

  68. [70]

    et al.: Mon

    Elebert, P. et al.: Mon. Not. R. Astron. Soc. 395(2009)884

    2009

  69. [71]

    et al.: Astron

    Abubekerov, M.K. et al.: Astron. Rep. 52(2008)379

    2008

  70. [72]

    et al.: Astrophys

    Guver, T. et al.: Astrophys. J. 712(2010)964

    2010

  71. [73]

    Guver, T.: Astrophys. J. 719(2010)1807

    2010

  72. [74]

    Freire, P.C.C.: Mon. Not. R. Astron. Soc. 412(2011)2763

    2011

  73. [75]

    Demorest, P.B.: Nature 467(2010)1081

    2010

  74. [76]

    Ozel, F.: Astrophys. J. 693(2009)1775

    2009

  75. [77]

    Indian Acad

    Karmarkar, K.R.: Proc. Indian Acad. Sci. A 27(1948)56

    1948

  76. [78]

    et al: Eur

    Bhar, P. et al: Eur. Phys. J. C 77(2017)596

    2017

  77. [81]

    Buchdahl, A.H.: Phys. Rev. D 116(1959)1027

    1959

  78. [82]

    Ivanov, B.V.: Phys. Rev. D 65(2002)104011

    2002

  79. [83]

    et al.: Class

    Abreu, H. et al.: Class. Quantum Grav. 24(2007)4631

    2007

  80. [84]

    Herrera, L.: Phys. Lett. A 165(1992)206

    1992

Showing first 80 references.