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arxiv: 2606.06371 · v1 · pith:RDG5Z2P4new · submitted 2026-06-04 · 🌀 gr-qc

Evolution of Realistic Neutron star in the framework of f (Q) gravity

Samprity Das , Surajit Chattopadhyay This is my paper

Pith reviewed 2026-06-28 00:03 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(Q) gravityneutron starsKrori-Barua metricanisotropic fluidBuchdahl limitpulsarsnonmetricitycompactness
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The pith

Four pulsars fit as neutron stars in f(Q) gravity when f is linear in nonmetricity and the Krori-Barua metric is used for the interior.

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

The paper takes the f(Q) framework, sets f to a linear function of the nonmetricity scalar, and solves the field equations with the Krori-Barua metric for an anisotropic fluid. It computes the pressure anisotropy for the pulsars LMC X-4, SMC X-4, Cen X-3 and Vela X-1 and finds the anisotropy positive and rising outward, which the authors read as nuclear repulsion balancing gravity. Mass-radius relations are plotted for different values of the free parameter a, and all four objects lie inside the Buchdahl compactness bound. A chi-square comparison shows that the model masses are statistically consistent with observed masses for many choices of a, and surface redshifts remain in the range expected for compact stars.

Core claim

With f(Q) taken as a linear function of Q and the Krori-Barua line element adopted as the interior metric, the anisotropic solutions for the four named pulsars yield compactness values that remain below the Buchdahl limit for a range of the parameter a, permitting the interpretation that these objects are neutron stars whose structure is consistent with modified gravity sourced by nonmetricity.

What carries the argument

Linear f(Q) = a + bQ together with the Krori-Barua metric ansatz that supplies the interior geometry for an anisotropic fluid in f(Q) gravity.

If this is right

  • Positive, monotonically increasing anisotropy implies that nuclear forces can counteract gravitational collapse inside these objects.
  • The derived mass-radius curves for varying a produce families of stable neutron-star configurations.
  • Chi-square tests indicate that the model masses match observed values for many parameter choices without requiring fine tuning.
  • Surface redshifts computed from the solutions stay within the range observed for known compact stars.

Where Pith is reading between the lines

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

  • The same linear f(Q) plus Krori-Barua construction could be applied to additional pulsars or to merging neutron-star events to obtain further parameter constraints.
  • If the model holds, the parameter a might be bounded by combining compactness limits with independent equation-of-state information from nuclear physics.
  • The framework predicts that deviations from general relativity would appear first in the anisotropy profile rather than in the total mass.

Load-bearing premise

The Krori-Barua metric remains an acceptable interior solution and f(Q) is adequately described by a strictly linear function of the nonmetricity scalar.

What would settle it

A precise mass and radius measurement for any of the four pulsars that places its compactness above the Buchdahl limit would rule out the linear-f(Q) Krori-Barua description for that object.

Figures

Figures reproduced from arXiv: 2606.06371 by Samprity Das, Surajit Chattopadhyay.

Figure 1
Figure 1. Figure 1: FIG. 1: Density evolution with respect to radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Radial pressure evolution with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Tangential pressure evolution with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Anisotropic factor evolution with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Density gradient evolution with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Radial pressure gradient evolution with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Tangential pressure gradient evolution with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Evolution of the EoS parameter for the radial component with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Evolution of the EoS parameter for the tangential component with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Evolution of the squared speed of sound with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Evolution of the adiabatic index with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Evolution of the force components with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p013_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Evolution of the mass with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p014_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Equi-mass diagram with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p015_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Evolution of the compactness with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p016_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Evolution of the surface redshift with respect to the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
read the original abstract

This work analyses and evaluates a few realistic compact objects in the presence of a gravitational interaction between two particles with a nonmetricity $Q$. In the $f(Q)$ gravity framework, we have selected the anisotropic equation of motion and have determined $f(Q)$ to be a linear function of nonmetricity $Q$. To evaluate the field equations in our work, we have opted to employ the Krori-Barua metric. We calculated the anisotropic factor for each of the four compact objects and found that the anisotropic component is positive and increases monotonically and interpreted that the nuclear force can oppose the gravitational attraction. At last, the relationship between mass and radius has been determined and illustrated visually. We have noted that the compactness of the pulsars LMC X-4, SMC X-4, Cen X-3, and Vela X-1 is inside the Buchdahl's limit for varying values of $a$. This has led to the interpretation that these pulsars are neutron stars in a modified gravity background of $f(Q)$. In addition, we calculated the model mass and, using thirty distinct choices of $a$, ran the Chi-Square test to see if there was a noticeable difference between the observed and model-generated masses. We have also looked at how the surface redshift has changed over time and whether the compact objects in our model that were previously described are compact.

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 / 1 minor

Summary. The manuscript analyzes four pulsars (LMC X-4, SMC X-4, Cen X-3, Vela X-1) as anisotropic compact objects in f(Q) gravity. It adopts the Krori-Barua metric, assumes f(Q) is linear in the nonmetricity scalar Q, solves the field equations to obtain a positive monotonically increasing anisotropy factor, verifies that the compactness 2M/R lies inside the Buchdahl limit 8/9 for varying parameter a, performs a chi-square comparison of model versus observed masses over thirty discrete choices of a, and concludes that these objects can be interpreted as neutron stars in the f(Q) framework. Surface redshift is also examined.

Significance. If the central claims hold, the work would supply explicit interior solutions for anisotropic stars in f(Q) gravity that match observed pulsar data while satisfying a standard stability criterion, offering a concrete modified-gravity model for neutron-star structure. The explicit use of an ansatz and direct comparison to four named objects provides a falsifiable test, though the overall significance is reduced by the absence of a modified compactness bound.

major comments (2)
  1. [Abstract and compactness analysis] Abstract and compactness discussion: the central interpretation that the four pulsars are neutron stars in f(Q) gravity because their compactness satisfies 2M/R < 8/9 applies the GR-derived Buchdahl bound directly. The f(Q) field equations differ from Einstein's equations (depending on Q and its derivatives), so the bound must be re-derived from the modified Tolman-Oppenheimer-Volkoff equation or junction conditions; no such derivation or justification is supplied. This assumption is load-bearing for the main claim.
  2. [Abstract] Abstract: the manuscript states that f(Q) is taken to be a linear function of Q 'to evaluate the field equations' with the Krori-Barua ansatz. This choice closes the system but is not shown to be the unique or physically preferred form; the resulting solutions and the subsequent compactness check are therefore tied to this specific assumption rather than to the general f(Q) theory.
minor comments (1)
  1. [Abstract] Abstract: the statement that 'the relationship between mass and radius has been determined and illustrated visually' does not reference a specific equation or figure number, making it difficult to locate the explicit M(R) relation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive comments. Both major points identify limitations in the current manuscript that we will address through revision.

read point-by-point responses

  1. Referee: [Abstract and compactness analysis] Abstract and compactness discussion: the central interpretation that the four pulsars are neutron stars in f(Q) gravity because their compactness satisfies 2M/R < 8/9 applies the GR-derived Buchdahl bound directly. The f(Q) field equations differ from Einstein's equations (depending on Q and its derivatives), so the bound must be re-derived from the modified Tolman-Oppenheimer-Volkoff equation or junction conditions; no such derivation or justification is supplied. This assumption is load-bearing for the main claim.

    Authors: We agree that the GR-derived Buchdahl bound cannot be applied directly. In the revised manuscript we will derive the relevant compactness limit from the modified field equations and TOV equation in f(Q) gravity, or provide a clear justification based on existing results for symmetric teleparallel theories. This change will be made to support the central interpretation. revision: yes

  2. Referee: [Abstract] Abstract: the manuscript states that f(Q) is taken to be a linear function of Q 'to evaluate the field equations' with the Krori-Barua ansatz. This choice closes the system but is not shown to be the unique or physically preferred form; the resulting solutions and the subsequent compactness check are therefore tied to this specific assumption rather than to the general f(Q) theory.

    Authors: We agree that the linear f(Q) is a specific ansatz chosen for analytic tractability with the Krori-Barua metric. The revised version will explicitly clarify that the results apply to this particular model within f(Q) gravity rather than the general theory, and will discuss the motivation for the choice along with possible extensions to nonlinear forms. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard ansatz + fitting + external bound application

full rationale

The paper selects the Krori-Barua metric and linear f(Q) ansatz, solves the resulting field equations for the anisotropic factor and mass-radius relation, then compares compactness to the known GR Buchdahl bound (2M/R < 8/9) and runs chi-square on model vs observed masses for discrete a values. No quoted step reduces a claimed prediction or central result to its own inputs by construction. The chi-square comparison is ordinary parameter scanning against data, not a forced 'prediction'. The Buchdahl limit is imported from GR without re-derivation, but this is an assumption about applicability rather than a definitional loop or self-citation chain. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Central claim rests on choosing a linear f(Q) form and the Krori-Barua metric ansatz, plus a free parameter a adjusted via Chi-square to observed masses.

free parameters (1)
  • a
    Metric parameter scanned over thirty values and used in Chi-square comparison of model versus observed masses.
axioms (2)
  • ad hoc to paper f(Q) is a linear function of nonmetricity Q
    Selected to evaluate the field equations after choosing the anisotropic fluid.
  • domain assumption Krori-Barua metric describes the interior spacetime of the compact objects
    Employed to solve the modified field equations.

pith-pipeline@v0.9.1-grok · 5779 in / 1179 out tokens · 28675 ms · 2026-06-28T00:03:42.526968+00:00 · methodology

discussion (0)

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Reference graph

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