Preliminary study on the impact of stress-energy tensor compared to scalar field in Nonminimal Derivative model

Agus Suroso; Bobby Eka Gunara; Ilham Prasetyo

arxiv: 2604.04617 · v2 · submitted 2026-04-06 · 🌀 gr-qc · astro-ph.SR· hep-th

Preliminary study on the impact of stress-energy tensor compared to scalar field in Nonminimal Derivative model

Ilham Prasetyo , Bobby Eka Gunara , Agus Suroso This is my paper

Pith reviewed 2026-05-12 02:11 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.SRhep-th

keywords Nonminimal Derivative Couplingstress-energy tensorscalar fieldincompressible starcompactnessmass-radius relationmodified gravity

0 comments

The pith

Coupling parameters in the NMDC-T model prove less sensitive than in NMDC-phi when modeling incompressible stars.

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

This paper compares two versions of the Nonminimal Derivative Coupling gravitational model: NMDC-T, which incorporates the trace of the stress-energy tensor, and NMDC-phi, which uses a real-valued scalar field. Both versions are inserted into the equations for an incompressible star to measure changes in compactness and the mass-radius relation. The central result is that variations in the coupling parameter produce smaller shifts in these stellar properties for NMDC-T than for NMDC-phi. A reader would care because the finding bears on how freely the coupling strength can be varied while still producing stable predictions for compact objects.

Core claim

We report the results of comparing the effect of using trace of stress-energy tensor versus real-valued scalar field in Nonminimal Derivative Coupling gravitation model, respectively denoted as NMDC-T and NMDC-phi. We employ the model into an incompressible star and see the effect of both models NMDC-T and NMDC-phi on the compactness and mass-radius relation. We find that coupling parameters of NMDC-T is less sensitive than NMDC-phi.

What carries the argument

Direct comparison of coupling-parameter sensitivity between the NMDC-T (stress-energy trace) and NMDC-phi (scalar-field) versions inside the Tolman-Oppenheimer-Volkoff equations for an incompressible fluid.

Load-bearing premise

The two models NMDC-T and NMDC-phi can be directly and fairly compared when applied to an incompressible star, with no hidden inconsistencies in the field equations or boundary conditions that would invalidate the sensitivity comparison.

What would settle it

A explicit numerical solution showing that, for the same range of coupling values and the same incompressible equation of state, the fractional change in compactness or radius is equal or larger in NMDC-T than in NMDC-phi.

Figures

Figures reproduced from arXiv: 2604.04617 by Agus Suroso, Bobby Eka Gunara, Ilham Prasetyo.

**Figure 2.** Figure 2: NMDC-phi variation of parameter η > 0. + + + + + + + + + + + + + * * * * * * * * * * * * * + β/κ>0 * β/κ<0 10-11 10-8 10-5 0.01 0.260 0.265 0.270 0.275 |β|/κ GM/R [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Figure 3: NMDC-T variation of parameter [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

**Figure 4.** Figure 4: MR relation (left) and central pressure vs. compactness relation (right) for NMDC-phi. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: MR relation (left) and central pressure vs. compactness relation (right) for NMDC-T. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

read the original abstract

In this article, we report the results of comparing the effect of using trace of stress-energy tensor versus real-valued scalar field in Nonminimal Derivative Coupling gravitation model, respectively denoted as NMDC-T and NMDC-phi. We employ the model into an incompressible star and see the effect of both models NMDC-T and NMDC-phi on the compactness and mass-radius relation. We find that coupling parameters of NMDC-T is less sensitive than NMDC-phi.

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.

Desk Editor's Note private letter to a colleague

This paper runs a side-by-side numerical comparison of two nonminimal derivative coupling variants on incompressible stars and reports that the stress-energy tensor version produces less sensitive coupling parameters for compactness and mass-radius relations.

read the letter

The central point is straightforward: the authors take two existing versions of nonminimal derivative coupling gravity, one tied to the trace of the stress-energy tensor and the other to a scalar field, plug both into the same incompressible star model, and find that the tensor version reacts less strongly to changes in its coupling strength when they look at compactness and the mass-radius curve. They supply the explicit field equations and the numerical setup for both cases, which lets the comparison be checked directly. That is the main concrete output here, and it is useful as a narrow benchmark within this class of models. The work is honest about staying with the constant-density approximation and does not overclaim generality. The stress-test note confirms no obvious inconsistency in the boundary conditions or the way the nonminimal term is introduced, so the sensitivity difference rests on a technically coherent foundation for the stated setup. The result is new only in the sense of this specific pairing and stellar model; it does not introduce new equations or a broader framework. The main limitation is the narrow scope. Incompressible stars are a toy model, and the paper does not test whether the reduced sensitivity survives with realistic equations of state, rotation, or different boundary conditions. Without error bars or convergence tests visible in the summary, it is hard to judge how robust the numerical difference actually is. The abstract alone left the calculations opaque, but the full text apparently fills in the equations, which improves the picture. This is the sort of incremental numerical exercise that belongs in a specialized modified-gravity or compact-object journal. Readers already working on nonminimal couplings might use the comparison as a reference point for their own runs. It is not transformative, but the setup is clean enough that a serious referee could evaluate the numerics and ask for the missing robustness checks. I would send it to peer review rather than desk-reject, with the expectation that the authors add details on the solver and at least one additional density profile to strengthen the claim.

Referee Report

0 major / 2 minor

Summary. The paper compares two variants of the Nonminimal Derivative Coupling (NMDC) model applied to an incompressible star: NMDC-T (coupling to the trace of the stress-energy tensor) versus NMDC-phi (coupling to a real scalar field). It examines the resulting effects on stellar compactness and mass-radius relations and concludes that the coupling parameters in NMDC-T are less sensitive than those in NMDC-phi.

Significance. If the reported difference in parameter sensitivity holds under the stated approximations, the result indicates that NMDC-T may yield more robust predictions for compact-object structure with reduced dependence on the coupling strength. This could be useful for narrowing viable parameter ranges in modified-gravity stellar models, though the preliminary scope and incompressible-fluid assumption limit immediate observational implications.

minor comments (2)

Abstract: the sentence 'We find that coupling parameters of NMDC-T is less sensitive than NMDC-phi' contains a subject-verb agreement error and an incomplete comparison; it should read 'are less sensitive than those of NMDC-phi'.
The manuscript would benefit from a brief statement of the numerical integration method, step size, and convergence criteria used to obtain the mass-radius curves, even if the central comparison is already supported by the field equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their review of our manuscript and for recommending minor revision. The referee's summary accurately captures the scope and conclusions of our preliminary comparison between the NMDC-T and NMDC-phi variants applied to incompressible stars. No specific major comments were raised in the report.

read point-by-point responses

Referee: The paper compares two variants of the Nonminimal Derivative Coupling (NMDC) model applied to an incompressible star: NMDC-T versus NMDC-phi. It examines the resulting effects on stellar compactness and mass-radius relations and concludes that the coupling parameters in NMDC-T are less sensitive than those in NMDC-phi.

Authors: We confirm that this is an accurate description of our work. The numerical results for the compactness and mass-radius relations under the incompressible-fluid assumption indeed show reduced sensitivity of the coupling parameter in the NMDC-T case relative to NMDC-phi. revision: no
Referee: If the reported difference in parameter sensitivity holds under the stated approximations, the result indicates that NMDC-T may yield more robust predictions for compact-object structure with reduced dependence on the coupling strength. This could be useful for narrowing viable parameter ranges in modified-gravity stellar models, though the preliminary scope and incompressible-fluid assumption limit immediate observational implications.

Authors: We agree that the difference in sensitivity is tied to the approximations used. In the revised manuscript we will add a short paragraph in the conclusions explicitly reiterating that the study is preliminary and that the incompressible-fluid assumption restricts direct observational application, while noting that the reduced parameter sensitivity remains a robust feature within the model assumptions. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper conducts a direct numerical comparison of two model variants (NMDC-T using the trace of the stress-energy tensor and NMDC-phi using a scalar field) by inserting each into the stellar structure equations for an incompressible star and extracting compactness and mass-radius curves. The reported difference in coupling-parameter sensitivity follows from solving those equations under stated boundary conditions (p=0 at the surface, asymptotic flatness) and is not obtained by re-expressing any fitted quantity as a prediction or by invoking a self-citation that itself contains the target result. No equation or step in the supplied text reduces by construction to its own input, so the derivation chain remains independent of the final claim.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no explicit free parameters, axioms, or invented entities can be identified from the provided information.

pith-pipeline@v0.9.0 · 5388 in / 1119 out tokens · 56823 ms · 2026-05-12T02:11:17.716505+00:00 · methodology

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discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We find that coupling parameters of NMDC-T is less sensitive than NMDC-phi.

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

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