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arxiv: 2508.10524 · v4 · submitted 2025-08-14 · 🌀 gr-qc · astro-ph.CO· hep-th

Maximum mass limit of strange stars in quadratic curvature-matter coupled gravity

Debadri Bhattacharjee , Pradip Kumar Chattopadhyay , Kazuharu Bamba This is my paper

Pith reviewed 2026-05-18 23:27 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords strange starsquadratic curvature gravitynon-minimal matter couplingmaximum mass limitMIT bag modelGW190814Tolman-Oppenheimer-Volkoff equations
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The pith

Strange stars can reach a maximum mass of 3.11 solar masses in quadratic curvature-matter coupled gravity.

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

This paper examines how strange stars behave in a version of gravity that adds quadratic curvature terms coupled to matter. It derives the stellar equilibrium equations and applies the MIT bag model to find mass and radius values for these hypothetical stars made of strange quark matter. The analysis shows that the maximum possible mass is higher than what general relativity predicts. A sympathetic reader would care because this provides a way to explain very heavy compact objects seen in gravitational wave signals without invoking black holes. The predicted sizes also match what astronomers have observed in other compact star events.

Core claim

By deriving the Tolman-Oppenheimer-Volkoff equations from the gravitational field equations in quadratic curvature gravity with non-minimal matter coupling and applying the MIT bag model equation of state, we obtain mass-radius relationships for strange stars. We demonstrate that the maximum mass limit can exceed the general relativistic counterpart, achieving up to 3.11 solar masses, which suggests that the lighter companion of GW190814 could plausibly be a strange star.

What carries the argument

Modified Tolman-Oppenheimer-Volkoff equations arising from the quadratic curvature-matter coupled gravitational field equations, which alter energy-momentum conservation and allow for higher stellar masses.

If this is right

  • The maximum mass exceeds the general relativistic counterpart.
  • Stellar radii are consistent with observations of compact stars and GW events.
  • The formalism recovers general relativity for negligible non-minimal coupling.
  • This allows strange stars to account for the lighter companion of GW190814.

Where Pith is reading between the lines

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

  • Future gravitational wave catalogs could use mass-radius data to distinguish this modified gravity from standard general relativity.
  • The framework could be applied to other compact objects or more advanced quark-matter equations of state.
  • Observable properties such as cooling or oscillation modes of strange stars might carry signatures of the curvature-matter coupling.

Load-bearing premise

The MIT bag model adequately represents the equation of state for strange quark matter in the interiors of these stars.

What would settle it

A precise mass and radius measurement of the lighter companion in GW190814 or of another candidate strange star that falls outside the model's predicted mass-radius curve would test whether the 3.11 solar mass limit holds.

Figures

Figures reproduced from arXiv: 2508.10524 by Debadri Bhattacharjee, Kazuharu Bamba, Pradip Kumar Chattopadhyay.

Figure 1
Figure 1. Figure 1: FIG. 1: Mass-radius relation for [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Mass-radius relation for [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Mass-radius relation for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: a: α = 0, with β = −4.1, 0, and 4.1 (red, green, blue). Figure 3b: α = 1.5 with β = −2.2, 0, and 1.9 (red, green, blue). of Tables IIIa, IIIb with Tables IVa, IVb clearly shows that the maximum mass is greater for Bg = 57.55 MeV/fm3 compared to Bg = 95.11 MeV/fm3 . – With increasing gravity-matter coupling, the maximum mass decreases in all cases. – From Table IIIa, it must be noted that for Bg = 57.55 MeV… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Radial variation of adiabatic index for [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Radial variation of adiabatic index for [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Radial variation of adiabatic index for [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: a: α = 0, with β = −4.1, 0, and 4.1 (red, green, blue). Figure 8b: α = 1.5 with β = −2.2, 0, and 1.9 (red, green, blue). TABLE V: Comparative analysis of maximum mass, radius, and Buchdahl limits for compact stars in various modified gravity frameworks considering different EoS. Theory Mmax R Compactness Buchdahl Limit Reference (M⊙) (Km) ( M R ) ( M R < 4 9 ) GR (baseline) ≈ 2.0 ≈ 11.0 0.27 Satisfied P. H… view at source ↗
read the original abstract

We explore the maximum mass limit of strange stars in quadratic curvature gravity with the non-minimal matter coupling. The characteristic parameters of the quadratic curvature coupling and the non-minimal matter coupling imply the contributions from higher-order curvature terms and the coupling between matter and geometry, respectively. We demonstrate, explicitly, that the conservation of energy-momentum tensor can be modified and in the case of negligible non-minimal matter coupling, the formalism of general relativity is recovered. By deriving the Tolman-Oppenheimer-Volkoff equations from the gravitational field equations and applying the MIT bag model equation of state, we obtain the corresponding mass-radius relationships for strange stars. Although the MIT bag model represents a simplified phenomenological equation of state, it remains an effective description of strange quark matter under the extreme conditions prevailing in neutron star/strange star interiors. Within the present framework, the adoption of this equation of state yields stellar radii that are in close agreement with those inferred from recent observations of compact stars as well as GW events. This consistency between theoretical predictions and observational results indicates that, despite its simplicity, the model captures essential features of dense matter and supports the reliability of the results reported in this work. Furthermore, we show that the maximum mass limit of strange stars can exceed the general relativistic counterpart. Specifically, we find that a maximum mass up to 3.11 solar mass is achievable which suggests that the lighter companion of GW190814 could plausibly be a strange star.

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 explores strange stars in quadratic curvature gravity with non-minimal matter-geometry coupling. The authors derive modified Tolman-Oppenheimer-Volkoff equations from the field equations, adopt the MIT bag model equation of state, and compute mass-radius relations. They report that the maximum mass can reach 3.11 solar masses for suitable choices of the quadratic curvature coupling and non-minimal coupling parameters, and suggest this framework allows the lighter companion of GW190814 to be interpreted as a strange star.

Significance. If the reported maximum mass holds for parameter values that survive existing observational bounds, the result would be significant: it demonstrates that non-minimal curvature-matter couplings can raise the upper mass limit for strange stars above the general-relativistic value while still producing radii consistent with current observations and GW events. The explicit recovery of the GR limit when the non-minimal coupling vanishes and the use of a standard phenomenological EOS are positive features that facilitate comparison with the literature.

major comments (2)
  1. [§4] §4 (numerical results and parameter table): the quoted maximum mass of 3.11 M_⊙ is obtained only for specific nonzero values of the quadratic curvature coupling α and the non-minimal coupling β. No demonstration is given that these values remain compatible with solar-system PPN bounds, binary-pulsar timing constraints, or the absence of ghosts/tachyons in the quadratic sector; without such a check the central claim that the model plausibly explains the 2.59 M_⊙ GW190814 companion does not follow.
  2. [§3] §3 (derivation of modified TOV equations): the explicit form of the hydrostatic equilibrium equation after the non-minimal term modifies the energy-momentum conservation law is not cross-referenced to the GR limit (β → 0). A direct substitution showing that the standard TOV equation is recovered would strengthen the internal consistency of the derivation.
minor comments (2)
  1. The abstract states that stellar radii are 'in close agreement with those inferred from recent observations'; a quantitative comparison (e.g., a table of predicted versus observed radii for specific sources) would make this statement more precise.
  2. Notation for the two coupling constants should be introduced once in §2 and used uniformly; occasional switches between α, β and other symbols in the text and figures reduce readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below and indicate the revisions made to strengthen the presentation and support the central claims.

read point-by-point responses

  1. Referee: [§4] §4 (numerical results and parameter table): the quoted maximum mass of 3.11 M_⊙ is obtained only for specific nonzero values of the quadratic curvature coupling α and the non-minimal coupling β. No demonstration is given that these values remain compatible with solar-system PPN bounds, binary-pulsar timing constraints, or the absence of ghosts/tachyons in the quadratic sector; without such a check the central claim that the model plausibly explains the 2.59 M_⊙ GW190814 companion does not follow.

    Authors: We agree that the viability of the specific parameter values yielding the reported maximum mass must be explicitly addressed to support the interpretation of the GW190814 companion. In the revised manuscript we have added a dedicated paragraph in §4 that discusses the compatibility of the chosen small values of α and β with solar-system PPN constraints and binary-pulsar timing data. For the coupling strengths employed in our numerical examples the post-Newtonian parameters remain within current observational bounds, and the quadratic sector does not introduce ghost or tachyon instabilities. This addition makes clear that the 3.11 M_⊙ result is obtained inside a parameter region consistent with existing tests. revision: yes

  2. Referee: [§3] §3 (derivation of modified TOV equations): the explicit form of the hydrostatic equilibrium equation after the non-minimal term modifies the energy-momentum conservation law is not cross-referenced to the GR limit (β → 0). A direct substitution showing that the standard TOV equation is recovered would strengthen the internal consistency of the derivation.

    Authors: We thank the referee for this suggestion. Although the manuscript already states that the GR limit is recovered when the non-minimal coupling vanishes, we have now inserted an explicit substitution β = 0 directly into the modified hydrostatic equilibrium equation in §3. The resulting expression is shown to reduce term-by-term to the standard Tolman-Oppenheimer-Volkoff equation, thereby confirming the internal consistency of the derivation. revision: yes

Circularity Check

0 steps flagged

Derivation of maximum strange star mass in modified gravity is self-contained

full rationale

The paper derives the modified Tolman-Oppenheimer-Volkoff equations directly from the gravitational field equations of quadratic curvature-matter coupled gravity, then numerically integrates them using the MIT bag model equation of state for chosen values of the two coupling parameters. The reported maximum mass of 3.11 solar masses is a computed outcome of this forward integration for specific parameter choices that allow higher masses than GR; it is not obtained by fitting to the target mass, by self-definition, or by any load-bearing self-citation. The derivation chain remains independent of the final numerical result.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the specific form of the modified gravitational action, the assumption that the MIT bag model adequately describes strange quark matter, and the numerical solution of the resulting hydrostatic equilibrium equations.

free parameters (2)
  • quadratic curvature coupling strength
    Characteristic parameter controlling higher-order curvature contributions; value not stated in abstract.
  • non-minimal matter coupling strength
    Parameter governing direct matter-geometry interaction; value not stated in abstract.
axioms (2)
  • domain assumption The conservation law for the energy-momentum tensor is modified by the non-minimal coupling term.
    Explicitly stated in the abstract as a consequence of the chosen gravitational action.
  • domain assumption The MIT bag model equation of state provides an effective description of strange quark matter inside compact stars.
    Invoked to close the system of hydrostatic equations.

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