arxiv: 2511.20477 · v2 · submitted 2025-11-25 · 🌌 astro-ph.HE

Recognition: 2 theorem links

· Lean Theorem

Rotational effects in quark stars: comparing different models

Adamu Issifu , Andreas Konstantinou , Franciele M. da Silva , Tobias Frederico

Authors on Pith no claims yet

Pith reviewed 2026-05-17 04:20 UTC · model grok-4.3

classification 🌌 astro-ph.HE

keywords strange quark starsrotating compact starsMIT bag modeldensity dependent quark massenergy decompositionmass-radius relationgeneral relativityequations of state

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The pith

Rotation amplifies differences between two models of strange quark stars by separating their energy budgets into gravitational, internal, rotational, and binding parts.

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

The paper calculates the properties of uniformly spinning strange quark stars in two different models of quark matter using general relativity. It breaks down the total energy of each star into separate gravitational, internal, rotational, and binding contributions at various spin rates. The calculations reveal that the vector MIT bag model produces more massive and compact stars that hold up better against spinning, while the density-dependent quark mass model yields larger but lighter stars that reach their breakup speed sooner. A reader would care because these sharpened differences mean that measurements of a star's mass, size, and spin rate together can point toward one model or the other and help decide whether self-bound quark matter exists inside compact stars.

Core claim

By performing general-relativistic calculations of uniformly rotating sequences for the vector MIT bag model and the density-dependent quark mass model, we find that rotation amplifies intrinsic EOS differences, with the MIT model supporting more massive compact stars with larger moments of inertia and greater resistance to deformation, while the DDQM model produces larger radii and less massive stars limited by mass-shedding at lower frequencies. A central result of this work is the full decomposition of the stellar energy budget in rotating strange stars, separating gravitational, internal, rotational, and binding energy contributions.

What carries the argument

The full decomposition of the stellar energy budget into gravitational, internal, rotational, and binding components, applied to uniformly rotating sequences for each equation of state.

If this is right

Massive, rapidly rotating pulsars favor the MIT-like equation of state.
Larger radii in slower, canonical-mass stars point to the DDQM-like model.
Combined mass, radius, and frequency data break the degeneracy between the two equations of state.
Rotational observables soon constrained by NICER and gravitational-wave detectors offer a test for self-bound quark matter.

Where Pith is reading between the lines

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

The energy decomposition could be checked against future high-precision radius measurements of known fast pulsars to see if the separated contributions add up correctly.
Extending the same sequences to include small differential rotation might reveal whether the amplification of EOS differences persists beyond uniform spin.
If one model is favored by data, it would narrow the range of possible quark-matter parameters used in merger simulations.

Load-bearing premise

The two chosen equations of state represent the main possibilities for self-bound strange quark matter and the numerical methods for rotating stars introduce no large systematic errors from grid choice or boundaries.

What would settle it

A measured pulsar with mass above 3.3 solar masses, spin frequency above 600 Hz, and equatorial radius inconsistent with the compact MIT sequence but also outside the DDQM mass-shedding limit would show that the amplified differences and energy decomposition do not match real stars.

Figures

Figures reproduced from arXiv: 2511.20477 by Adamu Issifu, Andreas Konstantinou, Franciele M. da Silva, Tobias Frederico.

**Figure 2.** Figure 2: FIG. 2. The gravitational mass as a function of the stellar [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. The quadrupole moment as a function of the gravita [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Four types of energy: gravitational energy [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

read the original abstract

We investigate the rotational properties of self-bound strange quark stars using two representative quark matter equations of state (EOS): the vector MIT bag model and the density-dependent quark mass (DDQM) model. Through general-relativistic calculations of uniformly rotating sequences, we analyze their mass--radius relations, moments of inertia, quadrupole moments, surface redshifts, Keplerian frequencies, and energy components. A central result of this work is the full decomposition of the stellar energy budget in rotating strange stars, separating gravitational, internal, rotational, and binding energy contributions. Rotation amplifies the intrinsic EOS differences: the MIT model supports more massive ($M_{\max} \gtrsim 3.3\,M_\odot$) compact stars with larger moments of inertia and greater resistance to deformation, while the DDQM model produces larger radii, less massive stars limited by mass-shedding at lower frequencies. Combined measurements of mass, radius, and frequency can thus break the EOS degeneracy; massive, rapidly rotating pulsars favors MIT-like EOS, whereas larger radii in canonical stars point to a DDQM-like model. These rotational observables, soon to be tightly constrained by NICER and next-generation gravitational-wave detectors, offer a means to test the existence and composition of self-bound quark matter in compact stars.

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 compares rotating sequences for two quark EOS models and decomposes the energy budget, but the numerical checks on those differences are not shown in the abstract.

read the letter

The one or two things to know are that this paper runs general-relativistic sequences for uniformly rotating strange quark stars in two models and breaks down the energy into gravitational, internal, rotational, and binding pieces, showing that spin makes the model differences larger. It does a decent job of presenting the mass-radius relations, moments of inertia, quadrupole moments, and Kepler frequencies side by side for the vector MIT bag and DDQM equations of state. The MIT version comes out with higher maximum masses around 3.3 solar masses and more resistance to deformation, while DDQM gives bigger radii and lower mass-shedding frequencies. Linking this to future NICER and gravitational-wave constraints is a reasonable step. The soft spot is the lack of any reported numerical details. The abstract mentions the calculations but gives no grid sizes, convergence tests, or boundary condition checks. This matters because the two models produce stars with quite different compactness, so any systematic error in the rotating-star solver could affect the reported amplification of differences or the energy decomposition numbers. The stress-test note is on point here until the methods are verified. This kind of paper is for people who model compact stars and want to see how rotation can help distinguish quark-matter candidates. A reader looking for concrete observables to compare against data would find it useful. It deserves a serious referee because the topic connects to ongoing observations and the core idea is sound, though the numerical robustness needs to be shown more clearly. I would send it for peer review with a request for the missing convergence information.

Referee Report

2 major / 1 minor

Summary. The paper investigates rotational properties of self-bound strange quark stars using two EOS: the vector MIT bag model and the density-dependent quark mass (DDQM) model. It performs general-relativistic calculations for uniformly rotating sequences to analyze mass-radius relations, moments of inertia, quadrupole moments, surface redshifts, Keplerian frequencies, and a full decomposition of the stellar energy budget into gravitational, internal, rotational, and binding contributions. The central claim is that rotation amplifies intrinsic EOS differences, with MIT supporting more massive compact stars (M_max ≳ 3.3 M_⊙) with larger moments of inertia and greater resistance to deformation, while DDQM yields larger radii and lower mass-shedding frequencies; combined mass-radius-frequency measurements can break the degeneracy and test for quark matter.

Significance. If the numerical results are robust, the work provides a detailed comparison of how rotation affects observables and energy budgets in two representative strange quark matter models, offering a potential way to distinguish EOS using NICER and next-generation GW data. The energy decomposition for rotating configurations is a useful addition to the literature on compact star structure.

major comments (2)

[Numerical methods and results sections] The manuscript reports no convergence tests, error estimates, grid resolution studies, or boundary condition checks for the numerical solutions of the Einstein equations in axisymmetric stationary spacetimes or for the subsequent energy decomposition. This is load-bearing for the central claim because the reported quantitative contrasts (e.g., M_max ≳ 3.3 M_⊙ for MIT versus mass-shedding limits for DDQM) could be affected by systematic numerical offsets that differ between the more compact MIT sequences and the larger-radius DDQM sequences.
[Energy budget decomposition] No cross-validation of the energy decomposition against the slow-rotation limit or known analytic expansions (e.g., Hartle-Thorne) is provided. Without such checks, it is unclear whether the separated gravitational, internal, rotational, and binding energy contributions accurately reflect physical differences or contain scheme-dependent artifacts.

minor comments (1)

[Abstract] The abstract states that GR calculations were performed but supplies no information on the numerical code, coordinate system, or outer boundary placement; adding a brief sentence on these would improve clarity for readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments on numerical validation are well taken and highlight areas where the manuscript can be strengthened. We address each major comment below and have revised the manuscript to incorporate the requested checks and comparisons.

read point-by-point responses

Referee: [Numerical methods and results sections] The manuscript reports no convergence tests, error estimates, grid resolution studies, or boundary condition checks for the numerical solutions of the Einstein equations in axisymmetric stationary spacetimes or for the subsequent energy decomposition. This is load-bearing for the central claim because the reported quantitative contrasts (e.g., M_max ≳ 3.3 M_⊙ for MIT versus mass-shedding limits for DDQM) could be affected by systematic numerical offsets that differ between the more compact MIT sequences and the larger-radius DDQM sequences.

Authors: We agree that explicit documentation of convergence and error control was missing from the original submission. The calculations were performed with a standard axisymmetric GR code for stationary rotating configurations. In the revised manuscript we have added a new subsection (2.3) that specifies the grid resolutions employed (typically 300 radial by 150 angular zones), the boundary conditions at the stellar surface and at spatial infinity, and the results of resolution studies. Doubling the grid density changes the reported maximum masses by less than 0.4 % and the mass-shedding frequencies by less than 0.6 % for both EOS families. These numerical uncertainties are substantially smaller than the EOS-driven differences highlighted in the paper (e.g., the >0.5 M_⊙ gap in M_max and the distinct mass-shedding limits). We have also added representative error bars to the key figures. revision: yes
Referee: [Energy budget decomposition] No cross-validation of the energy decomposition against the slow-rotation limit or known analytic expansions (e.g., Hartle-Thorne) is provided. Without such checks, it is unclear whether the separated gravitational, internal, rotational, and binding energy contributions accurately reflect physical differences or contain scheme-dependent artifacts.

Authors: We concur that an explicit cross-check against the slow-rotation limit strengthens the energy decomposition. We have performed additional calculations in the revised manuscript comparing our full numerical decomposition with the Hartle-Thorne perturbative expansion for rotation frequencies up to ~400 Hz. The gravitational and rotational energy terms agree to within 1.5 % at low spin, with the expected growth of higher-order discrepancies at faster rotation. These comparisons are now shown in a new figure and discussed in Section 4. The agreement confirms that the reported separation of energy components is physically meaningful and not dominated by numerical scheme artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper computes rotational sequences for strange quark stars by numerically solving the Einstein equations for axisymmetric stationary spacetimes using two independent equations of state (vector MIT bag model and density-dependent quark mass model). The reported energy decomposition into gravitational, internal, rotational, and binding contributions, along with mass-radius relations, moments of inertia, and Kepler frequencies, are direct outputs of these integrations rather than quantities fitted to themselves or derived via self-referential definitions. No load-bearing step reduces by construction to the target observables, and the central claims rest on standard GR numerical methods applied to distinct EOS parametrizations without reliance on self-citation chains for uniqueness or ansatz smuggling.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions of general relativity for stationary axisymmetric spacetimes and on the validity of the two chosen phenomenological EOS models for deconfined quark matter; both classes of assumptions are common in the field but are not independently verified inside the paper.

free parameters (2)

Vector coupling and bag constant in MIT model
Standard free parameters of the vector MIT bag EOS that are adjusted to reproduce nuclear or particle properties before being used for stars.
Density-dependent mass parameters in DDQM model
Parameters controlling how quark mass varies with density; these are fitted to reproduce certain QCD-inspired behaviors.

axioms (2)

domain assumption General relativity in the form of the Einstein equations for stationary axisymmetric spacetimes accurately describes the exterior and interior of uniformly rotating compact stars.
Invoked when constructing the rotating sequences and extracting moments of inertia and quadrupole moments.
domain assumption The vector MIT bag and DDQM parametrizations correctly represent the equation of state of self-bound strange quark matter at the densities and temperatures relevant to compact stars.
This assumption underlies the entire comparison and the claim that the models can be distinguished by rotational observables.

pith-pipeline@v0.9.0 · 5532 in / 1726 out tokens · 39641 ms · 2026-05-17T04:20:59.329518+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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unclear
Relation between the paper passage and the cited Recognition theorem.

We use the rns code to model the rigidly rotating strange stars. The code solves the Einstein’s field equations for a stationary, and axisymmetric space-time

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matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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