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arxiv: 1907.03545 · v1 · pith:3TD32VWXnew · submitted 2019-07-05 · 🌀 gr-qc · astro-ph.HE· astro-ph.SR

Relativistic strange quark stars in Lovelock gravity

Grigoris Panotopoulos , \'Angel Rinc\'on This is my paper

Pith reviewed 2026-05-25 02:20 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEastro-ph.SR
keywords strange quark starsLovelock gravityGauss-Bonnet termTolman-Oppenheimer-Volkoff equationfive-dimensional spacetimecompactnessgravitational redshiftquark matter
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The pith

The Gauss-Bonnet parameter in five-dimensional Lovelock gravity modifies the mass-to-radius relation, compactness, and gravitational redshift of strange quark stars made from deconfined quarks.

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

The paper examines relativistic non-rotating stars in Lovelock gravity by retaining the Gauss-Bonnet term in five dimensions. It adopts an equation of state for a relativistic gas of de-confined massless quarks and solves the resulting modified Tolman-Oppenheimer-Volkoff equations numerically. The solutions produce families of mass-radius curves, compactness values, and gravitational redshifts that change with the Gauss-Bonnet coupling, for both isotropic and anisotropic pressure distributions. Maximum masses and radii are extracted for several values of the parameter.

Core claim

In five-dimensional Einstein-Gauss-Bonnet gravity the modified Tolman-Oppenheimer-Volkoff equations are integrated with the equation of state of massless deconfined quarks to obtain mass-to-radius profiles, compactness, and gravitational red-shift that depend on the Gauss-Bonnet parameter; results are given for both isotropic and anisotropic stars together with the maximum mass and radius attained.

What carries the argument

Modified Tolman-Oppenheimer-Volkoff equations obtained from the Einstein-Gauss-Bonnet field equations, closed by the equation of state for a relativistic gas of de-confined massless quarks.

If this is right

  • Maximum star mass and radius vary with the Gauss-Bonnet parameter.
  • Compactness of the configuration changes as the Gauss-Bonnet parameter is varied.
  • Gravitational red-shift takes different values for different Gauss-Bonnet couplings.
  • Both isotropic and anisotropic pressure distributions exhibit the reported dependence.

Where Pith is reading between the lines

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

  • The computed families of curves supply concrete targets for comparison with any future mass-radius measurements of candidate strange quark stars.
  • The same numerical setup can be reused with other equations of state to isolate the effect of the higher-curvature term.

Load-bearing premise

The matter inside the star is a relativistic gas of de-confined massless quarks that supplies the equation of state.

What would settle it

Independent numerical integration of the same modified Tolman-Oppenheimer-Volkoff system with the identical quark equation of state that produces mass-radius profiles independent of the Gauss-Bonnet parameter value.

Figures

Figures reproduced from arXiv: 1907.03545 by \'Angel Rinc\'on, Grigoris Panotopoulos.

Figure 1
Figure 1. Figure 1: Left panel: Mass-to-radius profiles (mass in solar masses and radius in km) for three different values of the Guass-Bonnet parameter. The case α = 0 is also shown for comparison reasons. Right panel: Compactness of the star β = (6π 2 ) −1 (M/R2 ) vs mass of the star (in solar masses) for three different values of the Guass-Bonnet parameter. The case α = 0 is also shown for comparison reasons. The color cod… view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: Gravitational red-shift vs mass (in solar masses) of the star for three different values of the Gauss-Bonnet parameter. Right panel: Gravitational red-shift vs radius (in km) of the star for three different values of the Guass-Bonnet parameter. The color code is as follows: i) green curve for α = 1, ii) magenta curve for α = 5 , iii) blue curve for α = 10 [PITH_FULL_IMAGE:figures/full_fig_p005… view at source ↗
Figure 3
Figure 3. Figure 3: Checking the energy conditions for isotropic stars for pc(0) = B and α = 1, 5, 10. Shown are: Normalized energy density (black curves), normalized pressure (blue curves), and four times the normalized pressure (red curves). We have considered three different cases: i) α = 1 (solid line), ii) α = 5 (long dashed line) and iii) α = 10 (short dashed line). Finally, if the wavelength of a photon emitted at the … view at source ↗
Figure 4
Figure 4. Figure 4: Interior solutions for anisotropic stars for i) α = 1 (solid black line), ii) α = 10 (dashed blue line), iii) α = 20 (dotted red line) for a = 2.5 and r0 = 45 km. Left panel: Energy density versus normalized radial coordinate. Middle panel: Radial pressure versus normalized radial coordinate. Right panel: Anisotropy versus normalized radial coordinate. 5 Conclusions To summarize, in the present work we hav… view at source ↗
read the original abstract

We study relativistic non-rotating stars in the framework of Lovelock gravity. In particular, we consider the Gauss-Bonnet term in a five-dimensional spacetime, and we investigate the impact of the Gauss-Bonnet parameter on properties of the stars, both isotropic and anisotropic. For matter inside the star, we assume a relativistic gas of de-confined massless quarks. We integrate the modified Tolman-Oppenheimer-Volkoff equations numerically, and we obtain the mass-to-radius profile, the compactness of the star as well as the gravitational red-shift for several values of the Gauss-Bonnet parameter. The maximum star mass and radius are also reported.

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

1 major / 0 minor

Summary. The manuscript studies non-rotating relativistic stars in five-dimensional Lovelock gravity including the Gauss-Bonnet term. It adopts an equation of state for a relativistic gas of de-confined massless quarks and numerically integrates the modified Tolman-Oppenheimer-Volkoff equations to obtain mass-to-radius profiles, compactness, gravitational redshift, and maximum masses/radii for several values of the Gauss-Bonnet parameter, considering both isotropic and anisotropic cases.

Significance. If the numerical integrations were consistent with the required boundary conditions, the results would quantify how the Gauss-Bonnet parameter alters the structure and observable properties of strange quark stars in higher-curvature gravity, providing a concrete extension of standard TOV analyses to Lovelock theories.

major comments (1)
  1. [Abstract / matter model] Abstract and matter-model section: the equation of state for de-confined massless quarks is p = ρ/3. Under this relation pressure vanishes only when energy density vanishes, so no finite radius R exists at which p(R) = 0 while ρ(R) > 0. This precludes standard matching to the exterior vacuum solution and renders all reported finite mass-radius profiles, compactness values, and maximum masses inconsistent. The issue is load-bearing for the central numerical claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting an important issue with our matter model. We respond to the major comment below and will make the necessary revisions.

read point-by-point responses

  1. Referee: [Abstract / matter model] Abstract and matter-model section: the equation of state for de-confined massless quarks is p = ρ/3. Under this relation pressure vanishes only when energy density vanishes, so no finite radius R exists at which p(R) = 0 while ρ(R) > 0. This precludes standard matching to the exterior vacuum solution and renders all reported finite mass-radius profiles, compactness values, and maximum masses inconsistent. The issue is load-bearing for the central numerical claims.

    Authors: We agree that the equation of state p = ρ/3 for massless quarks does not allow for a finite stellar radius where pressure vanishes while energy density remains positive. This is a valid criticism, as it affects the definition of the star's surface and the matching to the exterior solution. To rectify this, we will update the matter model to the standard MIT bag model for strange quark matter, given by p = (ρ - 4B)/3, where B is the bag constant. This permits a non-zero surface density at which p = 0. We will then re-integrate the modified TOV equations and update all results, including mass-radius profiles, compactness, gravitational redshift, and maximum masses, for the various values of the Gauss-Bonnet parameter in both isotropic and anisotropic cases. The abstract will also be revised accordingly. revision: yes

Circularity Check

0 steps flagged

No circularity: direct numerical integration of modified TOV with input EOS

full rationale

The paper's central procedure is numerical integration of the modified Tolman-Oppenheimer-Volkoff equations in 5D Lovelock gravity (with Gauss-Bonnet term) using the supplied equation of state p=ρ/3 for a relativistic gas of de-confined massless quarks. Mass-radius profiles, compactness, gravitational red-shift, and maximum mass/radius are reported as outputs of this integration for several values of the Gauss-Bonnet parameter. No load-bearing step reduces by construction to a fitted input, self-definition, or self-citation chain; the derivation chain consists of standard numerical solution of the differential system with given initial conditions, EOS, and parameter values. The result is therefore self-contained against external benchmarks and receives the default low circularity score.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the choice of Lovelock gravity in 5D and the massless-quark equation of state; both are domain assumptions rather than derived results.

free parameters (1)
  • Gauss-Bonnet parameter
    Explored parametrically over several values to map its impact; functions as a free parameter in the model.
axioms (2)
  • domain assumption Lovelock gravity in five-dimensional spacetime with Gauss-Bonnet term
    The gravitational framework is adopted without derivation.
  • domain assumption Equation of state for relativistic gas of de-confined massless quarks
    Supplies the pressure-density relation needed to integrate the stellar structure equations.

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Reference graph

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