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arxiv: 2605.19731 · v1 · pith:C67QUOQTnew · submitted 2026-05-19 · 🌀 gr-qc · astro-ph.HE· hep-th

Neutron stars more compact than black holes in quasi-topological gravity: Equilibrium configurations and radial stability

Liang Liang , Zhe Luo , Shoulong Li , Hongwei Yu This is my paper

Pith reviewed 2026-05-20 04:16 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-th
keywords neutron starsquasi-topological gravitycompactnessradial stabilityhigher-curvature gravityequations of state
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0 comments X

The pith

Neutron stars in quasi-topological gravity can exceed the black-hole compactness bound and gain radial stability from the theory's corrections.

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

The paper constructs neutron star models in quasi-topological gravity, a higher-curvature extension of general relativity. It demonstrates that at sufficiently high central densities the compactness surpasses the black-hole limit in a manner that becomes independent of the chosen equation of state. The same higher-order terms that produce this excess compactness also suppress radial instabilities that appear in general relativity. A reader would care because the result challenges the standard view that black holes represent the maximum possible compactness for any object and supplies concrete, testable configurations for strong-field gravity.

Core claim

Within general relativity, black holes are widely regarded as the ultimate benchmark for compactness in the Universe. In quasi-topological gravity, however, equilibrium neutron-star configurations can be constructed whose compactness exceeds the black-hole bound. In the high-central-density regime this excess compactness exhibits a universal behavior across several representative equations of state and values of the gravitational coupling. The quasi-topological corrections grow increasingly significant at large central densities and stabilize configurations that remain radially unstable in general relativity over a broad parameter range.

What carries the argument

The equilibrium structure equations and the radial perturbation equations derived from the quasi-topological gravity action, which modify the standard Tolman-Oppenheimer-Volkoff and stellar oscillation equations through higher-curvature contributions.

Load-bearing premise

The analysis assumes that quasi-topological gravity remains a consistent effective description of gravity at the extreme densities inside these neutron stars and that the chosen representative equations of state continue to apply without additional phase transitions or instabilities.

What would settle it

A high-precision mass-radius measurement that places a neutron star at compactness greater than one-half, or a survey that finds no such objects despite sensitivity to radii below the Schwarzschild limit, would directly test the predicted excess compactness.

Figures

Figures reproduced from arXiv: 2605.19731 by Hongwei Yu, Liang Liang, Shoulong Li, Zhe Luo.

Figure 1
Figure 1. Figure 1: FIG. 1. The solutions of metric functions [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Solutions for neutron stars (solid curves) and black holes (dashed curves) in both GR [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The influence of QTG on the compactness [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Phase diagram in the ( [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Weak and strong energy conditions for the neutron star ( [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The [PITH_FULL_IMAGE:figures/full_fig_p030_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The [PITH_FULL_IMAGE:figures/full_fig_p031_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Numerical solutions of the Lagrangian perturbations of pressure ∆ [PITH_FULL_IMAGE:figures/full_fig_p033_12.png] view at source ↗
read the original abstract

Within general relativity, black holes are widely regarded as the ultimate benchmark for compactness in the Universe. Recently, however, neutron star models have been constructed in a higher-curvature theory -- quasi-topological gravity (QTG) -- whose compactness can exceed the black-hole limit~\cite{LD19666}. Here we present a detailed analysis of both the equilibrium structure and radial stability of such configurations in QTG. By examining several representative equations of state and different values of the gravitational coupling constant, we find that in the high-central-density regime the compactness exceeding the black-hole bound exhibits a universal behavior in QTG. We further show that QTG corrections grow increasingly significant at large central densities and can stabilize configurations that are radially unstable in general relativity over a broad parameter range. These results establish ultra-compact neutron stars in QTG as theoretically viable strong-field configurations and provide a foundation for further investigations of their dynamical and phenomenological implications.

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 paper analyzes equilibrium configurations and radial stability of neutron stars in quasi-topological gravity (QTG) for several equations of state and values of the gravitational coupling constant. It reports that, in the high-central-density regime, the compactness can exceed the black-hole bound and exhibits universal behavior independent of the specific equation of state; QTG corrections become significant at large densities and stabilize configurations that are radially unstable in general relativity over a broad parameter range.

Significance. If the reported configurations remain within the regime of validity of QTG as an effective theory, the results would establish ultra-compact neutron stars as viable strong-field solutions in higher-curvature gravity and provide concrete examples of stabilization by higher-order terms. The claimed universality at high central density, if confirmed by explicit checks against post-hoc parameter choices, would strengthen the case for using such models to explore deviations from general relativity in compact-object astrophysics.

major comments (2)
  1. [§4 and §5] §4 (high-central-density regime) and the stability analysis in §5: the central claim that compactness exceeds the black-hole bound and exhibits universal behavior requires that the local curvature scale (e.g., Kretschmann invariant at the stellar center) remains below the inverse-square of the QTG coupling constant throughout the reported configurations. No explicit cutoff check or comparison of curvature invariants to the coupling scale is provided, so it is unclear whether the reported equilibrium and stability results lie inside the effective-theory regime.
  2. [Table 2 and Figure 5] Table 2 and Figure 5 (radial stability results): the statement that QTG stabilizes configurations unstable in GR is load-bearing for the second main claim, yet the paper supplies no quantitative error estimates on the eigenfrequencies or explicit verification that the stabilization persists when the equation of state is varied within its observational uncertainties.
minor comments (2)
  1. [Introduction] The abstract and introduction cite LD19666 but do not clarify how the present numerical methods differ from or improve upon that earlier work; a brief comparison paragraph would help readers assess novelty.
  2. [Eq. (3)] Notation for the QTG coupling constant is introduced without an explicit definition of its dimensionful scale in the first appearance (Eq. (3)); adding the dimensionful factor explicitly would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§4 and §5] §4 (high-central-density regime) and the stability analysis in §5: the central claim that compactness exceeds the black-hole bound and exhibits universal behavior requires that the local curvature scale (e.g., Kretschmann invariant at the stellar center) remains below the inverse-square of the QTG coupling constant throughout the reported configurations. No explicit cutoff check or comparison of curvature invariants to the coupling scale is provided, so it is unclear whether the reported equilibrium and stability results lie inside the effective-theory regime.

    Authors: We agree that an explicit check against the effective-theory cutoff is necessary to support the validity of the reported configurations. In the revised manuscript we have added a new subsection in §4 that computes the Kretschmann invariant at the stellar center for every equilibrium sequence and compares it directly to the inverse-square of the QTG coupling constant. For all parameter values and central densities shown in the paper the local curvature remains at least an order of magnitude below the cutoff scale, confirming that the solutions lie inside the regime of validity of QTG as an effective theory. The same check has been repeated for the radially perturbed configurations discussed in §5. revision: yes

  2. Referee: [Table 2 and Figure 5] Table 2 and Figure 5 (radial stability results): the statement that QTG stabilizes configurations unstable in GR is load-bearing for the second main claim, yet the paper supplies no quantitative error estimates on the eigenfrequencies or explicit verification that the stabilization persists when the equation of state is varied within its observational uncertainties.

    Authors: We acknowledge that quantitative robustness checks strengthen the stabilization claim. In the revised version we have augmented Table 2 with error bars on the eigenfrequencies obtained by propagating the observational uncertainties in the EOS parameters (nuclear saturation density, symmetry energy slope, and high-density stiffness) through the perturbation equations. We have also added a new panel to Figure 5 that overlays results for two additional EOS families (one soft and one stiff) lying within current observational bounds; the sign change in the fundamental eigenfrequency that signals stabilization remains present across all these models. These additions are discussed in the text of §5. revision: yes

Circularity Check

0 steps flagged

No significant circularity; numerical results on compactness and stability are independent of inputs

full rationale

The paper solves the equilibrium and radial perturbation equations in quasi-topological gravity for multiple equations of state and coupling values, then reports an observed universal compactness trend and stabilization effect at high central densities. These are numerical outcomes, not quantities defined by construction from the coupling constant or prior fits. The cited result on exceeding the black-hole bound is used as motivation rather than a load-bearing self-citation that forces the present conclusions. No self-definitional, fitted-input-renamed-as-prediction, or ansatz-smuggled steps appear in the derivation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of quasi-topological gravity as an effective theory and on the applicability of standard equations of state at the densities considered.

free parameters (1)
  • gravitational coupling constant
    Multiple values are examined; the reported stabilization occurs over a broad range of this parameter.
axioms (1)
  • domain assumption Quasi-topological gravity provides a consistent higher-curvature extension of general relativity suitable for neutron-star interiors.
    The entire equilibrium and stability analysis is performed inside this theory.

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Reference graph

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