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arxiv: 2602.02272 · v2 · pith:HMYNRAP7new · submitted 2026-02-02 · 🌀 gr-qc

Radial Oscillations of Neutron Stars with Vector-Induced Scalar Hair

Hamza Boumaza This is my paper

Pith reviewed 2026-05-16 08:13 UTC · model grok-4.3

classification 🌀 gr-qc
keywords neutron starsradial oscillationsmodified gravitySVT theoriesscalar hairquasinormal modesstabilitymass-radius relation
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The pith

In a subclass of scalar-vector-tensor theories, the vector-curvature coupling changes neutron star mass-radius curves and radial oscillation spectra while keeping the onset of instability tied to the maximum-mass configuration.

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

The paper studies neutron stars in a gauge-invariant scalar-vector-tensor theory that includes a vector-curvature coupling. It solves the modified Tolman-Oppenheimer-Volkoff equations for different values of the coupling strength to find how the extra interaction alters stellar structure. From the quadratic action for linear radial perturbations, the work computes both the ordinary matter normal modes and the additional scalar quasinormal modes that propagate outside the star. The central result is that the coupling parameter shifts the mass-radius relation, the frequencies of oscillation, and the stability boundaries, yet the point where radial instability first appears remains exactly the maximum-mass star, as it does in general relativity.

Core claim

Within this subclass of gauge-invariant SVT theories, the vector-curvature coupling produces vector-induced scalar hair. The generalized equilibrium equations show that varying the modified-gravity parameter changes the mass-radius relation of neutron stars. The quadratic action for radial perturbations yields a spectrum of matter normal modes inside the star and scalar quasinormal modes outside it. Across the family of solutions, the first unstable radial mode still appears precisely at the maximum-mass configuration, preserving the same stability criterion that holds in general relativity.

What carries the argument

The vector-curvature coupling in the SVT action, which sources an extra propagating scalar degree of freedom and supplies the quadratic action whose eigenvalues determine both matter normal modes and scalar quasinormal modes.

If this is right

  • Different values of the coupling parameter produce distinct mass-radius relations for neutron stars.
  • The frequencies of radial oscillation modes shift measurably with the coupling strength.
  • The stability boundary for radial perturbations continues to coincide with the maximum-mass star for any coupling value.
  • Scalar quasinormal modes appear outside the star and carry information about the modified gravity parameter.

Where Pith is reading between the lines

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

  • Future observations of neutron-star oscillation frequencies could place bounds on the allowed range of the vector-curvature coupling.
  • The preserved stability rule may hold in a wider class of theories that add vector-induced scalar degrees of freedom.
  • The same framework could be used to study non-radial modes or rotating configurations to test whether the stability coincidence survives.

Load-bearing premise

The quadratic action for perturbations fully captures the linear dynamics of the theory without higher-order corrections becoming important.

What would settle it

A measured neutron-star mass, radius, and radial oscillation frequency that, for every value of the coupling parameter, places the star beyond the calculated maximum-mass point while still showing only stable modes.

Figures

Figures reproduced from arXiv: 2602.02272 by Hamza Boumaza.

Figure 1
Figure 1. Figure 1: Mass-radius (M-R, left panel) and mass-central energy density (M-ρc, right panel) relations for various values of the coupling parameter β4. The curves correspond to β4 = 0 (solid lines), β4 = −0.0033 (dashed lines), β4 = −0.0046 (dot-dashed lines), and β4 = −0.0053 (dotted lines). Four different equations of state, distinguished by color, are considered: FPS (purple), SLy (blue), BSk20 (green), and BSk22 … view at source ↗
Figure 2
Figure 2. Figure 2: The first four normalized Lagrangian perturbations of the pressure ∆P/P(0) as a function of the radial coordinate for β4 = −0.00333. The numerical solutions satisfy the boundary condition (67) and (69) in the case of a neutron star with SLy EoS and central density ρc = 10ρ0. of real values of ω corresponding to the normal modes. In Fig.2, we plot the perturbation ∆P for the first four eigenvalues ωn, where… view at source ↗
Figure 3
Figure 3. Figure 3: Squared frequency of the fundamental oscillation mode versus compactness, for the beyond-GR param￾eters β4 = −0.00333 (dashed lines), β4 = −0.00467 (dotdashed lines) and β4 = −0.00533 (dotted lines), together with the GR (β4 = 0) results (black lines). Four distinct equations of state are considered: FPS , SLy , BSk20 and BSk22. equation behaves as1 Φ ∼ Φ− cos(ω r) + Φ+ sin(ω r) (r → 0), (72) where Φ+ and … view at source ↗
Figure 4
Figure 4. Figure 4: oscillation frequency as function of compactness, for the beyond-GR parameters β4 = −0.00333 (dashed lines), β4 = −0.00467 (dotdashed lines) and β4 = −0.00533 (dotted lines), together with the GR (β4 = 0) results (black lines). Four distinct equations of state are considered: FPS , SLy , BSk20 and BSk22. 7 Conclusion In this paper, we have investigated possible deviations from General Relativity (GR) in th… view at source ↗
Figure 5
Figure 5. Figure 5: Imaginary part of ω (ωI ) as function of compactness, for the beyond-GR parameters β4 = −0.00333 (dashed lines), β4 = −0.00467 (dotdashed lines) and β4 = −0.00533 (dotted lines), together with the GR (β4 = 0) results (black lines). Four distinct equations of state are considered: FPS , SLy , BSk20 and BSk22. A Coefficients in the gravitational equations of motion The coefficients ai , ei and qi in the acti… view at source ↗
read the original abstract

In this paper, we investigate the equilibrium configurations and radial perturbations of neutron stars within a subclass of gauge-invariant Scalar-Vector-Tensor (SVT) theories. By solving the generalized Tolman-Oppenheimer-Volkoff (TOV) equations for several values of the modified gravity parameter, we examine the impact of the vector-curvature coupling on the structure and properties of neutron stars. We then extend our analysis by deriving the quadratic action governing linear radial perturbations and computing both the normal modes associated with the matter sector and the scalar quasinormal modes arising from the additional propagating degree of freedom of the theory, which is able to propagate outside the neutron star. Our results show that the modified gravity parameter can significantly affect the mass-radius relation, the oscillation spectrum, and the stability properties of neutron stars, while preserving the coincidence between the onset of radial instability and the maximum-mass configuration, as in General Relativity.

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

0 major / 3 minor

Summary. The paper investigates equilibrium configurations and radial perturbations of neutron stars in a subclass of gauge-invariant Scalar-Vector-Tensor (SVT) theories with vector-curvature coupling. By solving generalized Tolman-Oppenheimer-Volkoff (TOV) equations for multiple values of the modified gravity parameter, the authors obtain mass-radius relations and then derive the quadratic action for linear radial perturbations to compute matter normal modes and scalar quasinormal modes that propagate outside the star. The central claim is that the parameter significantly modifies the mass-radius curve, oscillation spectrum, and stability properties while preserving the coincidence between the onset of radial instability and the maximum-mass configuration, as in general relativity.

Significance. If the numerical results hold, the work shows that vector-induced scalar hair provides a controlled modification to neutron-star structure and dynamics without breaking the GR-like radial stability criterion. This is useful for placing bounds on SVT parameters from mass-radius observations and asteroseismology, and the explicit separation of matter and scalar modes clarifies the role of the extra degree of freedom.

minor comments (3)
  1. The manuscript should include a brief statement of the numerical methods used to integrate the generalized TOV equations and to solve the perturbation eigenvalue problem, together with convergence tests or error estimates for the reported frequencies and mass-radius points.
  2. Figure captions and axis labels should explicitly state the equation of state and the range of the modified gravity parameter used in each panel.
  3. A short paragraph comparing the obtained quasinormal-mode frequencies with the corresponding general-relativity limit would help readers assess the magnitude of the SVT correction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the positive assessment of our results on neutron-star equilibria and radial perturbations in scalar-vector-tensor gravity. The referee's summary accurately captures the central findings, including the preservation of the maximum-mass–radial-instability coincidence. We will incorporate minor revisions to improve clarity and presentation as recommended.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper derives the generalized TOV equations and quadratic action for linear radial perturbations directly from the SVT theory action via standard variational procedures. Equilibrium configurations and normal modes are then obtained by numerical integration of these derived equations. The reported effects on mass-radius relations, oscillation spectra, and the preserved coincidence between radial instability onset and maximum mass are computed outputs, not inputs redefined by construction. No load-bearing self-citations, fitted parameters renamed as predictions, or smuggled ansatze appear in the central steps. The analysis remains self-contained against the theory's own field equations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the existence of a gauge-invariant SVT subclass with vector-curvature coupling, the validity of the generalized TOV equations, and the quadratic action for linear radial perturbations; the modified gravity parameter is introduced as a free input.

free parameters (1)
  • modified gravity parameter
    Controls the strength of the vector-curvature coupling and is varied across several values to produce the reported changes in mass-radius and oscillation spectra.
axioms (1)
  • domain assumption The theory belongs to a gauge-invariant subclass of scalar-vector-tensor theories
    Invoked as the starting framework for deriving the generalized TOV equations and perturbation action.
invented entities (1)
  • vector-induced scalar hair no independent evidence
    purpose: Provides an additional propagating scalar degree of freedom that modifies neutron-star structure and allows scalar modes outside the star
    Postulated within the SVT theory; no independent evidence supplied in the abstract.

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Reference graph

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