Pith. sign in

REVIEW 1 major objections 4 minor 2 cited by

Radial oscillations of neutron stars in Starobinsky gravity and its Gauss-Bonnet extension

T0 review · 1 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Birkhoff's theorem fails in Starobinsky gravity: a neutron star's exterior spacetime responds to its radial oscillations, flattening the fundamental frequency against central density at low densities while preserving the maximum-mass…

desk verdict Solid derivation and new physics in the exterior response, but the stability conclusions rest on an unjustified mode-selection rule and the Gauss-Bonnet part is unverifiable from the manuscript. read the letter →

arxiv 2507.18916 v1 pith:GGWZWNOC submitted 2025-07-25 gr-qc astro-ph.HE

Ziyi Li , Zhong-Xi Yu , Zhe Luo , Shoulong Li , Hongwei Yu This is my paper · ORCID
classification gr-qcastro-ph.HE MSC 83D0583C55
keywords Starobinskygravityhigher-curvatureradialoscillationsneutronstarstabilityBirkhofftheoremscalar-tensorGauss-BonnetextensionSLyequationofstate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper investigates whether neutron stars remain stable against radial collapse when the gravitational action contains a curvature-squared term, as in Starobinsky gravity, or a further Gauss-Bonnet extension. It argues that the higher-derivative character of these theories breaks Birkhoff's theorem, so the spacetime outside a pulsating star is not static but responds dynamically to the fluid's oscillations. Working in the Jordan-frame scalar-tensor representation and using the SLy equation of state, the authors compute fundamental-mode spectra and find two effects: at low central densities with a large curvature-squared coupling the squared fundamental frequency becomes nearly independent of the central density, while near the maximum-mass configuration the stability-to-instability transition still occurs approximately where $dM/d\rho_0$ changes sign, as in general relativity. If correct, the results imply that modified gravity can leave observable signatures in neutron-star pulsation frequencies and that the standard GR stability criterion is only partially preserved.

What carries the argument

The load-bearing object is the scalar-tensor representation of the theory with Lagrangian $L = R + \Phi R - \tfrac{1}{2}\mu^2\Phi^2 + U(\Phi)L_{GB}$, in which Starobinsky gravity corresponds to $\beta = 0$ and the Gauss-Bonnet extension to $\beta \ne 0$; the massive scalar $\Phi$ carries the higher-curvature physics. The argument runs through the modified Tolman-Oppenheimer-Volkoff equilibrium equations and a four-field radial perturbation system (fluid displacement $\xi$, metric perturbations $\delta\lambda$ and $\delta f$, scalar perturbation $\delta\phi$), solved by shooting with boundary conditions at the center, at the surface (vanishing Lagrangian pressure perturbation), and at infinity (exponential decay of $\delta f$ and $\delta\phi$). The key criterion is the sign of the lowest eigenvalue $\omega^2$ of this system together with the requirement that the perturbation functions decay, not oscillate, at infinity.

What would settle it

Compute the full complex-frequency spectrum of the linearized perturbation system, or evolve it numerically in the time domain, for a model the paper labels stable using the SLy equation of state and large $\alpha$ (for example $\rho_0 \approx 2.5 \times 10^{15}\,\mathrm{g/cm^3}$ with $\alpha = 1000\alpha_\star$); if any decaying-in-time (growing) mode with nonzero imaginary part of $\omega$ appears, the sign-of-$\omega^2$ criterion is incomplete and the stability conclusions change. Alternatively, recompute the nearly flat $\omega^2$ versus $\rho_0$ curve with a stiff polytropic equation of state: if the plateau disappears, the effect is an artifact of the SLy EOS rather than a generic property of the gravity theory.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that in Starobinsky gravity and its Gauss-Bonnet extension, radial stability of neutron stars is governed by a dynamical exterior spacetime rather than the static vacuum of general relativity. Because of the added massive scalar degree of freedom, Birkhoff's theorem fails; the exterior metric and scalar-field perturbations obey their own differential equations, and only the fundamental mode produces perturbation functions that decay exponentially at infinity, while overtones oscillate and are discarded. For the SLy equation of state, large values of the Starobinsky coupling $\alpha$ make the fundamental squared frequency $\omega^2$ nearly independent of central density across low-density stellar models, and for high central densities the sign change of $\omega^2$ still coincides approximately with the maximum-mass configuration. The authors verify that the same frequencies are obtained in the Jordan and Einstein frames of the equivalent scalar-tensor theory and extend the analysis to a Gauss-Bonnet coupling, noting that when $\alpha$ is large the Gauss-Bonnet coupling's effect on the frequency becomes negligible.

Load-bearing premise

The paper assumes that the sign of the fundamental-mode squared frequency, computed with a real frequency and with overtones discarded because they oscillate at infinity, fully determines stability; it does not rule out growing complex-frequency modes of the same system.

Editorial extensions

If this is right

  • In these theories the exterior of a radially pulsating neutron star moves: the metric and scalar field outside the star carry time-dependent perturbations, so GR's assumption of a static Schwarzschild exterior during pulsation does not apply.
  • For sufficiently large $\alpha$, the fundamental-mode squared frequency of low-density neutron stars becomes nearly constant with central density, meaning the oscillation frequency carries almost no information about the star's central density or mass in that regime.
  • Near the maximum-mass configuration, the criterion $dM/d\rho_0 > 0$ still marks the transition from stability to instability to within about a percent in mass, extending the GR static-stability result to these higher-curvature models.
  • Only the fundamental mode is admitted by the asymptotically flat boundary conditions; overtone radial modes, which oscillate rather than decay at infinity, cannot be used to characterize stellar oscillations in this framework.
  • The Jordan-frame and Einstein-frame computations agree for the same star, so the frame choice does not affect the predicted radial oscillation frequencies in Starobinsky gravity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the harmonic ansatz fixes real $\omega$, the paper does not compute damping timescales; if the exterior responds dynamically, the fundamental mode likely becomes quasi-normal and radiates scalar radiation, which a time-domain evolution could reveal.
  • The exclusion of overtone modes on asymptotic grounds suggests the perturbation problem is not a standard Sturm-Liouville system; a full spectral analysis allowing complex frequencies could uncover radiative or growing modes that would alter the stability verdict for some configurations.
  • The near-flatness of the frequency-density curve at large $\alpha$ suggests a possible observational discriminant: a population of low-mass neutron stars with nearly identical pulsation frequencies would be a signature of such curvature-squared gravity, though nuclear-physics EOS effects would have to be controlled first.
  • Whether the density-independence plateau and the persistence of the maximum-mass stability transition hold for other $f(R)$ or higher-derivative theories is left open by the paper; recomputing the same spectrum, for example in cubic quasi-topological gravity, would test its generality.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. This paper studies adiabatic radial oscillations of neutron stars in Starobinsky gravity and in a Gauss-Bonnet extension, working mainly in the Jordan-frame scalar-tensor representation with the SLy equation of state. It derives the modified TOV equations and the linear radial perturbation equations, solves them by a shooting method, and reports three main results: the exterior spacetime responds dynamically to fluid oscillations because Birkhoff's theorem fails; for large coupling α the fundamental-mode squared frequency becomes nearly independent of central density at low densities; and near the maximum-mass configuration the stability transition still approximates the GR behavior. The paper also verifies the α→0 GR limit and checks Jordan/Einstein frame consistency using a polytropic equation of state in Appendix A.

Significance. If the stability conclusions are correct, these are interesting results for higher-curvature gravity phenomenology: they identify a qualitative new feature (near-density-independence of the fundamental mode for large α) and a regime in which the standard dM/dρ0 stability criterion remains approximately valid. The paper is careful to state the GR limit and to provide a frame-consistency check, and the use of a realistic SLy equation of state increases the astrophysical relevance. However, the central claim depends on a mode-selection and stability criterion that is not established for the non-Sturm-Liouville problem considered here, and part of the Gauss-Bonnet analysis is deferred to unavailable supplemental material.

major comments (1)
  1. [Sec. II.B, II.C, II.D] The explicit equations for the Gauss-Bonnet extension are not available in the manuscript. The functions Fi in Eq. (24), the coefficients Aij in Eq. (34), the vacuum coefficients Ãij in Eq. (35), the boundary coefficients δλ2 and δf2 in Eqs. (38)-(39), and the Lagrangian pressure perturbation for β≠0 are all referred to the Supplemental Material, but no such material is included with the manuscript as reviewed. Since the β≠0 results in Figs. 1-5 and Tables I-II are a stated part of the paper's central claims, these expressions must either be included in the paper or the corresponding numerical results cannot be independently verified.
minor comments (4)
  1. [Table III and its caption] The caption states that entries marked with a dagger denote squared-frequency values, but the column header reads ω/(2π) [kHz]; the notation should be made uniform so that the reader can tell which entries are ω/(2π) and which are ω²/(2π)².
  2. [Sec. III, list of coupling sets] Set (5) is written as β = −10β, but Table I and the surrounding text indicate β = −10β⋆; the missing subscript should be restored.
  3. [Appendix A, after Eq. (A21)] The phrase 'the asymptotic asymptotic behavior' contains a duplicated word and should read 'the asymptotic behavior.'
  4. [General numerical analysis] The paper does not report numerical convergence tests or error estimates for the shooting method, although the claim that dM/dρ0 > 0 holds 'up to the second decimal place in mass' in Sec. III would benefit from such an estimate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported eigenfrequencies are obtained by solving the derived perturbation equations with an external equation of state; no fitted quantity is renamed as a prediction.

full rationale

The derivation chain is self-contained for the claimed result. The perturbation equations (32)–(35) are obtained by linearizing the field equations of the stated action, and the eigenvalue ω² is an output of a shooting method that imposes the boundary conditions (37)–(45), not an input fitted to any target frequency. The coupling constants α and β are scanned by hand, and the SLy and polytropic equations of state are external inputs (Refs. [52], [53], [50]). The reported α→0 reduction to GR and the Jordan/Einstein frame comparison in Appendix A are consistency checks rather than circular steps: they test the same physics through independent representations and against the GR benchmark of Table A.18 of Ref. [50]. The dependence on the authors' earlier equilibrium work [37] for background equations and expansion coefficients is a numerical input, but the stability calculation is a new boundary-value problem; Ref. [37] does not contain the fundamental-mode frequencies that are being predicted. The serious limitation noted in the pitch—that only exponentially decaying exterior modes are retained and no complex-frequency search is performed—is a completeness or correctness concern, not a circularity: the boundary condition (45) and mode selection are not defined in terms of the eventual stability conclusion. No step reduces, by the paper's own equations, to its own inputs. Therefore the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central calculation takes its physics from an external EOS and known scalar-tensor equivalence, and scans the two theory couplings by hand. No new particle, field, or force is introduced. The main unproved background assumptions are the boundary-condition choice at infinity and the restriction of stability analysis to the real-frequency fundamental mode.

free parameters (2)
  • alpha (Starobinsky coupling) = 10, 100, 1000 alpha_star
    Chosen by hand to represent increasing deviation from GR; the low-density plateau claim depends on large alpha. Not fitted to neutron star data.
  • beta (Gauss-Bonnet coupling) = 0, -10 beta_star, 50 beta_star
    Chosen by hand to explore the Gauss-Bonnet extension; used to show that the modification can restore stability. Not fitted to data.
assumptions (4)
  • standard math The scalar-tensor Lagrangian (3) is an exact rewritten form of (2), with Phi = 2 alpha R / (1 - 2 alpha beta L_GB).
    Used in Sec. II A to justify working in the Jordan frame; the inverse substitution is asserted via Eq. (9).
  • domain assumption Neutron star matter is a perfect fluid with a barotropic EOS p = P(rho); SLy and polytropic forms are adequate.
    Used throughout Sections II and III; no microphysics beyond the EOS is modeled.
  • domain assumption At infinity the background and perturbations have the Yukawa falloff (30) and vanish as in (45); matching at about ten stellar radii captures this behavior.
    Imposed as boundary conditions in Sections II B and II E; the numerical integration is only carried to a finite radius.
  • domain assumption Stability is decided by the sign of the fundamental-mode squared frequency; overtone modes that oscillate at infinity are not part of the spectrum.
    States the selection rule after Eq. (45); no completeness or complex-mode analysis is supplied.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Radial oscillations of neutron stars in Starobinsky gravity and its Gauss-Bonnet extension." pith.science (2026). https://pith.science/paper/GGWZWNOC

@misc{pith2026250718916,
  author       = {Pith},
  title        = {Pith review of: Radial oscillations of neutron stars in Starobinsky gravity and its Gauss-Bonnet extension},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GGWZWNOC}},
  note         = {Machine review of arXiv:2507.18916}
}
read the original abstract

Starobinsky gravity, as one of the simplest and best-behaved higher-curvature gravity theories, has been extensively studied in the context of neutron stars over the past few decades. In this work, we investigate the adiabatic radial oscillation stability of neutron stars within the framework of Starobinsky gravity. We find that gravitational modifications can significantly impact stellar stability. Specifically, the higher-derivative nature of the theory causes the exterior spacetime to dynamically respond to fluid oscillations, in contrast to general relativity where Birkhoff's theorem ensures a static exterior. For stellar models with low central densities, the fundamental frequency becomes nearly independent of the central density when the coupling constant is large. For stellar models with high central densities, the transition from stability to instability still approximately occurs near the maximum-mass configuration, similar to the case in general relativity. Our main analysis is conducted in the Jordan frame of the scalar-tensor gravity equivalent to Starobinsky gravity, and we explicitly verify consistency with results obtained in the Einstein frame. We further extend our study to a class of Gauss-Bonnet extensions of Starobinsky gravity.

Figures

Figures reproduced from arXiv: 2507.18916 by the authors.

Figure 1
Figure 1. FIG. 1: The [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The relationship between the scalar charge and the central density ( [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The relationship between frequency-squared for the fundamental oscillation mode and [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Numerical solutions for [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The relationship between frequency-squared for the fundamental oscillation mode and [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Black holes and neutron stars in massive Hellings-Nordtvedt theory

    gr-qc 2026-05 unverdicted novelty 7.0 of 10

    In massive Hellings-Nordtvedt theory, a nonzero vector vacuum asymptotically forbids both curvature-vector couplings at once, and the A²R sector yields Schwarzschild-like black holes plus neutron stars that can deviat...

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

    gr-qc 2026-05 unverdicted novelty 6.0 of 10

    Neutron stars in quasi-topological gravity can be more compact than black holes and radially stable across several equations of state.

Reference graph

Works this paper leans on

55 extracted references · 12 canonical work pages · cited by 2 Pith papers

  1. [1]

    Lanczos-Lovelock models of gravity,

    T. Padmanabhan and D. Kothawala, “Lanczos-Lovelock models of gravity,” Phys. Rept. 531, 115-171 (2013) [arXiv:1302.2151 [gr-qc]]

    arXiv 2013

  2. [2]

    Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom—a review,

    A. Belenchia, M. Letizia, S. Liberati and E. D. Casola, “Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom—a review,” Rept. Prog. Phys. 81, no.3, 036001 (2018) [arXiv:1612.07749 [gr-qc]]

    arXiv 2018

  3. [3]

    Modified theories of gravity: Why, how and what?,

    S. Shankaranarayanan and J. P. Johnson, “Modified theories of gravity: Why, how and what?,” Gen. Rel. Grav. 54, no.5, 44 (2022) [arXiv:2204.06533 [gr-qc]]

    arXiv 2022

  4. [4]

    f(R) Theories Of Gravity,

    T. P. Sotiriou and V. Faraoni, “f(R) Theories Of Gravity,” Rev. Mod. Phys. 82, 451-497 (2010) [arXiv:0805.1726 [gr-qc]]

    arXiv 2010

  5. [5]

    f(R) theories,

    A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Rel. 13, 3 (2010) [arXiv:1002.4928 [gr-qc]]

    arXiv 2010

  6. [6]

    Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution,

    S. Nojiri, S. D. Odintsov and V. K. Oikonomou, “Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution,” Phys. Rept. 692, 1-104 (2017) [arXiv:1705.11098 [gr-qc]]

    arXiv 2017

  7. [7]

    Renormalization of Higher Derivative Quantum Gravity,

    K. S. Stelle, “Renormalization of Higher Derivative Quantum Gravity,” Phys. Rev. D 16, 953-969 (1977)

    work page 1977

  8. [8]

    Classical Gravity with Higher Derivatives,

    K. S. Stelle, “Classical Gravity with Higher Derivatives,” Gen. Rel. Grav. 9, 353-371 (1978)

    work page 1978

Show all 55 references
  1. [9]

    Strings in Background Fields,

    C. G. Callan, Jr., E. J. Martinec, M. J. Perry and D. Friedan, “Strings in Background Fields,” Nucl. Phys. B 262, 593-609 (1985)

    1985

  2. [10]

    General relativity as an effective field theory: The leading quantum correc- tions,

    J. F. Donoghue, “General relativity as an effective field theory: The leading quantum correc- tions,” Phys. Rev. D 50, 3874-3888 (1994) [arXiv:gr-qc/9405057 [gr-qc]]

    1994 arXiv

  3. [11]

    A New Type of Isotropic Cosmological Models Without Singularity,

    A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. B 91, 99-102 (1980)

    1980

  4. [12]

    Neutron Stars in f(R) Gravity with Perturbative Con- straints,

    A. Cooney, S. DeDeo and D. Psaltis, “Neutron Stars in f(R) Gravity with Perturbative Con- straints,” Phys. Rev. D 82, 064033 (2010) [arXiv:0910.5480 [astro-ph.HE]]. 29

    2010 arXiv

  5. [13]

    Relativistic stars in f(R) and scalar-tensor theories,

    E. Babichev and D. Langlois, “Relativistic stars in f(R) and scalar-tensor theories,” Phys. Rev. D 81, 124051 (2010) [arXiv:0911.1297 [gr-qc]]

    2010 arXiv

  6. [14]

    Constraints on Perturbative f(R) Gravity via Neutron Stars,

    A. S. Arapoglu, C. Deliduman and K. Y. Eksi, “Constraints on Perturbative f(R) Gravity via Neutron Stars,” JCAP 07, 020 (2011) [arXiv:1003.3179 [gr-qc]]

    2011 arXiv

  7. [15]

    Structure of neutron stars in R-squared gravity,

    M. Orellana, F. Garcia, F. A. Teppa Pannia and G. E. Romero, “Structure of neutron stars in R-squared gravity,” Gen. Rel. Grav. 45, 771-783 (2013) [arXiv:1301.5189 [astro-ph.CO]]

    2013 arXiv

  8. [16]

    Neutron stars in the Starobinsky model,

    A. Ganguly, R. Gannouji, R. Goswami and S. Ray, “Neutron stars in the Starobinsky model,” Phys. Rev. D 89, no.6, 064019 (2014) [arXiv:1309.3279 [gr-qc]]

    2014 arXiv

  9. [17]

    Non-perturbative and self-consistent models of neutron stars in R-squared gravity,

    S. S. Yazadjiev, D. D. Doneva, K. D. Kokkotas and K. V. Staykov, “Non-perturbative and self-consistent models of neutron stars in R-squared gravity,” JCAP 06, 003 (2014) [arXiv:1402.4469 [gr-qc]]

    2014 arXiv

  10. [18]

    Slowly rotating neutron and strange stars in R2 gravity,

    K. V. Staykov, D. D. Doneva, S. S. Yazadjiev and K. D. Kokkotas, “Slowly rotating neutron and strange stars in R2 gravity,” JCAP 10, 006 (2014) [arXiv:1407.2180 [gr-qc]]

    2014 arXiv

  11. [19]

    Tidal Love numbers of neutron stars in f(R) gravity,

    S. S. Yazadjiev, D. D. Doneva and K. D. Kokkotas, “Tidal Love numbers of neutron stars in f(R) gravity,” Eur. Phys. J. C 78, no.10, 818 (2018) [arXiv:1803.09534 [gr-qc]]

    2018 arXiv

  12. [20]

    Orbital and epicyclic frequencies around neutron and strange stars in R2 gravity,

    K. V. Staykov, D. D. Doneva and S. S. Yazadjiev, “Orbital and epicyclic frequencies around neutron and strange stars in R2 gravity,” Eur. Phys. J. C 75, no.12, 607 (2015) [arXiv:1508.07790 [gr-qc]]

    2015 arXiv

  13. [21]

    The realistic models of rel- ativistic stars in f(R) = R +αR2 gravity,

    A. V. Astashenok, S. D. Odintsov and A. de la Cruz-Dombriz, “The realistic models of rel- ativistic stars in f(R) = R +αR2 gravity,” Class. Quant. Grav. 34, no.20, 205008 (2017) [arXiv:1704.08311 [gr-qc]]

    2017 arXiv

  14. [22]

    Neutron star masses in R2-gravity,

    F. Sbis` a, P. O. Baqui, T. Miranda, S. E. Jor´ as and O. F. Piattella, “Neutron star masses in R2-gravity,” Phys. Dark Univ. 27, 100411 (2020) [arXiv:1907.08714 [gr-qc]]

    2020 arXiv

  15. [23]

    Strongest constraint in f(R) = R +αR2 gravity: stellar stability,

    J. M. Z. Pretel, S. E. Jor´ as and R. R. R. Reis, “Strongest constraint in f(R) = R +αR2 gravity: stellar stability,” JCAP 11, 048 (2020) [arXiv:2008.00536 [gr-qc]]

    2020 arXiv

  16. [24]

    The I-Q relations for rapidly rotating neutron stars in f(R) gravity,

    D. D. Doneva, S. S. Yazadjiev and K. D. Kokkotas, “The I-Q relations for rapidly rotating neutron stars in f(R) gravity,” Phys. Rev. D 92, no.6, 064015 (2015) [arXiv:1507.00378 [gr- qc]]

    2015 arXiv

  17. [25]

    Gravitational wave asteroseismology of neutron and strange stars in R 2 gravity,

    K. V. Staykov, D. D. Doneva, S. S. Yazadjiev and K. D. Kokkotas, “Gravitational wave asteroseismology of neutron and strange stars in R 2 gravity,” Phys. Rev. D 92, no.4, 043009 (2015) [arXiv:1503.04711 [gr-qc]]. 30

    2015 arXiv

  18. [26]

    Mass-radius relation for neutron stars in f(R) = R +αR2 gravity: A comparison between purely metric and torsion formulations,

    P. Feola, X. J. Forteza, S. Capozziello, R. Cianci and S. Vignolo, “Mass-radius relation for neutron stars in f(R) = R +αR2 gravity: A comparison between purely metric and torsion formulations,” Phys. Rev. D 101, no.4, 044037 (2020) [arXiv:1909.08847 [astro-ph.HE]]

    2020 arXiv

  19. [27]

    Robust approach to f(R) gravity,

    L. G. Jaime, L. Patino and M. Salgado, “Robust approach to f(R) gravity,” Phys. Rev. D 83, 024039 (2011) [arXiv:1006.5747 [gr-qc]]

    2011 arXiv

  20. [28]

    Relativistic stars in f(R) gravity, and absence thereof,

    T. Kobayashi and K. i. Maeda, “Relativistic stars in f(R) gravity, and absence thereof,” Phys. Rev. D 78, 064019 (2008) [arXiv:0807.2503 [astro-ph]]

    2008 arXiv

  21. [29]

    The existence of relativistic stars in f(R) gravity,

    A. Upadhye and W. Hu, “The existence of relativistic stars in f(R) gravity,” Phys. Rev. D 80, 064002 (2009) [arXiv:0905.4055 [astro-ph.CO]]

    2009 arXiv

  22. [30]

    Relativistic stars in f(R) gravity,

    E. Babichev and D. Langlois, “Relativistic stars in f(R) gravity,” Phys. Rev. D 80, 121501 (2009) [erratum: Phys. Rev. D 81, 069901 (2010)] [arXiv:0904.1382 [gr-qc]]

    2009 arXiv

  23. [31]

    Mass-radius relation for neutron stars in f(R) gravity,

    S. Capozziello, M. De Laurentis, R. Farinelli and S. D. Odintsov, “Mass-radius relation for neutron stars in f(R) gravity,” Phys. Rev. D93, no.2, 023501 (2016) [arXiv:1509.04163 [gr-qc]]

    2016 arXiv

  24. [32]

    Further stable neutron star models from f(R) gravity,

    A. V. Astashenok, S. Capozziello and S. D. Odintsov, “Further stable neutron star models from f(R) gravity,” JCAP 12, 040 (2013) [arXiv:1309.1978 [gr-qc]]

    2013 arXiv

  25. [33]

    Revisiting compact star in F(R) gravity: Roles of chameleon potential and energy conditions,

    K. Numajiri, Y. X. Cui, T. Katsuragawa and S. Nojiri, “Revisiting compact star in F(R) gravity: Roles of chameleon potential and energy conditions,” Phys. Rev. D 107, no.10, 104019 (2023) [arXiv:2302.03951 [gr-qc]]

    2023 arXiv

  26. [34]

    On neutron stars in f(R) theories: Small radii, large masses and large energy emitted in a merger,

    M. Aparicio Resco, ´A. de la Cruz-Dombriz, F. J. Llanes Estrada and V. Zapatero Castrillo, “On neutron stars in f(R) theories: Small radii, large masses and large energy emitted in a merger,” Phys. Dark Univ. 13, 147-161 (2016) [arXiv:1602.03880 [gr-qc]]

    2016 arXiv

  27. [35]

    Consistency between dynamical and thermodynamical stabilities for perfect fluid in f(R) theories,

    X. Fang, X. He and J. Jing, “Consistency between dynamical and thermodynamical stabilities for perfect fluid in f(R) theories,” Eur. Phys. J. C 78, no.8, 623 (2018) [arXiv:1705.05977 [gr- qc]]

    2018 arXiv

  28. [36]

    The gravitational field of a star in quadratic gravity,

    A. Bonanno and S. Silveravalle, “The gravitational field of a star in quadratic gravity,” JCAP 08, 050 (2021) [arXiv:2106.00558 [gr-qc]]

    2021 arXiv

  29. [37]

    Neutron stars in Gauss-Bonnet extended Starobinsky gravity,

    Z. Liu, Z. Li, L. Liang, S. Li and H. Yu, “Neutron stars in Gauss-Bonnet extended Starobinsky gravity,” Phys. Rev. D 110, no.12, 124052 (2024) [arXiv:2410.14108 [gr-qc]]

    2024 arXiv

  30. [38]

    Testing general relativity with present and future astrophysical observations,

    E. Berti, E. Barausse, V. Cardoso, L. Gualtieri, P. Pani, U. Sperhake, L. C. Stein, N. Wex, K. Yagi and T. Baker, et al. “Testing general relativity with present and future astrophysical observations,” Class. Quant. Grav. 32, 243001 (2015) [arXiv:1501.07274 [gr-qc]]. 31

    2015 arXiv

  31. [39]

    Black holes, gravitational waves and fundamental physics: a roadmap,

    L. Barack, V. Cardoso, S. Nissanke, T. P. Sotiriou, A. Askar, C. Belczynski, G. Bertone, E. Bon, D. Blas and R. Brito, et al. “Black holes, gravitational waves and fundamental physics: a roadmap,” Class. Quant. Grav. 36, no.14, 143001 (2019) [arXiv:1806.05195 [gr-qc]]

    2019 arXiv

  32. [40]

    Stellar structure models in modified theories of gravity: Lessons and challenges,

    G. J. Olmo, D. Rubiera-Garcia and A. Wojnar, “Stellar structure models in modified theories of gravity: Lessons and challenges,” Phys. Rept. 876, 1-75 (2020) [arXiv:1912.05202 [gr-qc]]

    2020 arXiv

  33. [41]

    Quasinormal modes of stars and black holes,

    K. D. Kokkotas and B. G. Schmidt, “Quasinormal modes of stars and black holes,” Living Rev. Rel. 2, 2 (1999) [arXiv:gr-qc/9909058 [gr-qc]]

    1999 arXiv

  34. [42]

    Black hole scalarization in Gauss-Bonnet extended Starobinsky gravity,

    H. S. Liu, H. L¨ u, Z. Y. Tang and B. Wang, “Black hole scalarization in Gauss-Bonnet extended Starobinsky gravity,” Phys. Rev. D 103, no.8, 084043 (2021) [arXiv:2004.14395 [gr-qc]]

    2021 arXiv

  35. [43]

    Black Holes in Higher-Derivative Gravity,

    H. L¨ u, A. Perkins, C. N. Pope and K. S. Stelle, “Black Holes in Higher-Derivative Gravity,” Phys. Rev. Lett. 114, no.17, 171601 (2015) [arXiv:1502.01028 [hep-th]]

    2015 arXiv

  36. [44]

    New Taub-NUT black holes with massive spin-2 hair,

    Y. Q. Chen and H. S. Liu, “New Taub-NUT black holes with massive spin-2 hair,” Sci. China Phys. Mech. Astron. 68, no.2, 220411 (2025) [arXiv:2406.03692 [gr-qc]]

    2025 arXiv

  37. [45]

    Quasi-Topological Ricci Polynomial Gravities,

    Y. Z. Li, H. S. Liu and H. Lu, “Quasi-Topological Ricci Polynomial Gravities,” JHEP 02, 166 (2018) [arXiv:1708.07198 [hep-th]]

    2018 arXiv

  38. [46]

    Generalized quasitopological gravity,

    R. A. Hennigar, D. Kubizˇ n´ ak and R. B. Mann, “Generalized quasitopological gravity,” Phys. Rev. D 95, no.10, 104042 (2017) [arXiv:1703.01631 [hep-th]]

    2017 arXiv

  39. [47]

    Can a star be smaller than a black hole of the same mass?,

    S. Li, H. L¨ u, Y. Gao, R. Xu, L. Shao and H. Yu, “Can a star be smaller than a black hole of the same mass?,” [arXiv:2312.01406 [gr-qc]]

    arXiv

  40. [48]

    Gravitation,

    C. W. Misner, K. S. Thorne and J. A. Wheeler, “Gravitation,” W. H. Freeman, 1973, ISBN 978-0-7167-0344-0, 978-0-691-17779-3

    1973

  41. [49]

    Dynamical instability of gaseous masses approaching the Schwarzschild limit in general relativity,

    S. Chandrasekhar, “Dynamical instability of gaseous masses approaching the Schwarzschild limit in general relativity,” Phys. Rev. Lett. 12, 114-116 (1964)

    1964

  42. [50]

    Radial oscillations of relativistic stars,

    K. D. Kokkotas and J. Ruoff, “Radial oscillations of relativistic stars,” Astron. Astrophys. 366, 565 (2001) [arXiv:gr-qc/0011093 [gr-qc]]

    2001 arXiv

  43. [51]

    Black holes, white dwarfs, and neutron stars: The physics of compact objects,

    S. L. Shapiro and S. A. Teukolsky, “Black holes, white dwarfs, and neutron stars: The physics of compact objects,”

  44. [52]

    A unified equation of state of dense matter and neutron star structure,

    F. Douchin and P. Haensel, “A unified equation of state of dense matter and neutron star structure,” Astron. Astrophys. 380, 151 (2001) [arXiv:astro-ph/0111092 [astro-ph]]

    2001 arXiv

  45. [53]

    Analytical representations of unified equations of state of neutron-star matter,

    P. Haensel and A. Y. Potekhin, “Analytical representations of unified equations of state of neutron-star matter,” Astron. Astrophys. 428, 191-197 (2004) [arXiv:astro-ph/0408324 [astro- 32 ph]]

    2004 arXiv

  46. [54]

    Neutron stars 1: Equation of state and structure,

    P. Haensel, A. Y. Potekhin and D. G. Yakovlev, “Neutron stars 1: Equation of state and structure,” Astrophys. Space Sci. Libr. 326, pp.1-619 (2007) Springer, 2007,

    2007

  47. [55]

    General Relativity and its Applications,

    V. Ferrari, L. Gualtieri and P. Pani, “General Relativity and its Applications,” CRC Press, 2020, ISBN 978-0-429-49140-5, 978-0-367-62532-0 33 α[α⋆] β[β⋆] ρ0 [1015g/cm−3] M [M⊙] ω2[kHz2] 0 0 2 .70 2.047 20 .17 0 0 2 .80 2.048 7 .184 0 0 2 .90 2.048 −5.260 0 0 3 .00 2.047 −17.2...

    2020

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.