REVIEW 3 major objections 8 minor 58 references
On Modeling Anisotropic Quark Stars: The Role of Anisotropy in Radial Oscillation Spectra
T0 review · 3 major / 8 minor · reviewed 2026-08-15 · deepseek-v4-flash
Pith's one-line read The choice of anisotropy prescription shifts the predicted radial-mode frequencies of a strange quark star by 30 to 40 percent.
desk verdict A useful three-way comparison of anisotropy prescriptions for quark-star radial oscillations, but the surface boundary condition for models with nonzero Π(R) is taken from the isotropic limit without justification, and the fix may shift the headline 30–40% difference. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The machinery is the first-order system of linearized radial perturbation equations for anisotropic relativistic stars, Eqs. (36)-(37), in which the anisotropy factor $\Pi(r)=p_t-p_r$ enters alongside the radial pressure, density, and metric potentials. Each anisotropy prescription supplies a different $\Pi(r)$: the compactness-proportional ansatz $\Pi=\kappa(2m/r)p_r$ with $\kappa=-0.5$; the mass-function ansatz $m(r)=br^3/[2(1+ar^2)]$ combined with the color-flavor-locked quark-matter equation of state; and the vanishing-complexity condition $\Pi(r)=\frac{2}{r^3}\int_0^r x^{-3}\rho'(x)\,dx$. These enter both the hydrostatic equilibrium equations and the perturbation equations, so they change the pressure, density, and sound-speed profiles and hence the eigenfrequencies. The spectrum is obtained by integrating the ratio $\eta/\xi$ from center to surface and imposing the boundary conditions (34)-(35), with frequencies reported as $\nu_n = \frac{s_n}{2\pi}\sqrt{M/R^3}$.
What would settle it
Recompute the eigenfrequencies of models 2 and 3 using a surface boundary condition that explicitly includes the non-vanishing anisotropic factor at the surface; if the fundamental-mode frequency of model 3 changes by more than a few percent relative to the quoted 4.254 kHz, the claimed 30-40% gap between anisotropy prescriptions does not hold as stated.
Extended reading notes
Core claim
The central claim is that for the same compact object, the radial oscillation spectrum is not fixed by the equation of state and global mass and radius alone; the specific anisotropy prescription matters. Model 1 and model 2, despite being constructed very differently, produce nearly identical interior profiles of anisotropy and sound speed and therefore nearly identical spectra, with relative differences of 2.7% and 1.2% for the first two modes. Model 3, constructed from the vanishing-complexity condition rather than from an imposed equation of state, produces systematically higher frequencies: 4.254 kHz versus 3.046 kHz for the fundamental mode, with the gap staying near 32-40% across the ten modes. The paper further reports that the asymptotic large frequency separation rises from about 5.3 kHz in models 1 and 2 to about 7.1 kHz in model 3, and interprets these shifts as evidence that the choice of anisotropy prescription is a significant source of theoretical uncertainty in quark-star asteroseismology.
Load-bearing premise
The load-bearing premise is that the standard boundary condition used to fix the oscillation frequencies at the stellar surface stays valid even when the anisotropic pressure difference does not vanish at that surface.
Editorial extensions
If this is right
- For a fixed mass and radius, radial-mode frequencies and large frequency separations are not determined by the equation of state alone; the anisotropy prescription can change them by tens of percent.
- Models whose interior profiles of anisotropy and sound speed nearly coincide produce nearly identical spectra, so the spectrum is sensitive to the actual stress profile rather than to the formal construction of the model.
- If the vanishing-complexity model is the physically correct one, a given strange quark star would oscillate at substantially higher frequencies than the phenomenological models predict, changing mode identification and the inferred stability margin.
- The asymptotic large frequency separation is a compact diagnostic: about 5.3 kHz for the first two models versus about 7.1 kHz for the third, at this mass and radius.
Reading between the lines
- A matched test that forces the same equation of state onto all three anisotropy prescriptions would separate the anisotropy effect from the difference in effective equation of state, since model 3 is built without an imposed equation of state.
- If the 30-40% frequency gap survives a corrected surface boundary condition for models where $\Pi(R)\neq 0$, then a future measurement of one or two radial-mode frequencies of a known compact object could discriminate between anisotropy prescriptions at roughly 10% precision.
- The non-vanishing anisotropic factor at the surface in models 2 and 3 suggests the isotropic surface condition (35) may need an anisotropic generalization; the paper's quoted frequencies should be checked for stability under such a correction before the 30-40% gap is used as a physical prediction.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript computes the ten lowest radial oscillation frequencies of the compact object Cen X-3 (M = 1.5 M_sun, R = 9.1 km), modeled as an anisotropic strange quark star. Three anisotropy prescriptions are compared: (1) the Horvat ansatz Π = κ(2m/r)P with κ = −0.5 combined with a color-flavor-locked (CFL) quark matter EoS; (2) an analytic model based on the mass profile m(r) = br³/[2(1+ar²)] with the same CFL EoS, with a and b fixed by m(R) = M and P(R) = 0; and (3) Herrera's vanishing-complexity condition with the same mass profile and no EoS. The main result is that models 1 and 2 give nearly identical spectra (frequency differences of 0.7–2.7%) while model 3 gives frequencies 32–40% higher, which the paper interprets as showing that the anisotropy prescription is a leading systematic for quark-star asteroseismology. The equilibrium integration and the shooting solution of the Sturm–Liouville problem are standard, and Table 1 is internally consistent with the percentage differences quoted in Sec. 5.
Significance. If the quantitative claim were established, the paper would demonstrate that the choice of anisotropy prescription shifts the radial-mode spectrum of a quark star by tens of percent, a large effect relative to ordinary EoS variations, with direct implications for future gravitational-wave and X-ray asteroseismology of compact objects. The work has clear strengths: the numerical results are internally consistent (the differences quoted in Sec. 5 match Table 1 quantitatively), the anisotropic perturbation system (36)–(37) reduces correctly to the standard isotropic system (29)–(30) for Π = 0, the spectra are concrete and falsifiable predictions, and the paper is candid about its own limitations. The significance is, however, currently undercut by three load-bearing problems: the surface boundary condition used for models 2 and 3 is the isotropic one even though Π(R) ≠ 0 for those models; Eqs. (22), (25), and (26) do not form a consistent construction of model 3; and the headline deviation conflates the anisotropy prescription with other model differences. All three must be addressed before the 30–40% claim can be evaluated.
major comments (3)
- [Sec. 4, Eqs. (35)–(37); Sec. 5, Fig. 2] The surface boundary condition (35) is the isotropic condition (Ref. [48]) and is applied to all three models even though Sec. 5 and Fig. 2 state that only model 1 satisfies Π(R) = 0. When Π_s ≡ Π(R) ≠ 0, the terms in Eq. (37) that diverge as 1/P as P → 0 are not cancelled by Eq. (35). A direct regularity analysis of Eq. (37) near r = R, with P ≈ α(R−r), ρ → ρ_s, Π → Π_s, f = 1 − 2M/R, gives η/ξ|_R = −4 − ω²Rρ_s f^{−2}/α − M/(Rf) + 2Π_s/ρ_s − 8Π_s/(Rα) + 8πρ_sRΠ_s/(fα), where α = −P'(R) = ρ_sM/(R²f) − 2Π_s/R, and this reduces to Eq. (35) only when Π_s = 0. For model 3, with Π_s ≈ −0.65B0 and ρ_s ≈ (3–4)B0, the Π_s-dependent corrections are of order 0.1–1 relative to a base value near −5, and the ω²-dependent term is also modified through α. The eigenfrequencies of models 2 and 3 — and with them the quoted 39.7% and 34.1% differences — must therefore be recomputed with the appropriate anisotropic surface condition, which the manuscript neither derives nor cites.
- [Sec. 3.2(c), Eqs. (21)–(26)] The construction of model 3 is internally inconsistent as written. From the mass profile (21), the first TOV equation gives ρ(r) = m'(r)/(4πr²) = b(3+ar²)/(8π(1+ar²)²), so Eq. (22) as printed is missing the factor 1/(8π). In addition, substituting the density that follows from Eq. (21) into Eq. (25) — in either the printed form or the standard integral form with integrand x³ρ'(x) — yields an expression containing log(1+ar²) terms, not the purely algebraic expression −abr²/[8π(1+ar²)²] of Eq. (26). Since model 3 is the source of the headline 30–40% frequency deviation, the authors must correct Eqs. (22) and (25) (or provide the derivation of Eq. (26), including a citation if it is taken from Refs. [12] or [42]) and re-run the numerical analysis before the model-3 spectrum can be trusted.
- [Sec. 5, Fig. 4; Abstract and Sec. 6] The central claim attributes the 30–40% difference to the anisotropy prescription, but the comparison does not isolate anisotropy: model 3 has no EoS (its pressure is obtained from the TOV equation rather than from a matter model), a different sound-speed profile, and Π(R) ≠ 0, while model 2 shares the mass profile of model 3 but uses the CFL EoS. The acknowledgment in Sec. 5 that 'differences between oscillation spectra may arise due to anisotropies as well as model differences' is not carried into the abstract or Sec. 6, where the deviation is presented as the role of anisotropy. The authors should either restrict the claim accordingly or add a controlled comparison, for example the CFL EoS with continuously varied κ within the Horvat model, or the same mass profile with different anisotropy prescriptions.
minor comments (8)
- [Sec. 3.2(b), Eq. (22)] Computed from Eq. (21) via m'(r) = 4πr²ρ(r), the density is b(3+ar²)/(8π(1+ar²)²), so the printed denominator is missing a factor of 8π.
- [Sec. 3.2(c), Eq. (25)] As printed, the integrand ρ'(x)/x³ diverges as 1/x² at the origin for any regular density profile (ρ' ~ x), so the displayed integral cannot define Π near the center; presumably an integral of x³ρ'(x) with the appropriate prefactor was intended.
- [Sec. 4, Eq. (37)] The equation is barely legible in places (e.g., the term rendered as '−8π(P+ρ)re λP+ Π /P'); it should be typeset unambiguously, and the signs of the Π-dependent terms should be verified against Ref. [50], since only the isotropic limit can be checked directly from the text.
- [Sec. 5] The statement 'we have to solve graphically the algebraic equation (37)' is inaccurate: Eq. (37) is a differential equation, and what is solved graphically is the surface boundary condition, Eq. (35) or its anisotropic generalization.
- [Sec. 4] For model 3, the adiabatic index Γ is evaluated with c_s² = dP/dρ taken along the radial profile because no EoS exists; this treats the perturbed fluid as barotropic and should be stated explicitly as an assumption.
- [Secs. 2 and 5] For models 2 and 3 with Π(R) ≠ 0, the tangential pressure is discontinuous across the surface (p_t(R) = Π(R) inside vs. zero outside), so the Israel junction conditions require a surface layer; this is not acknowledged in the manuscript.
- [Fig. 3 and Sec. 5] Please clarify whether the plotted and quoted quantity is c_s² or c_s; the text says 'c²_s,r takes values in the range from 0 to unity' while the axis is labeled 'c_s,r²'.
- [Sec. 5] No numerical details are given (shooting tolerance, step size, number of iterations) and no code is provided; given the sensitivity of the surface treatment for Π(R) ≠ 0, sharing the code or tabulating the surface ratios used in the shooting would materially improve reproducibility.
Circularity Check
No significant circularity: the radial oscillation frequencies are genuine outputs of the equilibrium profiles, and no fitted parameter is renamed as a prediction.
full rationale
The paper's central output, the ten lowest radial-mode frequencies for three anisotropic models of Cen X-3, is not used to set any equilibrium or perturbation parameter. The input quantities are fixed independently: the CFL equation of state constants (B0 = 120 MeV/fm3, ms = 150 MeV, Δ = 150 MeV) are taken from the literature; the Horvat coupling κ = -0.5 is chosen by hand; the mass-function parameters a and b in model 2 are fixed by the matching conditions pr(R) = 0 and m(R) = M, i.e., by the observed mass and radius only; and model 3 is constructed from the prescribed mass profile plus Herrera's vanishing-complexity condition. The frequencies then follow from solving the Sturm-Liouville boundary-value problem (Eqs. 36-37 with boundary conditions 34-35), and the paper does not tune any quantity against the target frequencies. The anisotropic perturbation equations are quoted from the author's prior paper [50], but they are displayed explicitly and are standard linearized Einstein-fluid equations; the self-citation is attribution, not a load-bearing uniqueness argument. The paper even acknowledges that model differences may reflect model construction rather than anisotropy alone, which is a confound caveat, not circularity. The skeptical concern about using the isotropic surface boundary condition when Π(R)≠0 is a physical regularity and numerical-correctness issue, not a circularity: it does not make any output equal to an input by construction. No self-definitional reduction, fitted-input-called-prediction, or self-citation chain forces the claimed 30-40% difference.
Assumptions & free parameters
free parameters (6)
- B0 (bag constant) =
120 MeV fm^-3
- ms (strange quark mass) =
150 MeV
- Delta (CFL gap) =
150 MeV
- kappa (Horvat coupling) =
-0.5
- a (mass-profile parameter) =
8.67/(30 km)^2
- b (mass-profile parameter) =
9.51/(30 km)^2
assumptions (8)
- domain assumption Cen X-3 is a strange quark star with M=1.5 Msun and R=9.1 km
- domain assumption The CFL equation of state (Eq. 18) with B0, ms, Delta
- domain assumption The linear perturbation equations (36)-(37) for anisotropic stars
- domain assumption The surface boundary condition (35) is valid when Pi(R) is non-zero
- domain assumption The Horvat ansatz (20) with kappa = -0.5
- domain assumption Herrera's vanishing complexity condition (25)
- domain assumption The Harrison-Zel'dovich stability criterion dM/drho_c > 0
- standard math Einstein field equations and TOV equations for a spherically symmetric anisotropic fluid
Cite this review
Pith. "Pith review of On Modeling Anisotropic Quark Stars: The Role of Anisotropy in Radial Oscillation Spectra." pith.science (2026). https://pith.science/paper/ETA46CTU
@misc{pith2026260802761,
author = {Pith},
title = {Pith review of: On Modeling Anisotropic Quark Stars: The Role of Anisotropy in Radial Oscillation Spectra},
year = {2026},
howpublished = {\url{https://pith.science/paper/ETA46CTU}},
note = {Machine review of arXiv:2608.02761}
}
read the original abstract
We model the compact object Cen X-3, which is considered to be a good strange quark star candidate of known mass and radius, incorporating a negative anisotropic factor, and we compute the frequencies of the ten lowest radial oscillation modes. We introduce the anisotropy in three different manners and investigate its impact on the spectra.
Figures
Figures from the paper (2 more)
Reference graph
Works this paper leans on
-
[48]
Radial oscillations of zero-temperature white dwarfs and neutron stars below nuclear densities,
G. Chanmugan, “Radial oscillations of zero-temperature white dwarfs and neutron stars below nuclear densities,” ApJ217, 799 (1977)
work page 1977
-
[12]
Anisotropic stars made of exotic matter within the complexity factor formalism,
Á. Rincón, G. Panotopoulos and I. Lopes, “Anisotropic stars made of exotic matter within the complexity factor formalism,” Eur. Phys. J. C83, no.2, 116 (2023) [arXiv:2302.00125 [gr-qc]]. 15
arXiv 2023
-
[42]
A. Rincon, G. Panotopoulos and I. Lopes, “Anisotropic Quark Stars with an Interacting Quark Equation of State within the Complexity Factor Formalism,” Universe9, no.2, 72 (2023) [arXiv:2301.13684 [gr-qc]]
arXiv 2023
-
[1]
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,” John Wiley and Sons, New York 1983
work page 1983
-
[2]
The Physics of dense hadronic matter and compact stars,
A. Sedrakian, “The Physics of dense hadronic matter and compact stars,” Prog. Part. Nucl. Phys.58, 168-246 (2007) [arXiv:nucl-th/0601086 [nucl-th]]
arXiv 2007
-
[3]
J. M. Lattimer and M. Prakash, “The physics of neutron stars,” Science304, 536-542 (2004) [arXiv:astro- ph/0405262 [astro-ph]]
arXiv 2004
-
[4]
Masses, Radii, and the Equation of State of Neutron Stars,
F. Özel and P. Freire, “Masses, Radii, and the Equation of State of Neutron Stars,” Ann. Rev. Astron. Astrophys.54, 401-440 (2016) [arXiv:1603.02698 [astro-ph.HE]]
arXiv 2016
-
[5]
Strange quark matter and compact stars,
F. Weber, “Strange quark matter and compact stars,” Prog. Part. Nucl. Phys.54, 193-288 (2005) [arXiv:astro-ph/0407155 [astro-ph]]
arXiv 2005
Show all 58 references
-
[6]
Pulsars: structure and dynamics,
M. Ruderman, “Pulsars: structure and dynamics,” Ann. Rev. Astron. Astrophys.10, 427-476 (1972)
1972
-
[7]
Phase transitions in a superfluid neutron liquid,
A. I. Sokolov, “Phase transitions in a superfluid neutron liquid,” JETP79(1980) 1137
1980
-
[8]
Condensedπ− Phase in Neutron Star Matter,
R. F. Sawyer, “Condensedπ− Phase in Neutron Star Matter,” Phys. Rev. Lett.,29(1972) 823
1972
-
[9]
Kippenhahn and A
R. Kippenhahn and A. Weigert,Stellar structure and evolution, Springer, Berlin, 1990
1990
-
[10]
Asteroseismology of Compact Stars,
H. B. Li, Y. Gao, L. Shao and R. X. Xu, “Asteroseismology of Compact Stars,” Universe10, no.4, 157 (2024)
2024
-
[11]
New definition of complexity for self-gravitating fluid distributions: The spherically sym- metric, static case,
L. Herrera, “New definition of complexity for self-gravitating fluid distributions: The spherically sym- metric, static case,” Phys. Rev. D97, no.4, 044010 (2018) [arXiv:1801.08358 [gr-qc]]
2018 arXiv
-
[13]
Anisotropic dark energy stars within vanishing complexity factor formalism: Hydrostatic equilibrium, radial oscillations, and observational implications,
G. Panotopoulos, Á. Rincón and I. Lopes, “Anisotropic dark energy stars within vanishing complexity factor formalism: Hydrostatic equilibrium, radial oscillations, and observational implications,” Phys. Lett. B856, 138901 (2024) [arXiv:2407.17335 [gr-qc]]
2024 arXiv
-
[14]
The Field Equations of Gravitation,
A. Einstein, “The Field Equations of Gravitation,” Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. )1915(1915), 844-847
1915
-
[15]
On massive neutron cores,
J. R. Oppenheimer and G. M. Volkoff, “On massive neutron cores,” Phys. Rev.55(1939), 374-381
1939
-
[16]
Static solutions of Einstein’s field equations for spheres of fluid,
R. C. Tolman, “Static solutions of Einstein’s field equations for spheres of fluid,” Phys. Rev.55(1939), 364-373
1939
-
[17]
On the gravitational field of a mass point according to Einstein’s theory,
K. Schwarzschild, “On the gravitational field of a mass point according to Einstein’s theory,” Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. )1916, 189-196 (1916) [arXiv:physics/9905030 [physics]]
1916 arXiv
-
[18]
Constraining values of bag constant for strange star candidates,
A. Aziz, S. Ray, F. Rahaman, M. Khlopov and B. K. Guha, “Constraining values of bag constant for strange star candidates,” Int. J. Mod. Phys. D28, no.13, 1941006 (2019) [arXiv:1906.00063 [gr-qc]]
2019 arXiv
-
[19]
Refined Neutron-Star Mass Determinations for Six Eclipsing X-Ray Pulsar Binaries,
M. L. Rawls, J. A. Orosz, J. E. McClintock, M. A. P. Torres, C. D. Bailyn and M. M. Buxton, “Refined Neutron-Star Mass Determinations for Six Eclipsing X-Ray Pulsar Binaries,” Astrophys. J.730, 25 (2011) [arXiv:1101.2465 [astro-ph.SR]]
2011 arXiv
-
[20]
Strange star equation of state fits the refined mass measurement of 12 pulsars and predicts their radii,
T. Gangopadhyay, S. Ray, X. D. Li, J. Dey and M. Dey, “Strange star equation of state fits the refined mass measurement of 12 pulsars and predicts their radii,” Mon. Not. Roy. Astron. Soc.431, 3216-3221 (2013) [arXiv:1303.1956 [astro-ph.HE]]
2013 arXiv
-
[21]
Hydrostatic Equilibrium of Hypothetical Quark Stars,
N. Itoh, “Hydrostatic Equilibrium of Hypothetical Quark Stars,” Prog. Theor. Phys.44, 291 (1970)
1970
-
[22]
Collapsed nuclei,
A. R. Bodmer, “Collapsed nuclei,” Phys. Rev. D4, 1601-1606 (1971)
1971
-
[23]
Superhypernuclei in the Quark Shell Model,
H. Terazawa, “Superhypernuclei in the Quark Shell Model,” J. Phys. Soc. Jap.58, 3555-3563 (1989)
1989
-
[24]
Cosmic Separation of Phases,
E. Witten, “Cosmic Separation of Phases,” Phys. Rev. D30, 272-285 (1984)
1984
-
[25]
Enforced electrical neutrality of the color flavor locked phase,
K. Rajagopal and F. Wilczek, “Enforced electrical neutrality of the color flavor locked phase,” Phys. Rev. Lett.86, 3492-3495 (2001) [arXiv:hep-ph/0012039 [hep-ph]]
2001 arXiv
-
[26]
Color flavor locked strange matter,
G. Lugones and J. E. Horvath, “Color flavor locked strange matter,” Phys. Rev. D66, 074017 (2002) [arXiv:hep-ph/0211070 [hep-ph]]
2002 arXiv
-
[27]
A New Extended Model of Hadrons,
A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn and V. F. Weisskopf, “A New Extended Model of Hadrons,” Phys. Rev. D9, 3471-3495 (1974)
1974
-
[28]
Baryon Structure in the Bag Theory,
A. Chodos, R. L. Jaffe, K. Johnson and C. B. Thorn, “Baryon Structure in the Bag Theory,” Phys. Rev. D10, 2599 (1974)
1974
-
[29]
Strange Matter,
E. Farhi and R. L. Jaffe, “Strange Matter,” Phys. Rev. D30, 2379 (1984)
1984
-
[30]
Constraining color flavor locked strange stars in the gravitational wave era,
C. Vásquez Flores and G. Lugones, “Constraining color flavor locked strange stars in the gravitational wave era,” Phys. Rev. C95, no.2, 025808 (2017) [arXiv:1702.02081 [astro-ph.HE]]
2017 arXiv
-
[31]
From hadrons to quarks in neutron stars: a review,
G. Baym, T. Hatsuda, T. Kojo, P. D. Powell, Y. Song and T. Takatsuka, “From hadrons to quarks in neutron stars: a review,” Rept. Prog. Phys.81, no.5, 056902 (2018) [arXiv:1707.04966 [astro-ph.HE]]
2018 arXiv
-
[32]
Gapless color flavor locked quark matter,
M. Alford, C. Kouvaris and K. Rajagopal, “Gapless color flavor locked quark matter,” Phys. Rev. Lett. 92, 222001 (2004) [arXiv:hep-ph/0311286 [hep-ph]]
2004 arXiv
-
[33]
Complexity Factor For Static Anisotropic Self-Gravitating Source inf(R) Gravity,
G. Abbas and H. Nazar, “Complexity Factor For Static Anisotropic Self-Gravitating Source inf(R) Gravity,” Eur. Phys. J. C78, no.6, 510 (2018) [arXiv:1806.05042 [gr-qc]]
2018 arXiv
-
[34]
Complexity Factor for Charged Spherical System,
M. Sharif and I. I. Butt, “Complexity Factor for Charged Spherical System,” Eur. Phys. J. C78, no.8, 688 (2018) [arXiv:1808.00903 [gr-qc]]. 16
2018 arXiv
-
[35]
Complexity Factor For Anisotropic Source in Non-minimal Coupling Metric f(R)Gravity,
G. Abbas and H. Nazar, “Complexity Factor For Anisotropic Source in Non-minimal Coupling Metric f(R)Gravity,” Eur. Phys. J. C78, no.11, 957 (2018) [arXiv:1811.04858 [gr-qc]]
2018 arXiv
-
[36]
Complexity factor for dynamical spherically symmetric fluid distributions in f(R) gravity,
H. Nazar and G. Abbas, “Complexity factor for dynamical spherically symmetric fluid distributions in f(R) gravity,” Int. J. Geom. Meth. Mod. Phys.16, no.11, 1950170 (2019)
2019
-
[37]
Complexity factor for static sphere in self-interacting Brans–Dicke gravity,
M. Sharif and A. Majid, “Complexity factor for static sphere in self-interacting Brans–Dicke gravity,” Chin. J. Phys.61, 38-46 (2019) [arXiv:1910.06105 [gr-qc]]
2019 arXiv
-
[38]
Complexity factor for self-gravitating system in modified Gauss–Bonnet gravity,
M. Sharif, A. Majid and M. M. M. Nasir, “Complexity factor for self-gravitating system in modified Gauss–Bonnet gravity,” Int. J. Mod. Phys. A34, no.32, 1950210 (2019)
2019
-
[39]
Framework for generalized polytropes with complexity factor,
S. Khan, S. A. Mardan and M. A. Rehman, “Framework for generalized polytropes with complexity factor,” Eur. Phys. J. C79, no.12, 1037 (2019)
2019
-
[40]
Complexity factor for anisotropic self- gravitating sphere in Rastall gravity,
H. Nazar, A. H. Alkhaldi, G. Abbas and M. R. Shahzad, “Complexity factor for anisotropic self- gravitating sphere in Rastall gravity,” Int. J. Mod. Phys. A36, no.31n32, 2150233 (2021)
2021
-
[41]
Anisotropic star models in the context of vanishing complexity,
C. Arias, E. Contreras, E. Fuenmayor and A. Ramos, “Anisotropic star models in the context of vanishing complexity,” Annals Phys.436, 168671 (2022) [arXiv:2208.10594 [gr-qc]]
2022 arXiv
-
[43]
Radialpulsationsandstabilityofanisotropicstarswithquasi-local equation of state,
D.Horvat, S.IlijicandA.Marunovic, “Radialpulsationsandstabilityofanisotropicstarswithquasi-local equation of state,” Class. Quant. Grav.28, 025009 (2011) [arXiv:1010.0878 [gr-qc]]
2011 arXiv
-
[44]
A Class of relativistic stars with a linear equation of state,
R. Sharma and S. D. Maharaj, “A Class of relativistic stars with a linear equation of state,” Mon. Not. Roy. Astron. Soc.375, 1265-1268 (2007) [arXiv:gr-qc/0702046 [gr-qc]]
2007 arXiv
-
[45]
The Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity,
S. Chandrasekhar, “The Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity,” Astrophys. J.140(1964), 417-433 [erratum: Astrophys. J.140(1964), 1342]
1964
-
[46]
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(1964), 114-116
1964
-
[47]
Radial oscillations of relativistic stars,
K. D. Kokkotas and J. Ruoff, “Radial oscillations of relativistic stars,” Astron. Astrophys.366(2001), 565 [arXiv:gr-qc/0011093 [gr-qc]]
2001 arXiv
-
[49]
Radial oscillations of neutron stars and strange stars,
H. M. Väth and G. Chanmugan, “Radial oscillations of neutron stars and strange stars,” Astron. Astro- phys.260, 250-254 (1992)
1992
-
[50]
Tidal deformability and radial oscillations of anisotropic poly- tropic spheres,
J. D. V. Arbañil and G. Panotopoulos, “Tidal deformability and radial oscillations of anisotropic poly- tropic spheres,” Phys. Rev. D105, no.2, 024008 (2022) [arXiv:2112.09729 [gr-qc]]
2022 arXiv
-
[51]
Radial Oscillations of Dark Matter Stars Admixed with Dark Energy,
C. Sepúlveda and G. Panotopoulos, “Radial Oscillations of Dark Matter Stars Admixed with Dark Energy,” Universe10, no.1, 41 (2024)
2024
-
[52]
Asymptotic approximations for stellar nonradial pulsations,
M. Tassoul, “Asymptotic approximations for stellar nonradial pulsations,” ApJS, 43, 469 (1980)
1980
-
[53]
Asteroseismology of Solar-Type and Red-Giant Stars,
W. J. Chaplin and A. Miglio, “Asteroseismology of Solar-Type and Red-Giant Stars,” Ann. Rev. Astron. Astrophys.51, 353 (2013) [arXiv:1303.1957 [astro-ph.SR]]
2013 arXiv
-
[54]
The impact of composition choices on solar evolution: age, helio- and astero- seismology, and neutrinos,
D. Capelo and I. Lopes, “The impact of composition choices on solar evolution: age, helio- and astero- seismology, and neutrinos,” Mon. Not. Roy. Astron. Soc.498, no.2, 1992-2000 (2020) [arXiv:2010.01686 [astro-ph.SR]]
2020 arXiv
-
[55]
B. K. Harrison, K. S. Thorne, M. Wakano, and J. A. Wheeler,Gravitation Theory and Gravitational Collapse, 1965. 17
1965
-
[56]
Y. B. Zeldovich and I. D. Novikov,Relativistic astrophysics. Vol.1: Stars and relativity, 1971
1971
-
[57]
Quark models and radial oscillations: decoding the HESS J1731-347 compact object’s equation of state,
I. A. Rather, G. Panotopoulos and I. Lopes, “Quark models and radial oscillations: decoding the HESS J1731-347 compact object’s equation of state,” Eur. Phys. J. C83, no.11, 1065 (2023) [arXiv:2307.03703 [astro-ph.HE]]
2023 arXiv
-
[58]
Modeling compact objects with quark matter and dark energy: A comparative study of the radial oscillation modes of HESS J1731-347 and PSR J0740+6620,
C. Sepúlveda and G. Panotopoulos, “Modeling compact objects with quark matter and dark energy: A comparative study of the radial oscillation modes of HESS J1731-347 and PSR J0740+6620,” Chin. J. Phys.91, 773-783 (2024). 18
2024
Reviewed August 15, 2026 · model on record in the stance chip above.
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