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Influence of density-dependent bag function $B(n)$ on strange stars for non-zero strange quark mass ($m_s\neq0$) in $f(R,T)$ gravity consistent with observational validation

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

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Pith's one-line read A strange-star model with a density-dependent quark bag in $f(R,T)$ gravity reaches $2.03\,M_\odot$ and radius $11.49$ km, passing its stability and tidal checks.

desk verdict The density-dependent bag advertised in the title never enters the stellar-structure equations; the paper actually solves a constant-bag f(R,T) star, and the 'predicted' radii are fits to each object. read the letter →

arxiv 2505.08379 v2 pith:UGIIULDF submitted 2025-05-13 gr-qc

Rohit Roy , Debadri Bhattacharjee , Koushik Ballav Goswami , Pradip Kumar Chattopadhyay This is my paper · ORCID
classification gr-qc MSC 83D0585A15 PACS 04.50.Kd97.60.Jd
keywords strangequarkstarsMITbagmodelbaryonnumberdensitydependentconstantf(RT)gravitymassTolman-Oppenheimer-Volkoffequationenergypertidaldeformability
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

This paper claims that strange quark stars can be modeled in $f(R,T)=R+2\zeta T$ gravity by joining the MIT bag equation of state $p=(\rho-4B_1)/3$ to a baryon-number-density-dependent bag function $B(n)$ and a non-zero strange quark mass $m_s$. With a modified quadratic density profile and numerical solution of the relativistic hydrostatic equilibrium equations, the model reaches a maximum mass of $2.03\,M_\odot$ and a radius of $11.49$ km for $m_s=0$ MeV, $n=0.36\,\mathrm{fm}^{-3}$, and $\zeta=-0.1$. The aim is to let the bag constant respond to the medium while keeping the analytic solution tractable, and to show that such stars satisfy causality, energy conditions, dynamical stability, and the tidal-deformability bound from GW170817. Finite $m_s$ narrows the stable baryon-density window because the energy per baryon must stay below $930.4$ MeV, the value for $^{56}\mathrm{Fe}$.

What carries the argument

The load-bearing object is the linear bag relation $p=(\rho-4B_1)/3$, where $B_1=(4B_g+\rho_s-3p_s)/4$ packages the bag constant together with the pressure and energy density of the strange quark. The density dependence enters through Eq. (11), a two-parameter exponential $B(n)=B_0e^{-(a_1x^2+a_2x)}$ with $x=n/n_0$, which fixes $B_1$ once a baryon number density is chosen. The third component is a modified quadratic density profile for $\rho(r)$ that reduces to the standard compact-star profile when $\zeta=0$; this choice is what keeps the field equations solvable in closed form. Together these pieces convert a microphysical bag parameter into explicit metric potentials, a mass formula, and mass-radius sequences without numerical integration of the stress-energy profile.

What would settle it

Evaluate the same model with a radial baryon-density profile: derive $n(r)$ from the local chemical potentials, set $B(n(r))$ at each shell, integrate the TOV equations without assuming constant $B_1$, and compare the mass-radius curves and maximum mass with the paper's fixed-$n$ results; any significant shift would show that the reported $2.03\,M_\odot$ maximum depends on the constant-$B_1$ ansatz rather than on the density-dependent bag itself.

Watch

Extended reading notes

Core claim

Within $f(R,T)=R+2\zeta T$, the paper solves the isotropic stellar structure problem for deconfined $u,d,s$ quarks plus electrons, using the linear bag EoS $p=(\rho-4B_1)/3$ with $B_1=(4B_g+\rho_s-3p_s)/4$ and the density profile $\rho(r)=\rho_c[1-(1-\rho_0/\rho_c)(r^2/R^2)]+\zeta\rho_c(1-r^2/R^2)$. The bag constant follows the exponential parametrization $B(n)=B_0e^{-(a_1x^2+a_2x)}$, with $x=n/n_0$ and $n_0=0.17$ fm$^{-3}$, chosen so that the energy per baryon $E_B$ lies in the absolutely stable window below $930.4$ MeV. Numerical TOV integration gives $M_{\max}=2.03\,M_\odot$ and $R=11.49$ km for $m_s=0$, $n=0.36$ fm$^{-3}$, $\zeta=-0.1$, with $1.98\,M_\odot$ and $11.20$ km for $m_s=100$ MeV; increasing $\zeta$ lowers both quantities. The paper reports that the resulting stars obey all energy conditions, have sound speed $v^2=1/3$, adiabatic index above $4/3$, positive radial eigenfrequencies, and tidal deformabilities below the GW170817 constraint.

Load-bearing premise

The paper's solutions treat $B_1$ as constant throughout each stellar model even though $B(n)$ is a density-dependent bag; if the local baryon density were used to evaluate $B(n)$ at every radius, Eq. (10) would no longer be the simple linear EoS and the closed-form solutions and TOV results would change.

Editorial extensions

If this is right

  • Strange stars in $f(R,T)=R+2\zeta T$ with this EoS can reach $2.03\,M_\odot$, crossing the two-solar-mass threshold that rules out many softer quark-matter equations of state.
  • Larger $\zeta$ lowers both maximum mass and radius, while the negative-coupling branch supports the heaviest stars, so a confirmed $\sim2\,M_\odot$ strange star would favour $\zeta<0$ in this theory.
  • Within the stable window, higher baryon density $n$ gives heavier and larger stars, while higher $m_s$ gives smaller, lighter stars and a narrower stable window.
  • The constant sound speed $v^2=1/3$ automatically satisfies causality and the Zeldovich condition for every admissible parameter choice.
  • The predicted tidal deformabilities stay below the GW170817 bound, so the model is not ruled out by the first binary-neutron-star merger constraint.

Reading between the lines

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

  • The density dependence is implemented between configurations: each star gets one fixed $n$ and hence one fixed $B_1$. A fully self-consistent model with $B$ evaluated on the local density profile is the natural testable extension and could change the reported maximum mass.
  • The paper's own stability windows imply that low-density solutions classed as metastable or unstable would look like hybrid or purely hadronic stars; under this model, objects whose radii are reproduced only at low $n$ are not clean strange-star candidates.
  • If the model is right, simultaneous mass and radius measurements for several sources could constrain $m_s$ and $\zeta$ together, potentially turning the strange quark mass into an astrophysical observable.
  • The same $B(n)$ machinery could be extended to anisotropic or rotating configurations, where the constant-$B_1$ simplification is less tenable and where the mass-radius predictions would be directly comparable to precision radius measurements.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. This manuscript constructs analytical models of static, spherically symmetric strange stars in f(R,T)=R+2ζT gravity, using a modified Mak-Harko density profile and the MIT bag equation of state p=(ρ-4B1)/3 with a finite strange quark mass ms. A baryon-density-dependent bag function B(n) is introduced in Sec. 3 following Prasad and Bhalerao, and the energy-per-baryon stability window is used to select values of n. Exact metric potentials are derived, the TOV equations are claimed to be integrated numerically, and maximum masses, radii, energy conditions, stability criteria, and tidal deformabilities are computed and compared with candidate compact objects. The headline result is M_max≈2.03 M_sun at R≈11.49 km for ms=0, n=0.36 fm^-3, and ζ=-0.1.

Significance. If the density-dependent bag function were actually fed into the stellar-structure equations, the paper could be a useful contribution to strange-star modeling in modified gravity, since the medium dependence of the bag constant is a genuine open issue and f(R,T) extensions are widely explored. The manuscript also supplies explicit algebraic metric potentials and a broad parameter scan. However, the main advertised novelty, the influence of B(n) on the stellar structure, is not implemented in the calculation: the solved model is the constant-B bag model with B1 set at a chosen reference density. In addition, the TOV system is not written out, the 'predicted radii' in Table 3 are parameter fits rather than blind predictions, and the tidal and oscillation analyses rely on imported equations whose validity in this setting is not demonstrated. The paper is therefore not currently a reliable basis for the physical conclusions it draws.

major comments (4)
  1. [Secs. 3, 5, 7.1] The density-dependent bag function is not used in the stellar-structure calculation. Equation (11) defines B(n), but the equation of state actually used in the field equations is Eq. (10), p=(ρ-4B1)/3, with B1 treated as a constant; Sec. 7.1 then obtains v^2=dp/dρ=1/3. The quantity n in Tables 1 and 2 enters only as a label that selects the constant value B1=B(n) via Eq. (11). If B were evaluated at the local baryon density n(r), the pressure would be p(r)=(ρ(r)-4B1(n(r)))/3, the sound speed would contain a dB1/dρ term, and the closed-form solutions (22)-(27), the mass formula (29), and the M-R curves in Figs. 3-6 would no longer follow. The paper nowhere states or justifies the constant-B1 approximation, so the central claim that B(n) influences the stellar structure is not realized in the calculation.
  2. [Table 3 and Sec. 5.2] The claimed observational validation is based on fitting rather than prediction. For each object in Table 3, the authors choose ζ and n separately (see the columns 'ζ' and 'n') to reproduce the observed radius, and the resulting model radii track the observed values. This is not a prediction of the model: the parameters are not fixed a priori, no common selection rule is given, and there is no discussion of uncertainties or of how many degrees of freedom are being tuned. Moreover, the ζ values used in Table 3 include 0.42 and -0.3, which lie outside the set ζ=-0.1, -0.2, 0.2 that the text in Sec. 5.2 states is used, and no justification is provided for those outliers. The statement that the model has been 'validated observationally' is therefore overstated.
  3. [Sec. 6] The TOV calculation is not reproducible from the text. The paper provides an analytic solution (22)-(27) based on the density ansatz (21) and the constant-B equation of state, but it does not write the modified TOV equations, the boundary conditions, or the relation between the numerically integrated M-R curves in Figs. 3-6 and the surface mass formula (29). The sentence that 'the TOV equations, as presented in references [52, 131], have been solved numerically' is insufficient, because in f(R,T)=R+2ζT the energy-momentum tensor is not conserved and the hydrostatic equilibrium equation takes the modified form (34). Without the explicit ODE system and the definition of the central density used in the integrations, the entries in Table 2 cannot be checked.
  4. [Sec. 8.3 and 8.4] The stability and tidal results are based on imported equations whose applicability is not established. The radial perturbation equations (36)-(37) are taken from Pretel et al. [147], and the tidal equation (41)-(43) and Love-number formula (44) are taken from earlier f(R,T) studies, but the present paper does not derive these equations, specify the junction conditions for the f(R,T) exterior, or justify using the standard GR boundary term y=RH'(R)/H(R) when the trace T is discontinuous at the stellar surface. The positive eigenfrequencies in Fig. 24 and the numerical values of k2 and Λ in Table 4 therefore rest on an unverified theoretical basis.
minor comments (4)
  1. [Sec. 5.2] The derivation of the coupling bounds (30) and (31) is not shown; the steps from the assumptions ρc>0 and ρc>ρ0 to the two inequalities are omitted, and the text later uses ζ values outside the range it claims to adopt.
  2. [Abstract and Table 1] The abstract and title emphasize non-zero strange quark mass (ms≠0), but Table 1 and Fig. 1 include the case ms=0, which is also used for the headline maximum mass. The wording should be adjusted to say that both zero and non-zero ms are considered.
  3. [Notation throughout] The notation and typography need cleanup: expressions such as 'n¡ 0.103' should read n<0.103, the object name '4U 1820−30' is typeset inconsistently, and the chemical-potential equations (4)-(7) should be checked for consistent subscript conventions for mu, md, ms, and me.
  4. [Fig. 24 caption] The caption of Fig. 24 lists ζ=-0.1, 0.0, and -0.1; the third value should presumably be 0.1, and the line styles should be described consistently with the legend in the figure.

Circularity Check

1 steps flagged · score 6.0 of 10

Table 3 radius 'predictions' are per-object fits of ζ and n; the density-dependent bag B(n) is not implemented locally in the TOV solutions.

  1. fitted input called prediction [Sec. 7, Table 3 (and Fig. 17)]
    "the radii of several compact objects are predicted within the allowed parameter space of the model and the results are tabulated in Table 3. ... V ELA X− 1 1.77[135] 9.56 ±0.08 0.18 0.25 9.87 0.15 0.30 10.33; 4U 1820− 30 1.58[143] 9.11 ±0.4 0.14 0.15 9.14 0.42 0.30 10.39"

    Each object in Table 3 is assigned its own free pair (ζ, n), with n fixing the constant bag value through Eq. (11). For example, VELA X−1 uses ζ=0.18, n=0.25; 4U 1820−30 uses ζ=0.14, n=0.15; SMC X−4 uses ζ=0.08, n=0.15. The model's M−R curves are then read at the observed mass to produce R. Because ζ and n are not fixed a priori but are chosen separately for each object, the calculation is equivalent to selecting free parameters so that the M−R curve passes through the observed mass-radius point. The observed radius is thus an input to the parameter choice, not an independent output, so the 'predicted radius' is a fit by construction rather than a genuine prediction.

full rationale

The core TOV construction in Secs. 4–6 is self-contained: given the Ansatz density profile (21), the EoS (10), and a chosen constant B1, the metric potentials (22)–(23), the mass formula (29), and the M−R curves follow algebraically/numerically with no hidden circularity, and the maximum-mass values in Table 2 are genuine outputs for stated parameters. The circular part is the observational validation in Table 3. There the radii are called 'predicted' while each object gets its own (ζ, n) pair, so the model is tuned to reproduce the observed radius; varying these free parameters moves the M−R curve through the observed mass-radius point. This is aggravated by the fact that the advertised density-dependent bag is not actually evaluated inside the star: the stellar-structure equations use Eq. (10) with constant B1, as confirmed by the sound speed v^2 = 1/3 in Sec. 7.1, so n enters only as a label selecting a constant bag value. The self-citations to [121] for the junction condition and tidal equations are auxiliary formalism and are not the source of the fitted radius claim; they are not counted as load-bearing circularity here. The score of 6 reflects that one or more 'predictions' reduce to fitted inputs, while the maximum-mass and stability calculations retain independent content.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The model relies on two free parameters per fitted object (ζ and n), plus a scanned strange quark mass and central density. The bag parametrization constants are inherited from a prior fit. No new entities are introduced. The key axioms are the modified gravity action, the MIT bag EoS, the ad hoc density profile, and the strange matter stability criterion.

free parameters (5)
  • ζ (coupling constant) = 0.04 to 0.42 in Table 3; -0.3 to 0.2 in Table 2
    Chosen per compact object in Table 3 to reproduce observed masses and radii; no independent constraint is used to fix it.
  • n (baryon number density) = 0.15 to 0.36 fm^-3
    Selected per object in the stability windows of Table 1; determines the bag constant B1 via Eq. (11).
  • m_s (strange quark mass) = 0, 50, 100, 120, 200 MeV
    Scanned to study stability windows; physical range is 80-110 MeV but values outside are used, so it acts as a free parameter.
  • ρ_c (central energy density) = 1.91 to 2.71 x 10^15 g/cm^3 (Table 2)
    Varied in TOV integration to generate mass-radius curves and locate the maximum mass.
  • Bag parametrization constants B0, a1, a2 = B0=114 MeV/fm^3, a1=0.0125657, a2=0.29522
    Inherited from Prasad and Bhalerao's fit to Liu et al.; the model's EoS and stability windows depend on these fitted values.
assumptions (7)
  • domain assumption f(R,T)=R+2ζT is the correct gravitational theory.
    The entire model is built in this modified gravity framework; no derivation of the theory from first principles is provided.
  • domain assumption The MIT bag model EoS p=(ρ-4B1)/3 describes strange quark matter.
    Used in Eq. (10) to close the system; inherited from the bag model literature.
  • domain assumption The matter Lagrangian is Lm = p (or equivalently -ρ).
    Invoked in Sec. 4 following Harko et al.; different choices can alter field equations.
  • ad hoc to paper The modified Mak-Harko density profile Eq. (21) is a valid interior density distribution.
    The profile is an ansatz, not derived from microphysics; if it does not represent real strange star interiors, the solution loses physical relevance.
  • domain assumption Strange quark matter is stable if E_B ≤ 930.4 MeV relative to 56Fe.
    Standard strange matter hypothesis used to restrict n; cited to Witten and Madsen.
  • domain assumption The bag constant range 57.55-95.11 MeV/fm^3 is the allowed physical range.
    Used to set the upper limit of n in Table 1; taken from literature without re-derivation.
  • domain assumption Darmois junction conditions apply in f(R,T) gravity.
    Used for boundary matching to Schwarzschild exterior; justified by citation to Goswami et al. [121].

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Cite this review

Pith. "Pith review of Influence of density-dependent bag function $B(n)$ on strange stars for non-zero strange quark mass ($m_s\neq0$) in $f(R,T)$ gravity consistent with observational validation." pith.science (2026). https://pith.science/paper/UGIIULDF

@misc{pith2026250508379,
  author       = {Pith},
  title        = {Pith review of: Influence of density-dependent bag function $B(n)$ on strange stars for non-zero strange quark mass ($m_s\neq0$) in $f(R,T)$ gravity consistent with observational validation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UGIIULDF}},
  note         = {Machine review of arXiv:2505.08379}
}
abstract

In this work, a new class of solution of the Einstein field equation for an isotropic strange star using the modified Mak-Harko type density profile along with the equation of state as proposed in the MIT bag model and considering finite mass of the strange quark ($m_s$) is presented in the framework of $f(R,T)$ gravity with $f(R,T)=R+2\zeta T$, where, $\zeta$ is the coupling parameter. To incorporate the quark matter hypothesis with a physically viable stellar framework, a baryon number density ($n$) dependent bag function $B(n)$ is analysed, using exponential type parametrisation. The energy per baryon ($E_B$) has been investigated to restrict $B(n)$ and corresponding $n$ within a stable window, specifically satisfying the condition $E_B\leq 930.4~MeV$, which corresponds to the binding energy of $\isotope[56]{Fe}$. We note a lower limit of $n$ below which $E_B>930.4~MeV$ as $E_B$ increases with the decrease of $n$. This value, however, depends on $m_s$. Additionally, $n$ has a maximum value of $0.36~fm^{-3}$ irrespective of $m_s$ depending on the range of bag function. All the essential characteristics are satisfactorily fulfilled within the stellar interior for the selected set of parameter space. In this model, the maximum mass and radius are found by solving the TOV equations numerically which yields $M=2.03~M_{\odot}$ with a radius of $11.49~km$ for $m_s=0~MeV$ and $n=0.36~fm^{-3}$ and $\zeta=-0.1$. It is also noted that the maximum mass and the corresponding radius are the function of $m_s$, $\zeta$ and $n$. The proposed model has been shown to comply with the required energy conditions and satisfies the criterion for dynamical stability, thereby confirming its physical plausibility as a physically consistent stellar model within the parameter space used.

Figures

Figures reproduced from arXiv: 2505.08379 by the authors.

Figure 1
Figure 1. Variation of EB with n for different parametric choices of ms . The red and green lines represent the variations for ms = 0 and 120 MeV, respectively. where, x = n n0 is the normalized baryon number density, n0 is known as the baryon number density related to the ordinary nuclear matter (n0 = 0.17 f m−3 ), a1 = 0.0125657, a2 = 0.29522 and B0 = 114 MeV/ f m3 . In this model, the value of Bg is obtained form Eq. (11) … view at source ↗
Figure 2
Figure 2. Variation of different chemical potentials with baryon number density. The red and green lines indicate the variation corresponding to [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Mass-radius relation for a parametric choice of [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (12 more)
Figure 5
Figure 5. Figure 5: Variation of mass (M) with central density (ρc) for a parametric choice of ζ = −0.1. Here the solid black, blue and red lines represent the M −ρc variation for n = 0.15 f m−3 , 0.25 f m−3 and 0.35 f m−3 , respectively with ms = 0 MeV. The dashed black, blue and red lin…
Figure 7
Figure 7. Figure 7: Variation of maximum mass (Mmax) with coupling pa￾rameter ζ for a parametric choice of n = 0.3 f m−3 . The solid and dashed lines represent the variation for ms = 0 MeV and ms = 100 MeV, respectively. -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 10.4 10.5 10.6 10.7 10.8 10.9 Ζ RmaxH…
Figure 9
Figure 9. Figure 9: Plot showing the variation of maximum mass ( [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 12
Figure 12. Figure 12: Radial variation of metric potentials inside 4 [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 14
Figure 14. Figure 14: Variation of pressure (p) with r inside 4U 1820 − 30. The solid and dashed lines represent (i) ms = 0 MeV, n = 0.3 f m−3 and (ii) ms = 100 MeV, n = 0.3 f m−3 , respectively. The blue, red and green lines represent ζ = −0.1, 0.0 and 0.10, respectively. content, can be …
Figure 15
Figure 15. Figure 15: Radial variation of energy density (ρ) inside 4U 1820− 30 for different n taking ζ = −0.1. The solid and dashed lines rep￾resent ms = 0 MeV and ms = 100 MeV respectively. The blue, red and green lines represent n = 0.3, 0.33 and 0.36 f m−3 respec￾tively. 0 2 4 6 8 10 …
Figure 17
Figure 17. Figure 17: Variation of predicted radius of 4U 1820−30 with baryon number density (n) for a parametric choice of coupling ζ = −0.1. The solid and dashed line represent the variation for ms = 0 MeV and ms = 100 MeV, respectively. Substituting Eq. (33) into (32), the final form of…
Figure 18
Figure 18. Figure 18: Variation of different energy conditions inside [PITH_FULL_IMAGE:figures/full_fig_p017_18.png]
Figure 20
Figure 20. Figure 20: Variation of different forces inside 4U 1820−30 with r for n = 0.3 f m−3 and ms = 0 MeV. The black, blue and red lines represent the gravity force (Fg), hydrostatic force (Fh) and force due to modified gravity (Fζ ), respectively. Here the solid, dashed and dotdashed …
Figure 23
Figure 23. Figure 23: Radial variation of the adiabatic index ( [PITH_FULL_IMAGE:figures/full_fig_p019_23.png]
Figure 24
Figure 24. Figure 24: Variation of absolute value of pressure ( [PITH_FULL_IMAGE:figures/full_fig_p019_24.png]
Figure 26
Figure 26. Figure 26: Variation of tidal deformability (Λ) with n for the com￾pact object 4U 1820 − 30 for parametric choices of ζ . The solid and dashed lines represent the variation for ζ = −0.2 and 0.0, respectively. The black and red lines represent the variation for ms = 0 MeV and 100…

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Works this paper leans on

154 extracted references · 65 canonical work pages

  1. [147]

    J. M. Z. Pretel, E. S. Jor ´as, R. R. R. Reis, D. V . J. Arba ˜nil, JCAP 04 (2021) 064; doi:10.1088/1475-7516/2021/04/064

    doi:10.1088/1475-7516/2021/04/064 2021

  2. [1]

    I. H. Stairs, Living Rev. Rel. 6 (2003) 5

    2003

  3. [2]

    B. P. Abbott et al. (Virgo, LIGO Scientific), Phys. Rev. Lett. 116 (2016) 061102

    2016

  4. [3]

    B. P. Abbott et al. (Virgo, LIGO Scientific), Annalen der Physik 529 (2017) 1600209

    2017

  5. [4]

    Weyl, Eine neue Erweiterung der Relativit ¨atstheorie

    H. Weyl, Eine neue Erweiterung der Relativit ¨atstheorie. Ann. der Phys. 364 (1919) 101

    1919

  6. [5]

    A. G. Riess et al., Astron. J. 116 (1998) 1009. [astro-ph/9805201v1]

    arXiv 1998

  7. [6]

    Perlmutter et al., Astrophys. J. 517 (1999) 565. [astro-ph/9812133]

    arXiv 1999

  8. [7]

    Bernardis et al., Nature (London) 404 (2000) 955

    2000

Show all 154 references
  1. [8]

    Hanany et al., Astrophys. J. 545 (2000) L5. [astro-ph/0005123]

    2000 arXiv

  2. [9]

    P. J. E. Peebles and B. Ratra, Rev. Mod. Phys. 75 (2003) 559. [astro-ph/0207347]

    2003 arXiv

  3. [10]

    Padmanabhan, Phys

    T. Padmanabhan, Phys. Rep. 380 (2003) 235. [hep-th/0212290]

    2003 arXiv

  4. [11]

    Perivolaropoulos, F

    L. Perivolaropoulos, F. Skara, New Astron. Rev. 95 (2022) 101659

    2022

  5. [12]

    Bullock, M.B

    J.S. Bullock, M.B. Kolchin, Annu. Rev. Astron. Astrophys. 55 (2017) 343

    2017

  6. [13]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov, Phys. Rev. D 68 (2003) 123512

    2003

  7. [14]

    Carroll, V

    S.M. Carroll, V . Duvvuri, M. Trodden, M.S. Turner, Phys. Rev. D70 (2004) 042528

    2004

  8. [15]

    Starobinsky, J

    A.A. Starobinsky, J. Exp. Theor. Phys. Lett. 86 (2007) 157

    2007

  9. [16]

    Bamba, S

    K. Bamba, S. Nojiri, S.D. Odintsov, J. Cosmol. Astropart. Phys. 0810 (2008) 045

    2008

  10. [17]

    Setare, M

    M.R. Setare, M. Jamil, Gen. Relativity Gravitation 43 (2011) 293

    2011

  11. [18]

    Jamil, F.M

    M. Jamil, F.M. Mahomed, D. Momeni, Phys. Lett. B 702 (2011) 315

    2011

  12. [19]

    Hussain, M

    I. Hussain, M. Jamil, F.M. Mahomed, Astrophys. Space Sci. 337 (2012) 373. 22

    2012

  13. [20]

    Shomer, arXiv:0709.3555v2 [hep-th]

    A. Shomer, arXiv:0709.3555v2 [hep-th]

    arXiv

  14. [21]

    Doboszewski, N

    J. Doboszewski, N. Linnemann, Found. Phys. 48 (2018) 237

    2018

  15. [22]

    Bajardi, F

    F. Bajardi, F. Bascone, S. Capozziello, Universe 2021 (2021) 148

    2021

  16. [23]

    Singh, L.N

    T. Singh, L.N. Rai, Gen. Relativity Gravitation 15 (1983) 875

    1983

  17. [24]

    Bahamonde, et al., Rep

    S. Bahamonde, et al., Rep. Progr. Phys. 86 (2023) 026901

    2023

  18. [25]

    Nordstr ¨om, Phys

    G. Nordstr ¨om, Phys. Z. 13 (1912) 1126

    1912

  19. [26]

    Nordstr ¨om, Ann

    G. Nordstr ¨om, Ann. Phys. 42 (1913) 533

    1913

  20. [27]

    Page, B.O.J

    C. Page, B.O.J. Tupper, Mon. Not. R. Astron. Soc. 138 (1968) 67

    1968

  21. [28]

    Kaluza, Sitz

    T. Kaluza, Sitz. Preuss. Acad. Wiss. F1 (1921) 966

    1921

  22. [29]

    Klein, Z

    O. Klein, Z. Phys. 37 (1926) 895

    1926

  23. [30]

    R. Howl, R. Penrose, I. Fuentes, New J. Phys. 21 (2019) 043047

    2019

  24. [31]

    Capozziello, Internat

    S. Capozziello, Internat. J. Modern Phys. D 483 (2002) 11

    2002

  25. [32]

    T.Harko, F.S.N.Lobo, S.Nojiri and S.D.Odintsov, Phys.Rev.D, 84, (2011) 024020

    2011

  26. [33]

    Harko, Phys

    T. Harko, Phys. Rev. D 81 (2010) 044021

    2010

  27. [34]

    Chakraborty, Gen

    S. Chakraborty, Gen. Relativ. Gravit. 45 (2013) 2039

    2013

  28. [35]

    Sharif, M

    M. Sharif, M. Zubair, J. Cosmol. Astropart. Phys. 03 (2012) 028

    2012

  29. [36]

    Momeni, P.H.R.S

    D. Momeni, P.H.R.S. Moraes, R. Myrzakulov, Astrophys. Space Sci. 361 (2016) 228

    2016

  30. [37]

    Moraes, J.D.V

    P.H.R.S. Moraes, J.D.V . Arba ˜nil, M. Malheiro, J. Cosmol. Astropart. Phys. 06 (2016) 005

    2016

  31. [38]

    Alves, P

    M. Alves, P. Moraes, J. de Araujo, M. Malheiro, Phys. Rev. D 94 (2016) 024032

    2016

  32. [39]

    A. Das, S. Ghosh, B.K. Guha, S. Das, F. Rahaman, S. Ray, Phys. Rev. D 95 (2017) 124011

    2017

  33. [40]

    Rahaman, Ksh

    M. Rahaman, Ksh. N. Singh, A. Errehymy, F. Rahaman, M. Daoud, Eur. Phys. J. C 80 (2020) 272

    2020

  34. [41]

    A. Das, F. Rahaman, B. K. Guha and S. Ray, Eur. Phys. J. C, 76, (2016) 654

    2016

  35. [42]

    Ksh. N. Singh, A. Errehymy, F. Rahaman, M. Daoud, Chinese Phys. C 44 (2020) 105106

    2020

  36. [43]

    Carvalho, S.I

    G.A. Carvalho, S.I. Dos Santos, P.H.R.S. Moraes, M. Malheiro, Int. J. Mod. Phys. D 29 (2020) 2050075

    2020

  37. [44]

    P. Bhar, P. Rej, M. Zubair, Chinese J. Phys. 77 (2022) 2201

    2022

  38. [45]

    P. Bhar, P. Rej, A. Siddiqa, G. Abbas, Int. J. Geom. Methods Mod. Phys. 18 (2021) 2150160

    2021

  39. [46]

    P. Rej, P. Bhar, M. Govender, Eur. Phys. J. C 81 (2021) 316

    2021

  40. [47]

    Mondal, F

    M. Mondal, F. Rahaman, Universe 2023 (2023) 122

    2023

  41. [48]

    D Bhattacharjee and P K Chattopadhyay, Phys. Scr. 100 (2025) 055016

    2025

  42. [49]

    Srinivasan, Bull

    G. Srinivasan, Bull. Astron. Soc. India 30 (2002) 523

    2002

  43. [50]

    Chandrasekhar, An Introduction to the Study of Stellar Structure (The University of Chicago Press, Chicago, Illinois) (1938)

    S. Chandrasekhar, An Introduction to the Study of Stellar Structure (The University of Chicago Press, Chicago, Illinois) (1938)

    1938

  44. [51]

    Mukhopadhyay, Phys

    D.Das, B. Mukhopadhyay, Phys. Rev. Lett., 110 (2013) 071102

    2013

  45. [52]

    Oppenheimer, G.M

    J.R. Oppenheimer, G.M. V olkoff, Phys. Rev.55 (1939) 374

    1939

  46. [53]

    C. E. Rhoades and R. Ruffini, Phys. Rev. Lett. 32 (1974) 324

    1974

  47. [54]

    Nauenberg and G

    M. Nauenberg and G. Chapline Jr, Astrophys. J. 179 (1973) 417

    1973

  48. [55]

    A. G. Sabbadini and J. B. Hartle, Astrophys. Space Sci. 25 (1973) 117

    1973

  49. [56]

    Haensel, Equation of state of dense matter and maximum mass of neutron stars Final Stages of Stellar Evolution vol

    P. Haensel, Equation of state of dense matter and maximum mass of neutron stars Final Stages of Stellar Evolution vol. 7 (EAS Publications Series) ed J M Hameury and C Motch (Les Ulis, France: EDP Sciences, CERN Document Server), (2003) p 35 [astro-ph/0301073]

    2003 arXiv

  50. [57]

    Annala, T

    E. Annala, T. Gorda, A. Kurkela, A. Vuorinen, Phys. Rev. Lett. 120 (2018) 172703

    2018

  51. [58]

    Itoh, Prog

    N. Itoh, Prog. Theor . Phys.44 (1970) 291

    1970

  52. [59]

    J Madsen, 1999 Physics and astrophysics of strange quark matter , In Hadrons in Dense Matter and Hadrosynthesis(Lecture Notes in Physics) vol 516, ed. J. Cleymans, H.B. Geyer, F. G. Scholtz, (Springer, Berlin, Heidelberg, 1998) p-42

    1999

  53. [60]

    Baym G and S.A

    G. Baym G and S.A. Chin, Phys. Lett. B, 62 (1976) 241

    1976

  54. [61]

    Alcock, E

    C. Alcock, E. Farhi and A. Olinto, Astrophys. J., 310 (1986) 261

    1986

  55. [62]

    N. K. Glendenning, Mod. Phys. Lett. A, 5 (1990) 2197

    1990

  56. [63]

    Witten, Phys

    E. Witten, Phys. Rev. D 30 (1984) 272

    1984

  57. [64]

    Alford, Annu

    M. Alford, Annu. Rev. Nucl. Part. Sci. 51 (2001) 131. [hep-ph/0102047]

    2001 arXiv

  58. [65]

    A.Chodos,R. L. Jaffe, K. Jonson, C. B. Thern and V . F. Weisskopf, Phys. Rev. D9 (1974) 3471

    1974

  59. [66]

    Naseer, Phys

    M Sharif and T. Naseer, Phys. Scr., 97 (2022) 125016

    2022

  60. [67]

    Sharif and T

    M. Sharif and T. Naseer, Fortschr. Phys., 71 (2023) 2200147

    2023

  61. [68]

    Sharif and T

    M. Sharif and T. Naseer, Phys. Scr., 98 (2023) 105009

    2023

  62. [69]

    Naseer and M

    T. Naseer and M. Sharif, Chin. J. Phys. 88 (2024) 10

    2024

  63. [70]

    Naseer and M

    T. Naseer and M. Sharif Phys. Scr., 99 (2024) 095028

    2024

  64. [71]

    Reinhardt, B

    H. Reinhardt, B. V . Dang, Phys. Lett. B 173 (1986) 473

    1986

  65. [72]

    G. F. Burgio, et al., 2002. Phys. Lett. B 526 (2002) 19

    2002

  66. [73]

    Sharif, T

    M. Sharif, T. Naseer and A. Tabassum, Chin. J. Phys. 92 (2024) 579

    2024

  67. [74]

    Naseer, J.L

    T. Naseer, J.L. Said, M. Sharif, et al. Eur. Phys. J. C 85 (2025) 471

    2025

  68. [75]

    Naseer, J.L Said, Eur

    T. Naseer, J.L Said, Eur. Phys. J. C, 84 (2024) 808

    2024

  69. [76]

    Sharif, T

    M. Sharif, T. Naseer, A. Tabassum, Nucl. Phys. B, 1017 (2024) 116960

    2024

  70. [77]

    M.K. Mak, T. Harko, Chin. J. Astron. Astrophys. 2 (2002) 248

    2002

  71. [78]

    Kettner, F

    Ch. Kettner, F. Weber, M.K. Weigel and N.K. Glendenning, Phys. Rev. D, 51 (1995) 1440

    1995

  72. [79]

    G. X. Peng et al., Phys. Rev. C, 62, (2000) 025801

    2000

  73. [80]

    Kapusta, Finite-Temperature Field Theory(United Kingdom: Cambridge Univ

    J. Kapusta, Finite-Temperature Field Theory(United Kingdom: Cambridge Univ. Press), (1994) 163

    1994

  74. [81]

    Annala, et al., Nat

    E. Annala, et al., Nat. Phys. 16, (2020) 907

    2020

  75. [82]

    P. A. Guichon, Phys. Lett. B 200, (1988) 235. 23

    1988

  76. [83]

    D. H. Lu, K. Tsushima, A. W. Thomas, A. G. Williams and K. Saito, Nucl. Phys. A 634 (1998) 443

    1998

  77. [84]

    X. Jin, B. K. Jennings, Phys. Lett. B 374, (1996) 13

    1996

  78. [85]

    Jin and B

    X. Jin and B. K. Jennings, Phys. Rev. C, 54 (1996) 1427

    1996

  79. [86]

    Jin and B

    X. Jin and B. K. Jennings, Phys. Rev. C 55 (1997) 1567

    1997

  80. [87]

    M ¨ullar, B

    H. M ¨ullar, B. K. Jennings, Nucl. Phys. A, 626, (1997) 966; A 640 (1998) 55

    1997

  81. [88]

    H. Guo, J. Phys. G 25 (1999) 1701

    1999

  82. [89]

    P. Wang, R. K. Su, H. Q. Song and L. L. Zhang, Nucl. Phys. A 653 (1999) 166

    1999

  83. [90]

    L. L. Zhang, H. Q. Song, P. Wang and R. K. Su, J. Phys. G 26 (2000) 1301

    2000

  84. [91]

    R. T. Cahill , C. D. Roberts, Phys. Rev. D 32 (1985) 2419

    1985

  85. [92]

    R. T. Cahill, C. D. Roberts, and J. Praschifka, Ann. Phys. (N.Y.) 188 (1988) 20

    1988

  86. [93]

    C. D. Roberts, R. T. Cahill, M. E. Sevior and N. Iannella, Phys. Rev. D 49 (1994) 125

    1994

  87. [94]

    M. R. Frank and P. C. Tandy, Phys. Rev. C 46 (1992) 338; C. W. Johnson and G. Fai, Phys. Rev. C 56 (1997) 3353

    1992

  88. [95]

    P. C. Tandy, Prog. Part. Nucl. Phys. 39 (1997) 177

    1997

  89. [96]

    X. F. L ¨u, Y . X. Liu, H. S. Zong and E. G. Zhao,Phys. Rev. C 58 (1998) 1195

    1998

  90. [97]

    Liu, D.f

    Y .X. Liu, D.f. Gao and H. Guo, Nucl. Phys. A, 695 (2001) 353

    2001

  91. [98]

    Aguirre, Phys

    R. Aguirre, Phys. Lett. B, 559 (2003) 207

    2003

  92. [99]

    Prasad and R.S

    N. Prasad and R.S. Bhalerao, Phys.Rev.D 69 (2004) 103001

    2004

  93. [100]

    Tanabashi et al., Phys

    M. Tanabashi et al., Phys. Rev. D, 98 (2018) 030001

    2018

  94. [101]

    Particle Data Group, P. A. Zyla et al., Prog. Theor. Exp. Phys. 2020 (2020) 083C01

    2020

  95. [102]

    L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Butterworth-Heinemann, Oxford (1998)

    1998

  96. [103]

    Faraoni, Phys

    V . Faraoni, Phys. Rev. D, 80 (2009) 124040

    2009

  97. [104]

    Pretel Mod

    J.M.Z. Pretel Mod. Phys. Lett. A , 37 (2022) 2250188

    2022

  98. [105]

    F. G. Alvarenga, A. de la Cruz-Dombriz, M. J. S. Houndjo, M. E. Rodrigues,and D. S ´aez-G ´omez, Phys. Rev. D., 87 (2013) 103526

    2013

  99. [106]

    Lobato et al., J

    R. Lobato et al., J. Cosmol. Astropart. Phys., 2020 (2020) 039

    2020

  100. [107]

    G. A. Carvalho et al., Eur . Phys. J. C, 77 (2017) 871

    2017

  101. [108]

    Bhattacharjee and P

    S. Bhattacharjee and P. K. Sahoo, Gravitation and Cosmology, 26 (2020) 281

    2020

  102. [109]

    Velten and T

    H. Velten and T. R. P. Caram ˆes, Phys. Rev. D, 95 (2017) 123536

    2017

  103. [110]

    Shabani and M

    H. Shabani and M. Farhoudi, Phys. Rev. D, 88 (2013) 044048. [gr-qc/1306.3164]

    2013 arXiv

  104. [111]

    Shabani and M

    H. Shabani and M. Farhoudi, Phys. Rev. D, 90 (2014) 044031. [gr-qc/1407.6187]

    2014 arXiv

  105. [112]

    Singh and C

    V . Singh and C. P. Singh, Astrophys. Space Sci., 356 (2015) 153

    2015

  106. [113]

    P. H. R. S. Moraes, Astrophys. Space Sci., 352 (2014) 273

    2014

  107. [114]

    P. H. R. S. Moraes, Eur. Phys. J. C, 75 (2015) 168

    2015

  108. [115]

    P. H. R. S. Moraes, Int. J. Theor. Phys., 55 (2016) 1307

    2016

  109. [116]

    P. H. R. S. Moraes, R. A. C. Correa and R. V . Lobato, J. Cosmol. Astropart. Phys. 07, (2017) 029 [gr-qc/1701.01028]

    2017 arXiv

  110. [117]

    Sharif and M

    M. Sharif and M. Zubair, Astrophys. Space Sci. 349 (2014) 457

    2014

  111. [118]

    D. R. K. Reddy and R. Shantikumar, Astrophys. Space Sci. 344 (2013) 253

    2013

  112. [119]

    Kumar and C

    P. Kumar and C. P. Singh, Astrophys. Space Sci. 357 (2015) 120

    2015

  113. [120]

    M. F. Shamir, Eur. Phys. J. C, 75, (2015) 354

    2015

  114. [121]

    K. B. Goswami, D. Bhattacharjee, P. K. Chattopadhyay and A. Saha, Phys. of the Dark Universe 47 (2025) 101752

    2025

  115. [122]

    Sarkar, N

    S. Sarkar, N. Sarkar and F. Rahaman, Chin. J. Phys., 77 (2022) 2028

    2022

  116. [123]

    Sharif and Z

    M. Sharif and Z. Yousaf, Astrophys. Space Sci., 354 (2014) 471

    2014

  117. [124]

    A. K. Yadav, M. Mondal and F. Rahaman, Pramana J. Phys., 94 (2020) 90

    2020

  118. [125]

    Bhar and P

    P. Bhar and P. Rej, New Astronomy, 100 (2023) 101990

    2023

  119. [126]

    D. Deb, F. Rahaman, S. Ray and B. K. Guha, J. Cosmol. Astropart. Phys., 03 (2018) 044

    2018

  120. [127]

    G. A. Carvalho, S. I. Dos Santos, P. H. R. S. Moraes and M. Malheiro, Int. J. Mod. Phys. D, 29 (2019) 2050075

    2019

  121. [128]

    Darmois, Memorial des Sciences Mathematiques XXV , Fasticule XXV , Gauthier-Villars, Paris, France, Chap

    G. Darmois, Memorial des Sciences Mathematiques XXV , Fasticule XXV , Gauthier-Villars, Paris, France, Chap. V (1927)

    1927

  122. [129]

    Mafa Takisa, S.D

    P. Mafa Takisa, S.D. Maharaj, C. Mulangu, Pramana J. Phys. 92 (2019) 40

    2019

  123. [130]

    Zel’dovich, Zh

    Y .B. Zel’dovich, Zh. Eksp. Teor. Fiz.41 (1961) 1609. [Engl. transl: Sov. Phys. JETP 14, 1143 (1962)]

    1961

  124. [131]

    R. C. Tolman, Phys. Rev. 55 (1939) 364

    1939

  125. [132]

    Y . B. Zeldovich, I. D. Novikov, Relativistic Astrophysics V ol. 1: Stars and Relativity (University of Chicago Press, Chicago), (1971)

    1971

  126. [133]

    B. K. Harrison, K. S. Thorne, M.Wakano, J. A. Wheeler,Gravitational Theory and Gravitational Collapse (University of Chicago Press, Chicago), (1965)

    1965

  127. [134]

    Bhattacharya, R

    S. Bhattacharya, R. Sharma and S. D. Maharaj, Eur. Phys. J. C, 84 (2024) 64

    2024

  128. [135]

    Gangopadhyay, S

    T. Gangopadhyay, S. Ray, X.D. Li, J. Dey, M. Dey, Mon. Not. R. Astron. Soc. 431 (2013) 3216

    2013

  129. [136]

    C. A. Kolassis, N. O. Santos and D. Tsoubelis, Class. Quantum Gravity 5 (1988) 1329

    1988

  130. [137]

    S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Spacetime (Cambridge University Press: Cambridge, UK), (1973)

    1973

  131. [138]

    Wald, General Relativity (University of Chicago Press: Chicago, IL, USA), (1984)

    R. Wald, General Relativity (University of Chicago Press: Chicago, IL, USA), (1984)

    1984

  132. [139]

    Brassel, S.D

    B.P. Brassel, S.D. Maharaj, and R. Goswami, Entropy 23 (2021) 1400

    2021

  133. [140]

    Brassel, S.D

    B.P. Brassel, S.D. Maharaj and R. Goswami Prog. Theor. Exp. Phys. 2021 103E01 (2021)

    2021

  134. [141]

    Demorest, et al., Nature 467 (2010) 1081

    P.B. Demorest, et al., Nature 467 (2010) 1081

    2010

  135. [142]

    G ¨uver, et al., Astrophys

    T. G ¨uver, et al., Astrophys. J. 712 (2010) 964

    2010

  136. [143]

    G ¨uver, et al., Astrophys

    T. G ¨uver, et al., Astrophys. J. 719 (2010) 1807

    2010

  137. [144]

    Miller, et al., Astrophys

    M.C. Miller, et al., Astrophys. J. Lett. 887 (2019) L24

    2019

  138. [145]

    Grøn, Phys

    Ø. Grøn, Phys. Rev. D 31 (1985) 2129

    1985

  139. [146]

    Heintzmann, W

    H. Heintzmann, W. Hillebrandt, Astron. Astrophys. 38 (1975) 51. 24

    1975

  140. [148]

    E. E. Flanagan, T. Hinderer, Phys.Rev.D 77 (2008) 021502

    2008

  141. [149]

    K. S. Thorne and A. Campolattaro, ApJ, 149 (1967) 591

    1967

  142. [150]

    Regge, J

    T. Regge, J. A. Wheeler, Phys. Rev. 108 (1957) 1063

    1957

  143. [151]

    Hinderer, Astrophys

    T. Hinderer, Astrophys. J. 677 (2008) 1216

    2008

  144. [152]

    Hinderer, B.D

    T. Hinderer, B.D. Lackey, R.N. Lang, J.S. Read, Phys. Rev. D 81, (2010) 123016

    2010

  145. [153]

    Abbott R

    B.P. Abbott R. Abbott, (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 119 (2017) 161101

    2017

  146. [154]

    Bauswein, et al., AIP Conf

    A. Bauswein, et al., AIP Conf. Proc. 2127 (2019) 020013. 25

    2019

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