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REVIEW 3 major objections 4 minor 80 references

Maximum mass of singularity-free anisotropic compact stars in Rastall theory of gravity

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that Rastall gravity with the Krori-Barua ansatz supports singularity-free anisotropic compact stars whose maximum mass rises with the Rastall parameter, reaching 2.36 solar masses at ξ=0.09.

desk verdict The headline maximum masses are not supported as Rastall predictions: the TOV equation is never written, and the fitted EoS contradicts the stated central sound speed. read the letter →

arxiv 2505.21583 v1 pith:PFIZUTF2 submitted 2025-05-27 gr-qc

Sourav Biswas , Debadri Bhattacharjee , Pradip Kumar Chattopadhyay This is my paper
classification gr-qc
keywords compactstarsequationofstatemaximummassRastallgravitypressureanisotropyKrori-BaruametricTOVneutron
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 tries to establish that Rastall gravity, a modified theory in which the energy-momentum tensor is not conserved, can support heavier anisotropic compact stars than a plain GR model built with the same metric ansatz. Using the Krori-Barua ansatz, the authors derive singularity-free analytic expressions for density and pressures, then fit a linear equation of state and integrate the TOV equations to obtain a mass-radius relation. Their headline numbers: as the dimensionless Rastall parameter ξ grows from 0.01 to 0.09, the maximum mass rises from 2.24 to 2.36 solar masses and the radius from 9.48 to 10.15 km. The paper argues that a stronger matter-curvature coupling reduces effective gravity at high density, letting the star resist collapse even though the fitted equation of state looks softer. A sympathetic reader would care because this offers a concrete, observationally testable route to compact objects above 2.3 solar masses, relevant to heavy pulsars and the GW190814 companion.

What carries the argument

The central objects are the Rastall field equations $G_{\mu\nu}+\xi g_{\mu\nu}R = 8\pi\,[(4\xi-1)/(6\xi-1)]\,T_{\mu\nu}$, which encode the non-conservation of the energy-momentum tensor, and the Krori-Barua metric ansatz $e^{2\lambda}=e^{ar^2}$, $e^{2\nu}=e^{br^2+c}$, whose Gaussian potentials turn the field equations into algebraic expressions for $\rho$, $p_r$, and $p_t$. The argument for the maximum mass is carried by a fitted linear equation of state, obtained by imposing $v_r^2(0)=1$ and curve fitting the model's pressure-density relation. Numerical TOV integration of that fitted equation of state produces the mass-radius curve whose peak is the reported maximum mass for each $\xi$.

What would settle it

Integrate the Rastall-modified TOV equations derived from Eq. (8), using the Table 1 equation of state and the boundary condition $p_r(R)=0$, and compare the mass-radius peaks with the paper's values; if the maximum mass does not increase with $\xi$, or if the peaks do not land near 2.24, 2.28, and 2.36 $M_\odot$, the central claim fails. A simpler check is to integrate the displayed GR TOV equation with the same fits: if it reproduces the paper's numbers exactly, then the $\xi$ effect lives in the fitted equation of state rather than in Rastall hydrostatics.

Watch

Extended reading notes

Core claim

Within Rastall gravity, the paper constructs exact, singularity-free interior solutions for spherically symmetric anisotropic stars using the Krori-Barua ansatz, where both metric potentials are Gaussians in the radial coordinate. Matching to the Schwarzschild exterior fixes the ansatz constants through the stellar mass and radius. The authors then fit a linear equation of state $p_r = \alpha\rho - \beta$ to their pressure-density relation by imposing the causal limit $v_r^2(0)=1$, integrate the TOV equations, and report maximum masses of $2.24\,M_\odot$, $2.28\,M_\odot$, and $2.36\,M_\odot$ for $\xi=0.01$, $0.05$, and $0.09$, with corresponding radii of 9.48, 9.70, and 10.15 km. The central claim is that a larger Rastall parameter yields a higher maximum mass and radius even though the fitted equation of state appears softer, because the non-minimal matter-curvature coupling weakens effective gravity at high densities. The same solutions also reproduce the observed radii of several known compact stars for suitable choices of $\xi$.

Load-bearing premise

The whole mass-radius curve rests on the assumption that the model's pressure-density relation can be replaced by a fitted linear equation of state, found by imposing $v_r^2(0)=1$, and that integrating a TOV equation with that fit gives the true Rastall-model maximum mass; the paper shows neither the fitting procedure nor a Rastall-modified TOV equation, and the TOV equation it displays is the standard GR one.

Editorial extensions

If this is right

  • The maximum mass rises monotonically with the Rastall parameter: 2.24 $M_\odot$ at $\xi=0.01$, 2.28 $M_\odot$ at $\xi=0.05$, and 2.36 $M_\odot$ at $\xi=0.09$.
  • The model predicts maximum configurations with radii of about 9.5 to 10.2 km, which are noticeably smaller than the 12.39 km radius adopted for PSR J0740+6620.
  • For suitable choices of $\xi$, the predicted radii of 4U 1820-30, LMC X-4, Cen X-3, HER X-1, and 4U 1608-52 fall within the observed error bars.
  • Causality, the null/weak/strong/dominant energy conditions, TOV hydrostatic equilibrium, Herrera's cracking condition, and the adiabatic-index bound are all reported as satisfied throughout the stellar interior.
  • Values of $\xi$ above 0.09 are reported to give unphysical results, so the model is restricted to $0<\xi\le 0.09$.

Reading between the lines

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

  • If the reported trend holds, Rastall gravity gives a tunable parameter that shifts the neutron-star maximum mass; a single well-measured compact object above roughly 2.3 $M_\odot$ with a radius near 10 km would favor $\xi$ near 0.09, while a firm cap near 2.0-2.1 $M_\odot$ would push $\xi$ toward zero.
  • Because the TOV equation displayed in Section 5.1 is the standard general-relativistic form, the $\xi$-dependence of the maximum mass may enter through the fitted equation of state of Table 1 rather than through Rastall corrections to hydrostatic equilibrium; recomputing with a properly Rastall-modified TOV equation would settle which mechanism the reported numbers actually test.
  • The same fitting procedure, imposing $v_r^2=1$ at the centre and fitting a linear equation of state, could be applied to other metric ansätze or to a bag-model equation of state; this would show whether the 2.24-2.36 $M_\odot$ window is a property of Rastall gravity or an artifact of the Krori-Barua choice.
  • A direct observational discriminator would be a precision radius measurement for a neutron star with mass above 2.2 $M_\odot$: the model's compact radii around 9.5-10.2 km are measurably smaller than canonical 12 km fits, so a future NICER-type measurement could distinguish this Rastall scenario from standard GR neutron-star models.
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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

3 major / 4 minor

Summary. The paper constructs spherically symmetric, anisotropic, singularity-free compact star solutions in Rastall gravity using the Krori-Barua metric ansatz. It derives explicit expressions for energy density and pressures (Eqs. 14--16), matches the interior to the Schwarzschild exterior, and then turns to the mass-radius relation. Using a 'best-fit' linear equation of state obtained by curve fitting the model's own pressure-density relation under a stated central sound-speed constraint, the authors solve the TOV equation numerically and report maximum masses of 2.24--2.36 M_sun with radii 9.48--10.15 km for Rastall parameter ξ = 0.01--0.09 (Table 2). They also list 'predicted' radii for five known pulsars by assigning a separate ξ per object (Table 3), and check causality, energy conditions, and stability.

Significance. If the maximum-mass calculation were a genuine Rastall-theory prediction, it would give a concrete, observationally testable consequence of Rastall gravity in the strong-field regime, and the claimed monotonic increase of M_max with ξ would be a nontrivial qualitative signature. The analytic solution in Eqs. (14)--(16) is explicit and potentially useful, and the stability checks (TOV force balance, Herrera cracking, adiabatic index) follow standard practice. However, the central quantitative claim is not supported as presented: the TOV equation actually used is not shown and differs from the Rastall hydrostatic equilibrium, and the equation of state is fitted from the model itself without a transparent procedure. Because the headline numbers depend on these defective steps, the significance of the paper as it stands is primarily as a proposal for how such an analysis could be done, not as a validated prediction.

major comments (3)
  1. [§4.3 and Eq. (25)] The maximum masses in Table 2 are said to come from 'numerical solution of the TOV equations', but the paper never writes the Rastall-modified TOV equation. The only TOV equation displayed, Eq. (25), is the standard GR anisotropic hydrostatic equilibrium equation with no Rastall term; in Rastall gravity the non-conservation of T^{μν} adds extra terms to the hydrostatic equilibrium condition. Consequently, the reported masses and radii are not established as predictions of the Rastall model.
  2. [§4.3 and Table 1] The fitting procedure is undisclosed and internally inconsistent. The text states that the constraint v_r^2|_{r=0} = dp_r/dρ|_{r=0} = 1 is imposed, but the slopes in Table 1 are 0.9056, 0.8803, and 0.8441, all below 1. No data range, number of points, or fitting algorithm is specified, so the reader cannot reproduce the EoS. Moreover, because the linear EoS is fitted to the model's own p_r(ρ) relation, integrating it in the TOV equation yields a mass-radius curve that reflects the fit, not the original Rastall solution; the monotonic increase of M_max with ξ may therefore be an artifact of the fitting and integration scheme.
  3. [Table 3 and Discussion] The 'predicted' radii in Table 3 are obtained by choosing a different Rastall parameter ξ for each pulsar (0.01, 0.05, 0.09, 0.01). A free parameter that is refitted per object cannot produce a falsifiable prediction; agreement with the observed radii is thus a check of the interpolation formula rather than a test of Rastall gravity. The Discussion statement that radii 'may be predicted with great accuracy by varying ξ' is a concession of this circularity, not a validation.
minor comments (4)
  1. [Eq. (20)] The constants A, B, C appear in Eq. (20) without being defined in terms of the earlier a, b, c; the exponent in K^-_{00} also has mismatched variables. Please make the notation uniform.
  2. [Section 5.1] Eq. (25) is labelled the 'generalised TOV equation', but it is the standard GR form. If it is intended to hold in Rastall gravity, the derivation and the role of ξ should be stated explicitly.
  3. [Reference list] Reference [56] (Oppenheimer and Volkoff) is cited as 'Phys. Rev. 55, 374 (1904)'; the year should be 1939.
  4. [§4.3 text] The paragraph after Table 1 says that a softer EoS is 'demonstrated in Table 2', but Table 2 lists maximum masses and radii, not EoS parameters; the sentence appears to refer to the slopes in Table 1.

Circularity Check

3 steps flagged · score 6.0 of 10

Maximum mass and radius claims reduce to a curve-fit EoS integrated with GR TOV; pulsar radii are matched by per-object tuning of ξ.

  1. fitted input called prediction [Section 4.3, Table 1 and Table 2]
    "we employ this apex of causality at the centre, i.e., v 2 r|r=0 = dp r dρ |r=0 =1 along with the method of curve fitting to determine the best fit EoS for different choices of Rastall parameter (ξ). The results are tabulated in Table 1. Using Table 1, we have obtained the numerical solution of the TOV equations to determine the maximum mass and the associated radius in the present model."

    The headline maximum masses in Table 2 (2.24–2.36 M☉) are outputs of a TOV integration whose only material input is the linear EoS fitted in Table 1. That fit is made to the model's own p_r(ρ) relation, and the reported slopes (0.9056, 0.8803, 0.8441) do not satisfy the stated central constraint v_r^2(0)=1. The maximum mass is therefore a property of an undisclosed curve-fitting procedure, not a prediction derived from the Rastall field equations; different fitting choices would give different 'predictions'.

  2. other [Section 5.1, Eq. (25), and Section 4.3]
    "− M G(r)(ρ+p r) r^2 e^{λ−ν} − dp_r/dr + 2Δ/r =0 (25)"

    The only TOV equation displayed in the paper is the standard general-relativistic anisotropic TOV equation, with no Rastall term. Yet the abstract and Section 4.3 attribute the increase of M_max with ξ to Rastall gravity, and the text states that 'Rastall gravity modifies the TOV equation'. Since the actual TOV integration uses Eq. (25), the mass-radius curve of Fig. 5 is not generated by the Rastall field equations of Section 2; the claimed Rastall dependence is inherited entirely from the fitted EoS, so the quoted prediction reduces to a GR TOV integration with a fitted input.

1 more flagged steps
  1. fitted input called prediction [Section 4.3, Table 3, and Discussion]
    "we note that in the framework of Rastall theory of gravity, radii of many compact stars may be predicted, theoretically, with great accuracy by varying parameterξ"

    In Table 3, each pulsar is assigned its own Rastall parameter ξ (0.01, 0.05, 0.01, 0.09, 0.01), and the 'predicted radius' is then read off the model with that tuned value. Because ξ is a free parameter adjusted separately for each object, the agreement between predicted and observed radii is achieved by construction rather than by an independent, parameter-free prediction. The paper provides no external constraint that fixes ξ per pulsar, so this is fitting dressed as prediction.

full rationale

The analytic KB-Rastall interior solution and the standard boundary matching are self-contained and are not circular. However, the two central quantitative outputs are fit-generated rather than derived from the Rastall field equations. First, the maximum mass is obtained by integrating the TOV equation with a linear EoS that is a best fit to the model's own p_r(ρ) curve under a central causality constraint that the fitted slopes contradict; the headline masses are therefore outputs of an undisclosed fitting procedure. Second, the TOV equation explicitly written in the paper is the GR equation, not the Rastall-modified hydrostatic equilibrium equation, so the claimed Rastall dependence of M_max is imported from the fitted EoS, not from the theory. Third, the pulsar radius agreement is obtained by choosing ξ separately for each object, making the 'predictions' matches by construction. No load-bearing self-citation chain or imported uniqueness theorem is involved. Because the paper's headline claims reduce to fitted inputs and a GR TOV integration, the circularity score is 6.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The model introduces no new entities, but it adds three effective free parameters, xi, alpha and beta, and several ad hoc assumptions, the most consequential being the fitted linear EoS and the unspecified TOV integration.

free parameters (3)
  • Rastall parameter xi = 0.01, 0.05, 0.09
    Chosen by hand; the range is restricted to xi <= 0.09 because larger values are said to give unphysical results. In Table 3 xi is selected separately for each pulsar to match radii, so it functions as a fitting parameter.
  • EoS slope alpha = 0.905609, 0.880296, 0.844125
    Best-fit slope of the linear EoS p_r = alpha rho + beta in Table 1, obtained by curve fitting under the central causality constraint; not derived from microphysics.
  • EoS intercept beta = -0.000563611, -0.000517796, -0.000447121
    Best-fit intercept of the linear EoS in Table 1, with units of Km^-2; also a fitted quantity.
assumptions (6)
  • domain assumption Rastall field equations with the rescaled coupling constant (Eq. 8) are the correct gravitational equations.
    The entire construction assumes Rastall gravity; the coupling rescaling in Eq. 6 is a convention that makes xi dimensionless.
  • ad hoc to paper The Krori-Barua metric ansatz e^{2 lambda} = e^{2 a r^2}, e^{2 nu} = e^{2 b r^2 + 2 c} is assumed.
    Introduced to make the field equations tractable; it is a geometric assumption not derived from physical matter conditions.
  • domain assumption The exterior is the Schwarzschild vacuum solution.
    Matching in Section 3 assumes the exterior is vacuum and described by Eq. 19; Rastall modifications are assumed absent outside the star.
  • ad hoc to paper A linear EoS p_r = alpha rho + beta is used for the TOV integration.
    Table 1; the EoS is fitted to the model's own profiles, with no connection to microphysical nuclear matter.
  • ad hoc to paper The central sound speed condition v_r^2(0)=1 is imposed to select the EoS.
    Stated in Section 4.3; this is a calibration rule, not a consequence of the field equations.
  • domain assumption The standard TOV equation governs the mass-radius relation.
    The paper cites the standard TOV references and does not display a Rastall-modified version; the displayed stability TOV in Eq. 27 contains no xi, so the role of Rastall corrections in the mass integration is unclear.

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Pith. "Pith review of Maximum mass of singularity-free anisotropic compact stars in Rastall theory of gravity." pith.science (2026). https://pith.science/paper/PFIZUTF2

@misc{pith2026250521583,
  author       = {Pith},
  title        = {Pith review of: Maximum mass of singularity-free anisotropic compact stars in Rastall theory of gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PFIZUTF2}},
  note         = {Machine review of arXiv:2505.21583}
}
abstract

The current model explores spherically symmetric anisotropic compact stars within the Rastall theory of gravity. By employing the Krori and Barua metric ansatz (K.D. Krori and J. Barua, J. Phys. A: Math. Gen. 8 (1975) 508), we derive a set of tractable, singularity-free relativistic solutions to the Einstein field equations. Using a best-fit equation for the numerical solution of the TOV equation, we determine the maximum mass and corresponding radius in this model. Our findings reveal that an increase in the Rastall parameter $(\xi)$ leads to a higher maximum mass, indicating a stiffer nature of the equation of state. For $\xi$ values ranging from 0.01 to 0.09, we calculate the maximum mass to be between $2.24M_{\odot}$ and $2.36M_{\odot}$, with corresponding radii from 9.48 to 10.15 km. Furthermore, our model's predictions for the radii of recently observed pulsars are consistent with observational data. The model satisfies essential criteria for causality, energy conditions, and stability, confirming its viability and physical acceptability as a stellar structure.

Figures

Figures reproduced from arXiv: 2505.21583 by the authors.

Figure 1
Figure 1. Variation of energy density [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Variation of radial pressure pr with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 4.2. Anisotropy In this segment, we analyse the graphical response of anisotropy parameter, which is represented by ∆ and defined as the difference between the transverse and radial pressure i.e. ∆ = pt − pr . Now, is ∆ is negative (pt < pr), the nature of the force will be attracti… view at source ↗
Figure 3
Figure 3. Variation of transverse pressure pt with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 0 2 4 6 8 10 12 0 5.´10-6 0.00001 0.000015 0.00002 0.000025 r HKmL D HKm -2 L [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Represantation of anisotropy ∆ with radius r. Here, Dashed, Solid and Dot-Dashed lines respectively represent ξ = 0.01, 0.05 and 0.09. 4.3. Mass-radius relation from TOV equation Here, the TOV equations [55, 56] is solved to obtain the possible maximum mass and the ass…
Figure 5
Figure 5. Figure 5: Mass-radius relationship from TOV equation. Here, Dashed, Solid and Dot-Dashed lines respectively represent [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Variation of v 2 r with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 0 2 4 6 8 10 12 0.14 0.16 0.18 0.20 0.22 0.24 r HKmL vt 2 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Variation of v 2 t with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 4.5. Energy condition Energy conditions are responsible for the qualitative description of the nature of the internal matter distribution of a gra…
Figure 8
Figure 8. Figure 8: Variation of (ρ + pr) with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 0 2 4 6 8 10 12 0.00025 0.00030 0.00035 0.00040 0.00045 0.00050 0.00055 r HKmL Ρ+pt HKm -2 L [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Variation of (ρ + pt) with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Variation of (ρ + pr + 2pt) with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 0 2 4 6 8 10 12 0.00020 0.00025 0.00030 0.00035 0.00040 r HKmL Ρ-pr HKm -2 L [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Variation of (ρ − pr) with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 5. Stability analysis The stability in Rastall theory of gravity is explored using the following methods: 1. Generalised TOV equation. 2. Crac…
Figure 12
Figure 12. Figure 12: Variation of (ρ − pt) with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. here, MG is termed the active gravitational mass evaluated from the Tolman-Whittaker [77] mass formula which is given below: MG(r) = r 2 ν ′ e…
Figure 13
Figure 13. Figure 13: Variation of different forces with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 14
Figure 14. Figure 14: Variation of sound parameter |v 2 t − v 2 r | with radius r. Here, Dashed, Solid and Dot-Dashed lines respectively represent ξ = 0.01, 0.05 and 0.09. 5.3. Adiabatic index The stiffness of EoS for a given energy density is described by adiabatic index (Γ). It verifies …
Figure 15
Figure 15. Figure 15: Variation of Γ with radius r. Here, Dashed, Solid and Dot-Dashed lines represent ξ = 0.01, 0.05 and 0.09 respectively. 6. Discussion The present article explores the structural and dynamical properties of a singularity-free anisotropic compact star within the Rastall …

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Reference graph

Works this paper leans on

80 extracted references · 76 canonical work pages

  1. [1]

    C. M. Will, Living Rev. Relativ.17, 4 (2014)

    work page 2014

  2. [2]

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

    2003

  3. [3]

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

    work page 2016

  4. [4]

    B. P. Abbott et al. (Virgo, LIGO Scientific), Annalen der Physik529, 1600209 (2017)

    work page 2017

  5. [5]

    Nojiri and S

    S. Nojiri and S. D. Odintsov, Int. J. Geom. Methods Mod. Phys.04, 115 (2007)

    work page 2007

  6. [6]

    Capozziello, Int

    S. Capozziello, Int. J. Mod. Phys. D11, 483 (2002)

    work page 2002

  7. [7]

    Elizalde et al., Phys

    E. Elizalde et al., Phys. Rev. D83, 086006 (2011). 16

    work page 2011

  8. [8]

    Bamba, C.-Q

    K. Bamba, C.-Q. Geng, C.-C. Lee and L.-W. Luo, Astropart. Phys.01, 021 (2011)

    work page 2011

Show all 80 references
  1. [9]

    M. J. S. Houndjo et al., Int. J. Mod. Phys. D26, 1750024 (2017)

    2017

  2. [10]

    Yousaf, M

    Z. Yousaf, M. Sharif, M. Ilyas and M. Z. Bhatti, Int. J. Geom. Methods Mod. Phys.15, 1850146 (2018)

    2018

  3. [11]

    Ilyas, Z

    M. Ilyas, Z. Yousaf and M. Z. Bhatti, Mod. Phys. Lett. A34, 1950082 (2019)

    2019

  4. [12]

    A. Das, F. Rahaman, B. K. Guha and S. Ray, Astrophys. Space Sci.358, 36 (2015)

    2015

  5. [13]

    A. Das, F. Rahaman, B. K. Guha and S. Ray, Eur. Phys. J. C76, 654 (2016)

    2016

  6. [14]

    Das et al., Phys

    A. Das et al., Phys. Rev. D95, 124011 (2017)

    2017

  7. [15]

    Biswas et al., Ann

    S. Biswas et al., Ann. Phys. (N. Y .)401, 1 (2019)

    2019

  8. [16]

    S. V . Lohakare et al., Mon. Not. R. Astron. Soc.526, 3796 (2023)

    2023

  9. [17]

    Xu et al., Eur

    Y . Xu et al., Eur. Phys. J. C79, 708 (2019)

    2019

  10. [18]

    D. D. Doneva, S. S. Yazadjiev and K. D. Kokkotas, Phys. Rev. D92, 064015 (2015)

    2015

  11. [19]

    S. S. Yazadjiev, D. D. Doneva and K. D. Kokkotas, Phys. Rev. D91, 084018 (2015)

    2015

  12. [20]

    Feola et al., Phys

    P. Feola et al., Phys. Rev. D101, 044037 (2020)

    2020

  13. [21]

    Rastall, Phys

    P. Rastall, Phys. Rev. D6, 3357 (1972)

    1972

  14. [22]

    Rastall, Can

    P. Rastall, Can. J. Phys.54, 66 (1976)

    1976

  15. [23]

    A. M. Oliveira et al., Phys. Rev. D92, 044020 (2015)

    2015

  16. [24]

    W. E. Hanafy, Astrophys. J.940, 51 (2022)

    2022

  17. [25]

    Hansraj, A

    S. Hansraj, A. Banerjee and P. Channuie, Ann. Phys. (N. Y .)400, 320 (2019)

    2019

  18. [26]

    Heydarzade, H

    Y . Heydarzade, H. Moradpour and F. Darabi, Can. J. Phys.95, 1253 (2017)

    2017

  19. [27]

    H. L. Parihadi et al., Int. J. Mod. Phys. D29, 2050021 (2020)

    2020

  20. [28]

    Kumar and S

    R. Kumar and S. G. Ghosh, Eur. Phys. J. C78, 750 (2018)

    2018

  21. [29]

    Xu and J

    Z. Xu and J. Wang, Eur. Phys. J. C78, 513 (2018)

    2018

  22. [30]

    M. S. Ma and R. Zhao, Eur. Phys. J. C77, 629 (2017)

    2017

  23. [31]

    Gergess and L

    G. Gergess and L. Nashed, Universe8, 510 (2022)

    2022

  24. [32]

    C. E. Mota et al., Int. J. Mod. Phys. D31, 2250023 (2022)

    2022

  25. [33]

    Abbas and M

    G. Abbas and M. R. Shahzad, Chinese J. Phys.63, 1 (2020)

    2020

  26. [34]

    Cromartie et al., Nature4, 72 (2020)

    H. Cromartie et al., Nature4, 72 (2020)

    2020

  27. [35]

    Abbott et al., Astrophys

    R. Abbott et al., Astrophys. J. Lett.896, L44 (2020)

    2020

  28. [36]

    Ruderman, Ann

    M. Ruderman, Ann. Rev. Astron. Astrophys.10, 427 (1972)

    1972

  29. [37]

    Canuto, S

    V . Canuto, S. M. Chitre, Phys. Rev. D9, 1587 (1974)

    1974

  30. [38]

    R. F. Sawyer, D. J. Scalapino, Phys. Rev. D8, 1260 (1973)

    1973

  31. [39]

    R. F. Sawyer, Phys. Rev. Lett.29, 382 (1972). 17

    1972

  32. [40]

    Carter, D

    B. Carter, D. Langlois, Nucl. Phys. B531, 478 (1998)

    1998

  33. [41]

    S. A. Mardan et al., Eur. Phys. J. Plus134, 242 (2019)

    2019

  34. [42]

    Herrera, N

    L. Herrera, N. O. Santos, Phys. Rep.286, 53 (1997)

    1997

  35. [43]

    R. L. Bowers, E. P. T. Liang, Astrophys. J.188, 657 (1974)

    1974

  36. [44]

    Heintzmann, W

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

    1975

  37. [45]

    S. K. Maurya, Y . K. Gupta, S. Ray, B. Dayanandan, Eur. Phys. J. C75, 225 (2015)

    2015

  38. [46]

    S. K. Maurya, Y . K. Gupta, B. Dayanandan, M. K. Jasim, A. Al-Jamel, Int. J. Mod. Phys. D26, 1750002 (2017)

    2017

  39. [47]

    S. K. Maurya, A. Banerjee, S. Hansraj, Phys. Rev. D97, 044022 (2018)

    2018

  40. [48]

    S. K. Maurya, A. Banerjee, Y . K. Gupta, Astrophys. Space Sci.363, 208 (2018)

    2018

  41. [49]

    D. Deb, S. R. Chowdhury, S. Ray, F. Rahaman, B. K. Guha, Ann. Phys. (Amsterdam)387, 239 (2017)

    2017

  42. [50]

    Kalam, F

    M. Kalam, F. Rahaman, S. Molla, S. M. Hossein, Astrophys. Space Sci.349, 865 (2014)

    2014

  43. [51]

    M. K. Mak, T. Harko, Proc. Roy. Soc. Lond. A459, 393 (2003)

    2003

  44. [52]

    M. K. Mak et al., Int. J. Mod. Phys. D11, 207 (2002)

    2002

  45. [53]

    Hernandez, L

    H. Hernandez, L. Nunez, Can. J. Phys.82, 29 (2004)

    2004

  46. [54]

    Kalam, F

    M. Kalam, F. Rahaman, S. M. Hossein, S. Ray, Eur. Phys. J. C73, 2409 (2013)

    2013

  47. [55]

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

    1939

  48. [56]

    J. R. Oppenheimer, G. M. V olkoff, Phys. Rev.55, 374 (1904)

    1904

  49. [57]

    K. D. Krori, J. Barua, J. Phys. A: Math. Gen.8, 508 (1975)

    1975

  50. [58]

    Varela et al., Phys

    V . Varela et al., Phys. Rev. D82, 044052 (2010)

    2010

  51. [59]

    Kalam et al., Eur

    M. Kalam et al., Eur. Phys. J. C73, 2409 (2013)

    2013

  52. [60]

    Hossein et al., Int

    M. Hossein et al., Int. J. Mod. Phys. D21, 1250088 (2012)

    2012

  53. [61]

    Rahaman et al., Phys

    F. Rahaman et al., Phys. Rev. D82, 104055 (2010)

    2010

  54. [62]

    Bhar, Astrophys

    P. Bhar, Astrophys. Space Sci.356, 365 (2015)

    2015

  55. [63]

    J. L. Rosa, N. Ganiyeva, F. N. S. Lobo, Eur. Phys. J. C83, 1040 (2023)

    2023

  56. [64]

    Schwarzschild, Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften Berlin (Mathe- matical Physics) 189-196 (1916)

    K. Schwarzschild, Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften Berlin (Mathe- matical Physics) 189-196 (1916)

    1916

  57. [65]

    T. E. Riley, Astrophys. J. Lett.918, L27 (2021)

    2021

  58. [66]

    M. K. Gokhroo, A. L. Mehra, Gen. Relativ. Gravit.26, 1 (1994)

    1994

  59. [67]

    J. M. Z. Pretel, C. E. Mota, Gen. Relativ. Gravit.56, 43 (2024)

    2024

  60. [68]

    Güver et al., Astrophys

    T. Güver et al., Astrophys. J.719, 1807 (2010)

    2010

  61. [69]

    M. L. Rawls et al., Astrophys. J.730, 25 (2011)

    2011

  62. [70]

    M. K. Abubekerov et al., Astron. Rep.52, 379 (2008). 18

    2008

  63. [71]

    Güver et al., Astrophys

    T. Güver et al., Astrophys. J.712, 964 (2010)

    2010

  64. [72]

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

    1988

  65. [73]

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

    1973

  66. [74]

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

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

    1984

  67. [75]

    B. P. Brassel, S. D. Maharaj, R. Goswami, Entropy23, 1400 (2021)

    2021

  68. [76]

    B. P. Brassel, S. D. Maharaj, R. Goswami, J. Exp. Theor. Phys.103E01, (20 pages) (2021)

    2021

  69. [77]

    Grøn, Phys

    Ø. Grøn, Phys. Rev. D31, 2129 (1985)

    1985

  70. [78]

    Herrera, Phys

    L. Herrera, Phys. Lett. A165, 206 (1992)

    1992

  71. [79]

    Abreu, H

    H. Abreu, H. Hernandez, L. A. Nunez, Class. Quantum Gravity24, 4631 (2007)

    2007

  72. [80]

    R. Chan, L. Herrera, N. O. Santos, Mon. Not. Roy. Astron. Soc.265, 533 (1993). 19

    1993

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