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Structure of Anisotropic Magnetized Neutron Stars in f(R,T) Gravity with Realistic Equation of State

T0 review · 4 major / 13 minor · reviewed 2026-07-07 · glm-5.2

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Pith's one-line read Modified gravity recasts mass-gap objects as neutron stars

desk verdict Paper derives modified TOV equations in f(R,T) gravity with AV18 EoS and anisotropy; can reach mass-gap masses but only via per-object parameter fitting with λ varying by three orders of magnitude. read the letter →

arxiv 2607.05333 v1 pith:X545L463 submitted 2026-07-06 gr-qc astro-ph.SRnucl-th

M. Savari , G. H. Bordbar , J. Sedaghat , A. Sheykhi This is my paper · ORCID
classification gr-qcastro-ph.SRnucl-th
keywords neutronstarsf(RT)gravitymassgapequationofstateanisotropymagneticfieldgravitationalwavesmodified
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that compact objects in the 2.5–5 solar-mass range—the so-called mass gap where conventional neutron-star equations of state in Einstein gravity cannot reach—can be reinterpreted as neutron stars if one works in the f(R,T) = R + 2λT framework of modified gravity, combined with a microscopic equation of state (AV18 nucleon-nucleon potential), Bowers-Liang pressure anisotropy, and strong density-dependent magnetic fields. The central mechanism is the coupling parameter λ: when λ takes negative values, pressure contributes to the effective gravitational mass, boosting the maximum mass a neutron star can sustain beyond what general relativity allows for the same equation of state. The anisotropy parameter β further increases masses and radii at fixed λ, while stronger surface magnetic fields soften the equation of state and reduce masses. By tuning (λ, β, B_surf), the authors reproduce the masses and radii of known pulsars (PSR J0740+6620, PSR J0952-0607), the binary merger GW170817, and—most strikingly—the secondary components of GW190814 (2.59 M☉) and GW200210-092254 (2.83 M☉), objects whose nature is otherwise unknown. The paper verifies that these configurations are not black holes by showing their Schwarzschild radii remain smaller than their stellar radii, their surface redshifts stay below 0.4, and the Kretschmann scalar remains finite everywhere.

What carries the argument

The modified TOV (Tolman-Oppenheimer-Volkoff) equations in f(R,T) = R + 2λT gravity, where the coupling parameter λ introduces an effective mass contribution from pressure (the m_f(R,T) term in the mass equation). The Bowers-Liang anisotropy model provides the pressure-splitting mechanism (Δ = β G/c^4 (εc^2 + P_r)(εc^2 + 3P_r) e^Ψ r^2). The AV18 nucleon-nucleon potential underlies the equation of state via the LOCV (lowest-order constrained variational) method. A Gaussian density-dependent magnetic field B(ρ) connects surface fields (10^16–10^17 G) to a central value (2×10^18 G).

What would settle it

A future gravitational-wave observation of a mass-gap object with a measured tidal deformability or moment of inertia inconsistent with any neutron-star equation of state—even allowing for modified gravity—would falsify the neutron-star interpretation. Alternatively, if independent constraints on λ from binary pulsar timing or solar-system tests force |λ| to be orders of magnitude smaller than the values used here (−1 to −3), the mass-enhancement mechanism collapses.

Watch

Extended reading notes

Core claim

The paper's central claim is that the linear f(R,T) = R + 2λT modification to gravity, combined with anisotropy and magnetization, provides enough parameter freedom to support neutron-star configurations with masses up to roughly 3.3 solar masses—well into the mass gap—using a realistic microscopic equation of state that in standard general relativity caps out near 1.68 solar masses. The key lever is negative λ, which mixes pressure into the mass equation and enhances the maximum mass monotonically as λ becomes more negative. The authors then show that for each observed compact object, a specific combination of λ (ranging from 0 to −3), β (0 to 1), and surface magnetic field (5×10^16 to 10^5

Load-bearing premise

Each observed compact object is matched with a different, independently chosen combination of the coupling parameter λ, the anisotropy parameter β, and the surface magnetic field, with no single parameter set reproducing all observations and no independent constraints on these parameters from other tests of gravity.

Editorial extensions

If this is right

  • If mass-gap objects like the GW190814 secondary are indeed neutron stars rather than black holes, their tidal deformability in future gravitational-wave events would differ markedly from black-hole predictions—potentially testable with next-generation detectors.
  • The f(R,T) coupling parameter λ, if it genuinely affects compact-star structure at the level claimed (λ ~ −1 to −3), would need to be reconciled with solar-system and binary-pulsar constraints on deviations from general relativity, which typically require λ to be extremely close to zero.
  • A single equation of state (AV18) plus three free parameters (λ, β, B_surf) can fit a wide range of observed masses and radii, but the paper fits each object with a different parameter triple—predictive power would require identifying a narrower allowed region or a correlation between the parameters that is physically motivated.
  • The finite Kretschmann scalar and sub-unity compactness for all mass-gap configurations provide a concrete criterion: if future observations measure compactness C > 1 or divergent curvature invariants for any mass-gap object, the neutron-star interpretation in this framework would fail.

Reading between the lines

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

  • The fact that no single (λ, β, B_surf) triple reproduces all observed compact objects simultaneously suggests either that the parameters are genuinely object-dependent (e.g., different neutron stars have different internal magnetic field topologies and anisotropy levels) or that the framework is functioning as a multi-parameter fit rather than a predictive theory. A joint Bayesian analysis across
  • If λ is constrained by cosmological or solar-system tests to be far smaller than the values used here (|λ| << 0.001), then the mass-gap objects cannot be explained as neutron stars in this specific f(R,T) model, and the paper's mechanism would be effectively ruled out for the mass-gap problem.
  • The Bowers-Liang anisotropy model is a phenomenological prescription, not derived from microphysics; if alternative anisotropy models (e.g., Horvat or Herrera-Barreto) produce different mass-radius relations for the same λ, then the results may be sensitive to this choice in ways the paper does not explore.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 13 minor

Summary. This paper studies neutron star structure in the f(R,T) = R + 2λT model of modified gravity, using the AV18 nucleon-nucleon potential to construct the equation of state (EoS). The authors derive modified isotropic and anisotropic TOV equations (the latter incorporating the Bowers-Liang anisotropy prescription and a density-dependent Gaussian magnetic field profile), solve them numerically, and compute structural quantities including maximum mass, radius, Schwarzschild radius, compactness, surface redshift, and the Kretschmann scalar. The central claim is that mass-gap objects (2.5–5 M☉), specifically the secondary components of GW190814 (2.59 M☉) and GW200210-092254 (2.83 M☉), can be interpreted as neutron stars rather than black holes within this framework. The authors present a table (Table VII) in which the parameters (λ, β, B_surf) are selected to reproduce the observed masses and radii of 17 compact objects.

Significance. The question of whether mass-gap compact objects are neutron stars or black holes is of substantial astrophysical interest, and the systematic derivation of the anisotropic modified TOV equations in f(R,T) gravity (Eqs. 37–38) is a useful technical contribution. The use of a microscopic EoS (AV18 via the LOCV method) and the verification of causality (Fig. 3) are commendable. The computation of the Kretschmann scalar and the demonstration that R_Sch < R for all models provide a self-consistency check that the configurations are not black holes. However, the significance of the central claim is substantially undermined by the treatment of λ as a per-object free parameter (see major comments).

major comments (4)
  1. Table VII and surrounding text (Sec. V): The central claim that mass-gap objects 'can be interpreted as neutron stars' is achieved by assigning a different λ value to each object — e.g., λ = −0.001 for PSR J0740+6620, λ = −3 for GW190814, λ = −2 for GW200210-092254. In f(R,T) = R + 2λT gravity, λ is a fundamental coupling constant of the gravitational theory, not a property of individual stars. Using different effective laws of gravity for different objects does not constitute a unified physical explanation. The paper does not address this issue; the acknowledgment in Sec. VI that results are 'model-dependent' refers to the choice of EoS and anisotropy prescription, not to the per-object variation of a fundamental constant. This is the load-bearing concern for the paper's central claim.
  2. Sec. III.A, text around Fig. 6 (p. 7): The paper states that the parameters are set 'such that the model simultaneously traverses the constraints from mass and radius of the component of GW170817, and masses of the components of GW190814 and GW200210-092254, as well as satisfies the constraints from masses and radii of PSR J0740+6620 and PSR J0030+0451.' This claim of simultaneous satisfaction is contradicted by Table VII, where no single (λ, β) pair reproduces more than one or two objects. The text should be revised to accurately describe what the table shows: individual a posteriori fitting, not simultaneous constraint satisfaction.
  3. Table VII, PSR J0740+6620 row: The observed radius is 13.7^{+2.6}_{−1.5} km, but the theoretical radius reported is 8.714 km (for B_surf = 5.0×10^16 G) or 8.415 km (for B_surf = 1.0×10^17 G, listed for PSR J0348+0432 with the same λ, β). These radii are more than 5σ below the NICER constraint. The paper does not discuss this discrepancy. If the model cannot reproduce the radius of a well-constrained NICER source at the λ value used for that source, the claim of consistency with observational data is overstated.
  4. Sec. IV, Eq. (39): The Schwarzschild radius in f(R,T) gravity is given as R_Sch = (2GM/c²)(1 + 3λ/8π). For λ = −3, the correction factor is 1 − 9/(8π) ≈ 0.642, a 36% reduction. For λ approaching −8π/3, R_Sch vanishes. The paper uses R_Sch < R as evidence that the objects are not black holes, but this criterion is modified by the f(R,T) correction itself. The paper should discuss whether this modified R_Sch criterion is the appropriate horizon condition in f(R,T) gravity, or whether the standard GR Schwarzschild radius (2GM/c²) should be used for the black-hole comparison.
minor comments (13)
  1. Abstract: 'We show that some compact objects residing in the mass gap interpreted as candidates of neutron stars' is grammatically incomplete; a verb is missing.
  2. Sec. III.B, Eq. (30) line: 'where u^μ defined benight Eq. (27)' — 'benight' appears to be a typo, likely 'by'.
  3. Sec. III.A, p. 7: 'the linear madel of f(R, T) gravity' — 'madel' should be 'model'.
  4. Table III caption: 'Schwarzchild' should be 'Schwarzschild' (also appears in the text on p. 12).
  5. Sec. VI: The stray text '0.00,0.07,1.00Collectively, inf(R, T) gravity' appears to be a formatting artifact and should be removed.
  6. Table VII: The B_surf entry for PSR J0952-0607 (first row) is listed as '−1.0×10^17 G', which is presumably a typo for '1.0×10^17 G'.
  7. Table VII: The B_surf entries for GW190814 and GW200210-092254 are listed as '−1.0×10^17 G', which should be '1.0×10^17 G'.
  8. Sec. II, Eq. (10): The parameters η and θ are introduced but their values are only specified in the text (η = 0.05, θ = 2.0 for the adopted slow-decay configuration). It would help to state these values in the caption of Fig. 2 or in a table for clarity.
  9. Sec. III.A, Eq. (29): The definition ζ ≡ 8π + 2λ is dimensionally inconsistent if λ is dimensionless and 8π is dimensionless in geometric units. The paper should clarify the units or conventions used.
  10. Fig. 5 and Fig. 8: The observational error regions for several objects (e.g., GW190814, GW200210) are shown without radius constraints. It would be helpful to explicitly state in the figure caption that these objects have mass-only constraints.
  11. Sec. IV, Eq. (43): The Kretschmann scalar expression contains a factor of λ in the second term and λ² in the third, but the first term has no explicit λ dependence. The derivation or reference for this expression should be provided.
  12. Table I: The entry for λ = −10^{−7} gives M_max = 1.750 M☉, which is lower than the λ = −0.001 entry (2.197 M☉) despite being closer to zero. The monotonicity of the mass–λ relation should be verified or the non-monotonicity explained.
  13. Sec. V, p. 14: The text states 'to reproduce the results of an event like the mass of GW230529A: (i) For B_surf = 5.0×10^16 G, the free parameters λ and β must take the values −2.0 and 1.0. (ii) Conversely, for B_surf = 1.0×10^17 G, the values must be −3.0 and 1.0.' However, Table VII lists GW230529A with λ = −3, β = 1.0, B_surf = 5.0×10^16 G. This inconsistency should be corrected.

Simulated Author's Rebuttal

4 responses · 1 unresolved

We thank the referee for a careful and substantive report. The major comments identify genuine issues that require revision of the manuscript's framing and claims. We address each below.

read point-by-point responses

  1. Referee: Table VII and surrounding text: λ is a fundamental coupling constant, not a per-object free parameter. Using different λ for different objects does not constitute a unified physical explanation.

    Authors: The referee is correct that in f(R,T) = R + 2λT gravity, λ is a fundamental coupling constant of the theory, not a property of individual stars. We acknowledge that assigning different λ values to different objects in Table VII does not constitute a unified explanation in which a single theory with fixed parameters accounts for all observations simultaneously. This is a fair and important criticism of how the central claim is framed. We will revise the manuscript to reframe the contribution honestly: the paper demonstrates that the parameter space of f(R,T) gravity with the AV18 EoS, Bowers-Liang anisotropy, and magnetized matter is broad enough to accommodate mass-gap objects as neutron stars — i.e., that there exist values of λ, β, and B for which the modified TOV equations yield stable configurations with masses and radii consistent with individual observed compact objects including those in the mass gap. We will remove or substantially soften language suggesting a unified explanation. We will also add an explicit discussion of this limitation, noting that a single λ value consistent with all objects simultaneously would be required for a truly unified model, and that our results should be interpreted as a proof-of-principle demonstration rather than a definitive identification. revision: yes

  2. Referee: Sec. III.A, text around Fig. 6: claim of 'simultaneous satisfaction' is contradicted by Table VII, where no single (λ, β) pair reproduces more than one or two objects.

    Authors: The referee is correct. The statement that the model 'simultaneously traverses the constraints' is not supported by Table VII, which shows individual a posteriori fitting with different parameter triples for each object. We will revise the text in Sec. III.A (around Fig. 6) and Sec. V to accurately describe what the table shows: that the explored parameter ranges (λ from 0 to −3, β from 0 to 1) collectively encompass the observational constraints, but no single parameter set reproduces all objects simultaneously. The word 'simultaneously' will be removed or replaced with 'collectively.' revision: yes

  3. Referee: Table VII, PSR J0740+6620 row: theoretical radius 8.714 km is more than 5σ below the NICER constraint of 13.7^{+2.6}_{−1.5} km. The paper does not discuss this discrepancy.

    Authors: The referee is correct that the theoretical radius of 8.714 km for PSR J0740+6620 is significantly below the NICER constraint. We acknowledge this discrepancy, which we failed to discuss in the original manuscript. The small radius arises from the combination of the AV18 EoS (which is relatively soft) with the chosen magnetic field and anisotropy parameters. We will add a discussion of this discrepancy in the revised manuscript, noting that the model underpredicts the radius of PSR J0740+6620 at the parameter values used, and that this indicates the model cannot simultaneously reproduce both the mass and radius of this well-constrained NICER source. This further reinforces the need to soften the claims of consistency with observational data, as discussed in our response to the first comment. We will also add a column or note in Table VII indicating which objects have radius constraints and whether the theoretical radius falls within the observational error bars. revision: yes

  4. Referee: Sec. IV, Eq. (39): The Schwarzschild radius in f(R,T) gravity is modified by the λ correction. The paper should discuss whether this modified R_Sch is the appropriate horizon condition, or whether the standard GR Schwarzschild radius should be used for the black-hole comparison.

    Authors: The referee raises a valid point. The expression R_Sch = (2GM/c²)(1 + 3λ/8π) is derived by matching the interior metric to the exterior Schwarzschild-like solution in f(R,T) gravity with the specific model f(R,T) = R + 2λT. However, the vacuum exterior solution in this model is not standard Schwarzschild, and the question of what constitutes the horizon condition in f(R,T) gravity requires careful treatment. We agree that using the modified R_Sch < R criterion as evidence against black-hole identification is circular to some degree, since the modification itself depends on λ. In the revised manuscript, we will: (i) add a discussion of this subtlety, (ii) note that for the standard GR Schwarzschild radius (2GM/c²), the criterion R > 2GM/c² is also satisfied for all our configurations (since 2GM/c² < R_Sch^{f(R,T)} < R for negative λ), so the conclusion that these objects are not black holes holds regardless of which criterion is used, and (iii) acknowledge that a rigorous determination of the horizon condition in f(R,T) gravity requires solving the full vacuum field equations, which is beyond the scope of this work. revision: yes

standing simulated objections not resolved
  • The fundamental issue raised in the first comment — that λ is a fundamental constant and should not vary per object — cannot be fully resolved within the current framework. While we can reframe the claims and soften the language, the paper as currently structured does not provide a single unified model with one λ value that reproduces all observed compact objects. A truly unified treatment would require either finding a single λ consistent with all observations (which our results suggest may not be possible with the AV18 EoS and Bowers-Liang anisotropy), or extending the model to include additional physics (e.g., a density-dependent coupling λ(ρ) or a more general f(R,T) functional form). We acknowledge this as a genuine limitation of the present work.

Circularity Check

1 steps flagged · score 4.0 of 10

The 'reproduction' of observational masses in Table VII is achieved by per-object parameter fitting (λ spanning three orders of magnitude), but the underlying framework (modified TOV equations, AV18 EoS, structural parameter derivations) is not itself circular.

  1. fitted input called prediction [Table VII and Section V (text around 'reproducing the observational outcomes')]
    "Our analysis concludes that 'reproducing' the observational outcomes necessitates imposing specific constraints on our computational model. For the gravitational model used in this work, in addition to the equation of state, consistency with observational data requires that its parameters satisfy specific constraints. These constraints are detailed in Table VII. [...] We set the parameters such that, in addition to satisfying the mass and radius of GW170817 and the masses of the secondary components GW190814 and GW200210-092254, the coupling and anisotropy parameters we employed not only [...]"

    Table VII assigns a different (λ, β, B_surf) triple to each observed object: PSR J0740+6620 uses λ=−0.001, GW190814 uses λ=−3, GW200210 uses λ=−2. The paper's own Table I shows that decreasing λ monotonically increases maximum mass (1.682 M☉ at λ=0 to 2.509 M☉ at λ=−3), and Table II shows that increasing β further increases mass (up to 3.337 M☉ at λ=−3, β=1). Thus for any target mass in the 1.4–3.3 M☉ range, a suitable (λ, β) pair exists by construction. The 'successful reproduction' of each observed mass is therefore a consequence of selecting the fitting parameters after the fact, not a prediction. The paper frames this as demonstrating that mass-gap objects 'might be interpreted as neutron stars,' but the demonstration reduces to: the parameter space is large enough to cover the mass范围.

full rationale

The paper's derivation chain for the modified TOV equations (Eqs. 26, 29, 37, 38), the EoS (Sec. II), and the structural parameters (Schwarzschild radius, compactness, redshift, Kretschmann scalar) is not circular — these follow from the stated model assumptions (f(R,T)=R+2λT, AV18 potential, Bowers-Liang anisotropy) via standard derivations. The key external citations (Harko et al. [42] for f(R,T) gravity, Bowers & Liang [63] for anisotropy) are not self-citations. The self-citation to Bordbar & Modarres [29] for the EoS is a nuclear physics calculation that is independently verifiable and not load-bearing for the circularity question. The circularity is confined to the observational comparison: the paper fits (λ, β, B_surf) per object in Table VII and calls this 'successful reproduction,' when the paper's own parameter tables show that any mass in the observed range can be produced by appropriate parameter choice. The paper is partially transparent about this (quoting 'reproducing' in Sec. V, acknowledging model dependence in Sec. VI), which prevents a higher score. The physical consistency checks (R > R_Schwarzschild, z < 0.4, causality, finite Kretschmann scalar) provide some independent content beyond the mass fit, though these too are consequences of the chosen parameter values.

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

The paper introduces no new particles, forces, or fields beyond the f(R,T) framework itself (which is from Harko et al. 2011). The free parameters λ and β are the primary fitting handles. The Gaussian magnetic field profile is a phenomenological ansatz, not a new entity. The key concern is that seven free parameters provide substantial fitting freedom for a claim that is tested against ~17 observational data points.

free parameters (7)
  • λ (f(R,T) coupling parameter) = 0 to −3.0
    The non-minimal coupling constant. Selected to produce masses in the desired range. Different values used for different objects in Table VII.
  • β (Bowers-Liang anisotropy parameter) = 0 to 1.0
    Controls the degree of pressure anisotropy. Selected per-object in Table VII to match observational masses and radii.
  • B_surf (surface magnetic field) = 5.0×10^16 G or 1.0×10^17 G
    Two values used across different objects without clear physical justification for the choice per object.
  • B_0 (central magnetic field) = 2.0×10^18 G
    Central magnetic field strength in the Gaussian profile. Fixed across calculations.
  • η (magnetic field decay parameter) = 0.02 or 0.05
    Controls spatial decay of magnetic field. Two sets mentioned; unclear which is used in final results.
  • θ (magnetic field decay exponent) = 3.0 or 2.0
    Controls decay profile shape. Paired with η values above.
  • δ (spin polarization parameter) = 0.1
    Approximate value used in the magnetic energy contribution (Eq. 7). Cited from Refs [69, 70] as an approximation.
assumptions (5)
  • domain assumption f(R,T) = R + 2λT is the correct functional form for the modified gravity action
    Sec. III, Eq. (19). Chosen for tractability; the paper acknowledges non-linear models would be 'overly complicated.' No independent motivation beyond mathematical convenience.
  • domain assumption L_m = P (matter Lagrangian equals pressure)
    Sec. III, stated before Eq. (18). The paper notes 'there is no unique definition' and simply assumes this standard choice.
  • domain assumption Bowers-Liang model for anisotropy (Eq. 31) is physically valid for neutron star interiors
    Sec. III.B. The paper acknowledges 'no universally accepted method' exists and selects this model because it is 'well-known.' No microscopic derivation is provided.
  • domain assumption LOCV two-body cluster expansion truncation is sufficient (three-body and higher terms subdominant)
    Sec. II, Eq. (3). Standard approximation in nuclear many-body theory; expected to be reasonable but not rigorously justified here.
  • ad hoc to paper Gaussian density-dependent magnetic field profile (Eq. 10) represents the interior magnetic field of a neutron star
    Sec. II, Eq. (10). A phenomenological ansatz with parameters η and θ chosen to produce 'rapid' or 'gradual' decay. No magnetohydrodynamic justification provided.

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Cite this review

Pith. "Pith review of Structure of Anisotropic Magnetized Neutron Stars in f(R,T) Gravity with Realistic Equation of State." pith.science (2026). https://pith.science/paper/X545L463

@misc{pith2026260705333,
  author       = {Pith},
  title        = {Pith review of: Structure of Anisotropic Magnetized Neutron Stars in f(R,T) Gravity with Realistic Equation of State},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X545L463}},
  note         = {Machine review of arXiv:2607.05333}
}
read the original abstract

In this study, within the framework of f(R,T) modified gravity, we investigate the influence of coupling parameter, magnetic field and anisotropy parameter on the neutron star structure. This work employs an accurate equation of state (EoS), derived from realistic microscopic calculations based on the AV18 nucleon-nucleon potential, to compute the structure of this compact object. Here, determination of Schwarzschild radius, compactness, gravitational surface redshift and Kretschmann scalar within the f(R, T) gravity, confirms that our theoretical results are consistent with the observational constraints. While established physical EoSs within the framework of Einstein gravity have successfully characterized a broad range of compact objects, they remain inadequate in explaining certain massive objects residing within the mass gap (2.5 to 5 Msun). We show that some compact objects residing in the mass gap interpreted as candidates of neutron stars within the framework of f(R, T) gravity. Finally, we compare our results with the observational data from LIGO/Virgo/KAGRA and NICER, setting the parameters of the f(R, T) theory and anisotropy to successfully reproduce the masses and radii of the GW170817, PSR J0952-0607 and PSR J0740+6620 and the masses of the secondary components of GW190814 and GW200210-092254.

Figures

Figures reproduced from arXiv: 2607.05333 by the authors.

Figure 1
Figure 1. Left panel: The radial pressure and tangential pressure vs energy density ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. The ratio of the squared speed of sound to the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. The radial pressure (Pr) and tangential pressure (Pt) vs energy density with the Gaussian form of magnetic field . The non-magnetized case has been also given for comparison. To ensure the physical validity of our model, we ex￾amine the causality condition for both the isotropic and anisotropic magnetized cases, where the radial pressure component exhibits slow decay. The condition of causal￾ity is given as follows,… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The mass-central energy density relation to [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: Monotonic behavior of the linear madel of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: The mass-central energy density panels for two magnetic fields [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: The mass-radius relations for two magnetic fields [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: The effect of the central magnetic field on the [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Comparison of the Schwarzschild radius with [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

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