pith. sign in

arxiv: 2605.21564 · v2 · pith:FNQ6K2IBnew · submitted 2026-05-20 · 🌀 gr-qc

Astrophysical Objects in Modified Theories of Gravity

Sneha Pradhan This is my paper

Pith reviewed 2026-06-30 17:02 UTC · model grok-4.3

classification 🌀 gr-qc
keywords compact starsmodified gravityf(Q) gravityf(T) gravitygravitational decouplingneutron starsstrange starsBayesian constraints
0
0 comments X

The pith

Modified gravity theories produce compact star models with altered masses and radii that still match observations.

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

The thesis constructs models of neutron stars and strange stars in f(Q) and f(T) gravity using conformal symmetry, the MIT Bag equation of state, and gravitational decoupling via geometric deformation. It matches these interiors to exterior solutions like Bardeen spacetime and checks viability through energy conditions, the Tolman-Oppenheimer-Volkoff equation, and stability criteria. Bayesian fitting to NICER mass-radius data then constrains the extra parameters. If the results hold, observers can describe the same stars inside frameworks that differ from general relativity yet remain compatible with existing measurements.

Core claim

Exact analytical solutions for charged isotropic stars in f(Q) gravity and anisotropic strange stars in f(T) gravity demonstrate that the modified gravity parameters directly shift maximum mass, radius, compactness, and stability ranges while satisfying physical regularity conditions and remaining consistent with astrophysical observations after Bayesian constraint.

What carries the argument

Gravitational decoupling through minimal and complete geometric deformation methods applied to f(T) gravity, together with conformal symmetry in f(Q) gravity, to incorporate extra sources and generate matched interior-exterior solutions.

If this is right

  • Increasing the modified gravity parameters can raise or lower the maximum stable mass of strange stars while preserving causality and energy conditions.
  • The generalized Tolman-Oppenheimer-Volkoff equation remains satisfied, allowing equilibrium configurations under additional gravitational sources.
  • Bayes factor analysis selects viable extensions of gravity that fit NICER data without requiring fine-tuning beyond observational bounds.
  • Inclusion of dark matter effects through extra sources produces stable anisotropic models that pass Herrera's cracking test.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Tighter future mass-radius measurements could shrink the allowed range of modified gravity parameters until only general relativity survives or until a clear deviation appears.
  • The same deformation techniques might generate black-hole solutions whose shadows or ringdown signals differ detectably from general relativity.
  • If the MIT Bag assumption is relaxed to other equations of state, the same geometric methods could map out how sensitive the mass-radius shifts are to the choice of microphysics.

Load-bearing premise

The MIT Bag equation of state together with conformal symmetry and geometric deformation accurately describes the matter and geometry inside real compact stars.

What would settle it

Discovery of a compact star whose measured mass and radius lie outside every parameter-tuned solution in these f(Q) or f(T) models yet inside the corresponding general-relativity solution would falsify the compatibility result.

Figures

Figures reproduced from arXiv: 2605.21564 by Sneha Pradhan.

Figure 1.1
Figure 1.1. Figure 1.1: Hertzsprung–Russell (HR) diagram displaying stellar luminosity against spectral type for approximately four million stars within 5000 light-years of the Sun. The main sequence (diagonal band), red giant branch, horizontal branch, and white dwarf region are clearly visible, representing different stages of stellar evolution.Credit: ESA/Gaia/DPAC [5]. However, as the nuclear fuel in the stellar core is gra… view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: First detect image of the supermassive black hole located at the center of the M87 galaxy. (Image credit: EHT Collaboration, 2019). The X-ray source Cygnus X-1, recognized as the first confirmed candidate for a stellar￾mass black hole, was independently discovered by Bolton [42] and Webster & Murdin [43]. Subsequent astronomical studies provided further evidence for the existence of stellar-mass black ho… view at source ↗
Figure 1.3
Figure 1.3. Figure 1.3: Moving a vector around a closed loop changes its direction, measured by Rν βαµ. In the framework of GR, the curvature tensor arises solely from the Levi-Civita connection, which is symmetric and metric-compatible. This ensures that torsion and non-metricity vanish, and curvature fully encodes the gravitational interaction. However, in more general geometric theories such as those incorporating torsion or… view at source ↗
Figure 1.4
Figure 1.4. Figure 1.4: Left panel: In Euclidean geometry, parallel transport along two vectors forms a closed parallelogram. Right panel: In a space with torsion, the parallelogram does not close; the separation between the endpoints measures the torsion tensor T α µν. Thus, The torsion tensor has an interesting geometrical interpretation: if one builds infinitesimal parallelograms in the manifold (by parallel transport), the … view at source ↗
Figure 1.5
Figure 1.5. Figure 1.5: Change in the length of a vector under parallel transport arises from non-metricity. However, in a non-metric geometry condition ∇λgµν ̸= 0 holds. In this case, the connection allows the metric itself to vary from point to point under parallel transport. Physically, this means that as a vector is carried along a path from one point p to another point q, its length or magnitude can change. From Fig. (1.5)… view at source ↗
Figure 1.6
Figure 1.6. Figure 1.6: The rotation of a vector transported along a closed curve given by Rα βµν. In contrast, the symmetric part Rα (β)µν arises in non-metric geometries and describes a change in the magnitude (length) of the vector after parallel transport. Hence, in a general affine geometry, curvature can induce both a rotational and a stretching effect on transported vectors. Fig. (1.6) illustrates the rotation of a vecto… view at source ↗
Figure 1.7
Figure 1.7. Figure 1.7: Schematic classification of higher-order gravity theories obtained by incorporating additional curvature invariants into the Lagrangian of GR. Higher-order field equations: Although Einstein’s field equations contain derivatives only up to the second order, several modified gravity theories extend this idea by including higher-order derivatives. Although such extensions often introduce mathematical compl… view at source ↗
Figure 1.8
Figure 1.8. Figure 1.8: Schematic classification of higher-order gravity theories obtained by incorporating additional curvature invariants into the Lagrangian of GR. Changing geometry: Non-Riemannian theories of gravity Another direction of modifying GR involves altering the underlying geometric structure of spacetime rather than adding new fields or higher-order invariants. These frameworks generalize Riemannian geometry by r… view at source ↗
Figure 1.9
Figure 1.9. Figure 1.9: Schematic classification of higher-order gravity theories obtained by incorporating additional curvature invariants into the Lagrangian of GR [PITH_FULL_IMAGE:figures/full_fig_p040_1_9.png] view at source ↗
Figure 1.10
Figure 1.10. Figure 1.10: A schematic diagram among the relation of energy condition: An arrow from A to B in the illustration indicates that A implies B. The NEC requires the energy density measured by any null observer to be non-negative. It serves as a foundational requirement upon which both the WEC and the SEC are built. Formally, for any null vector l m, Tmn l ml n ≥ 0, which translates to the effective inequalities ρ + pr… view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: , we observe that model-I exhibits finite, continuous, and monotonically increasing metric functions throughout the star. In contrast, model-II develops a central singularity owing to the linear choice of the conformal factor, although the metric potentials remain well behaved away from the core. This indicates that the power-law conformal factor is more suitable for constructing physically viable compac… view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: , both the pressure and energy density attain their maximum values at the stellar center and decrease smoothly towards the surface, where the pressure vanishes. This behavior confirms the physical acceptability of the constructed models, with the concave nature of the profiles arising from the combined effects of conformal symmetry and electric charge. PSR J1614-2230 PSR J1903+327 Vela X-1 Cen X-3 SMC X-… view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Behavior of pressure gradient and matter density gradient for model-I (upper panel) and model-II (lower panel). Here, we consider m = −2, n = 0.02 for model-I and m = 2, n = −1 for model-II. 3. Energy conditions: Energy conditions provide essential consistency checks for physically realistic stellar models and have been extensively discussed earlier. In the present analysis, we verify the null, weak, str… view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: Behavior of energy conditions for model-I (upper panel) and model-II (lower panel). Here, we consider m = −2, n = 0.02 for model-I and m = 2, n = −1 for model-II. 2. Relativistic adiabatic index: The relativistic adiabatic index provides an important criterion for assessing the dynamical stability of compact stars. As discussed earlier, stability requires Γ > 4/3. From [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
Figure 2.5
Figure 2.5. Figure 2.5: Behavior of adiabatic index for model-I (left panel) and model-II (right panel). Here, we consider m = −2, n = 0.02 for model-I and m = 2, n = −1 for model-II. 3. Equilibrium conditions: The equilibrium of a charged compact star is governed by the TOV equation, which ensures the balance between gravitational, hydrostatic, and electric [PITH_FULL_IMAGE:figures/full_fig_p067_2_5.png] view at source ↗
Figure 2.6
Figure 2.6. Figure 2.6: Behavior of different forces for model-I (left panel) and model-II (right panel). The different colors represents, PSR J1614-2230(⋆), PSR J1903+327 (⋆), Vela X-1 (⋆), Cen X-3 (⋆), and SMC X-1 (⋆). Here, we consider m = −2, n = 0.02 for model-I and m = 2, n = −1 for model-II. forces. For a static and spherically symmetric configuration, these forces are given by Fg = − ν ′ 2 (ρ eff + p eff), Fh = − dpeff … view at source ↗
Figure 2.7
Figure 2.7. Figure 2.7: Comparison between the Bardeen and R-N spacetime. 2.7 Conclusion In this chapter, we explored the structure of charged compact stars within the framework of f(Q) gravity by employing CKVs. The stellar interior is modeled as a charged perfect fluid obeying [PITH_FULL_IMAGE:figures/full_fig_p070_2_7.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: The density profile [ρ eff(r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.1 [Θ0 0 = ρ] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  -left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p083_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: The radial pressure profile [p eff r (r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.1 [Θ0 0 = ρ] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  -left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p083_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: The effective tangential pressure profile [p eff t (r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.1 [Θ0 0 = ρ] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  -left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p083_3_3.png] view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: The effective anisotropy profile [∆eff(r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.1 [Θ0 0 = ρ] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  -left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p084_3_4.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: The effective density profile [ρ eff(r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.2 [Θ1 1 = pr] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  - left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p084_3_5.png] view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: The effective radial pressure profile [p eff r (r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.2 [Θ1 1 = pr] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  -left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p084_3_6.png] view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: The effective tangential pressure profile [p eff t (r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.2 [Θ1 1 = pr] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  -left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p085_3_7.png] view at source ↗
Figure 3.8
Figure 3.8. Figure 3.8: The effective anisotropy profile [∆eff(r)] in [km−2 ] along to the radial distance r of the stellar model for solution 3.3.2 [Θ1 1 = pr] in context of GR α = 0.0, ζ1 = 1.0, ζ2 = 0.0 [km−2 ]  -left panel, f(T) [PITH_FULL_IMAGE:figures/full_fig_p085_3_8.png] view at source ↗
Figure 3.9
Figure 3.9. Figure 3.9: The M − R curves for different free parameters values α-left panel with fixed β = 0.33, γ = 20, ζ1 = 0.5 and right figure shows the M − R curves for different β with fixed α = 0.5, γ = 15, and ζ1 = 0.5. The both figures represent the mass-radius relation for solution 3.3.1 Θ0 0 = ρ [PITH_FULL_IMAGE:figures/full_fig_p086_3_9.png] view at source ↗
Figure 3.10
Figure 3.10. Figure 3.10: The M − R curves for different free parameters values γ-left panel with fixed β = 0.33, α = 0.5 km2 , ζ1 = 0.5 and right figure shows the M − R curves for different ζ1 with fixed α = 0.5, γ = 15, and β = 0.33. The both figures represent the mass-radius relation for solution 3.3.1 Θ0 0 = ρ [PITH_FULL_IMAGE:figures/full_fig_p086_3_10.png] view at source ↗
Figure 3.11
Figure 3.11. Figure 3.11: The M − R curves for different free parameters values α-left panel with fixed β = 0.33, γ = 20, ζ1 = 0.3 and right figure shows the M − R curves for different ζ1 with fixed α = 0.2, γ = 20, and β = 0.33. The both figures represent the mass-radius relation for solution 3.3.2 Θ1 1 = pr [PITH_FULL_IMAGE:figures/full_fig_p087_3_11.png] view at source ↗
Figure 3.12
Figure 3.12. Figure 3.12: Graphical analysis of adiabatic index for different values of the model parameter ζ1 for the solution ρ = Θ0 0 and pr = Θ1 1 respectively, where α = 0.5 km2 and α = 0.2 km2 respectively [PITH_FULL_IMAGE:figures/full_fig_p088_3_12.png] view at source ↗
Figure 3.13
Figure 3.13. Figure 3.13: Graphical analysis of mass and dM dρc with respect to central density (ρc) for different values of the model parameter for the solution ρ = Θ0 0 . ζ1 = 0.60 ζ1 = 0.65 δζ1 = 0.01 pr = θ1 1 0.005 0.006 0.007 0.008 0.009 0.010 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Central density (ρc) [km-2 ] Mass [M⊙] pr = θ1 1 ζ1 = 0.65 ζ1 = 0.60 δζ1 = 0.01 0.005 0.006 0.007 0.008 0.009 0.010 200 220 240 260 280 Central density (ρ… view at source ↗
Figure 3.14
Figure 3.14. Figure 3.14: Graphical analysis of mass and dM dρc w.r.t. central density (ρc) for different values of the model parameter for the solution pr = Θ1 1 . In this context, we analyze the stability of the solution ρ = Θ0 0 and pr = Θ1 1 in [PITH_FULL_IMAGE:figures/full_fig_p089_3_14.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Graphical analysis of energy density (left) [α = 0.1(⋆), α = 0.2(⋆), α = 0.3(⋆), α = 0.4(⋆), α = 0.5(⋆), α = 0.6(⋆)] and radial pressure (right) for C = 0.288 km−2 ; D = 0.1; A = 0.009 km−2 ; B = 0.000009 km−4 ;L = 0.0009 km−2 ; N = 0.0009 km−2 . model within the CGD framework of teleparallel gravity. The construction of a physically acceptable dark star model within the CGD framework requires a smooth m… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Graphical analysis of tangential pressure (left) and anisotropy (right) for C = 0.288 km−2 ; D = 0.1; A = 0.009 km−2 ; B = 0.000009 km−4 ;L = 0.0009 km−2 ; N = 0.0009 km−2 . ρ tot , p tot r , p tot t and anisotropy (∆tot) in Figs. 4.1 and 4.2 provides a comprehensive view of the energy distribution within the stellar model. Our analysis reveals that ρ tot , p tot r , and p tot t satisfy the essential cri… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Graphical analysis of the density gradient (left), the radial pressure gradient (middle) and the tangential pressure gradient (right) with respect to ’r,’ for C = 0.288 km−2 ; D = 0.1; A = 0.009 km−2 ; B = 0.000009 km−4 ;L = 0.0009 km−2 ; N = 0.0009 km−2 . From Figs. 4.1 and 4.2, it is evident that all energy conditions are satisfied throughout the stellar interior. The effective energy density remains p… view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Stability analysis via adiabatic index (Γ) for C = 0.288 km−2 ; D = 0.1; A = 0.009 km−2 ; B = 0.000009 km−4 ;L = 0.0009 km−2 ; N = 0.0009 km−2 . α=0.1 α=0.2 α=0.3 α=0.4 α=0.5 α=0.6 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 r [km] Vr 2 α=0.1 α=0.2 α=0.3 α=0.4 α=0.5 α=0.6 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 r [km] Vt 2 α=0.1 α=0.2 α=0.3 α=0.4 α=0.5 α=0.6 0 2 4 6 8 0.00 0.05 0.10 0.15 r [km] |Vr 2 - Vt 2 | [PITH… view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Stability analysis via speed of sound w.r.t. ’r’ for C = 0.288 km−2 ; D = 0.1; A = 0.009 km−2 ; B = 0.000009 km−4 ;L = 0.0009 km−2 ; N = 0.0009 km−2 . Smaller values of α are sufficient to maintain core stability, whereas near the stellar surface the influence of α becomes negligible, as the stability condition is satisfied throughout. 4.5.2 Causality criterion & Herrera’s cracking method The stability o… view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Graphical analysis of mass (M⊙) with respect to central density ρc for C = 0.288 km−2 ; D = 0.1; A = 0.009 km−2 ; B = 0.000009 km−4 ;L = 0.0009 km−2 ; N = 0.0009 km−2 . 4.5.3 Harrison–Zeldovich–Novikov criterion The stability of the anisotropic dark star model is further examined using the HZN criterion, which is based on the response of the stellar mass to variations in the central density. According to… view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Prediction of radii of some well-known compact objects from our model for different values of the decoupling parameter α (left) and model parameter ζ1 (right) [PITH_FULL_IMAGE:figures/full_fig_p100_4_7.png] view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: (Left panel) Equi-mass contour in ζ1 − ζ2 plane, (middle panel) in ζ1 − α plane, and (right panel) in ζ2 − α plane are shown. 4.7 Mass measurement via equi-mass planes In this section, a couple of contour plots are drawn for in-depth analysis of the mass of our current model. We have displayed the equi-mass contours in the ζ1 − ζ2 and ζ1 − α planes in the left and middle panels, respectively, of [PITH_F… view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: Energy exchange between the fluid and dark matter in the r − α plane (left) and r − ζ1 plane (right) for C = 0.288 km−2 ; D = 0.1; A = 0.009 km−2 ; B = 0.000009 km−4 ;L = 0.0009 km−2 ; N = 0.0009 km−2 . [170, 180], the energy exchanged between the two sources is quantified by the scalar δE, defined as δE = Φ ′ (r) 2 (ρ + pr), (4.27) where Φ(r) is the temporal deformation function. Since the energy densit… view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: The energy density (ε) (in MeV fm−3 )(left panel), pressure (p) (in MeV.fm−3 ) (middle panel), and speed of sound (c 2 s ) (in c 2 ) (right panel) as a function of baryon density (ρ) (in fm−3 ) for DDME2 [PITH_FULL_IMAGE:figures/full_fig_p111_5_1.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: The marginalized posterior distributions of the f(Q) model parameters, obtained through Bayesian inference, for linear (red), logarithmic (purple), and exponential (green) models. The vertical lines indicate the 68% confidence interval of the parameters. The confidence ellipses for two-dimensional posterior distributions are plotted with 1σ, 2σ and 3σ confidence intervals. only moderately constrained, su… view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Corner plots for the marginalized posterior distributions of the tidal deformability Λ1.4, radii R1.4 (km) and R2.07 (km) and the maximum mass Mmax (M⊙) for linear (red), logarithmic (purple), and exponential (green). 10.00 12.00 14.00 R [km] 1.0 1.5 2.0 2.5 M [ M ] J0740 J0030 J0614 J0437 250 500 750 1000 Linear Logarithmic Exponential 0.10 0.15 0.20 0.25 M/R [PITH_FULL_IMAGE:figures/full_fig_p115_5_3.png] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: The 95% confidence interval distributions for the radius R (km) (left panel), tidal deformability Λ (middle panel) and compactness M/R (right panel) as a function of NS mass M (M⊙) [PITH_FULL_IMAGE:figures/full_fig_p115_5_4.png] view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: The Pearson’s correlation coefficients among parameters and selected NS properties for linear (left panel), logarithmic (middle panel), and exponential(right panel). Lin Log Exp 15 10 5 0 5 10 15 Lin Log Exp 2 0 2 4 Lin Log Exp 1.0 0.5 0.0 0.5 1.0 Q [PITH_FULL_IMAGE:figures/full_fig_p116_5_5.png] view at source ↗
Figure 5.6
Figure 5.6. Figure 5.6: Violin plots of the posterior distributions for the f(Q) model parameters α (left), β (middle), and Q0 (right) for the linear (Lin), logarithmic (Log), and exponential (Exp) models [PITH_FULL_IMAGE:figures/full_fig_p116_5_6.png] view at source ↗
read the original abstract

This thesis investigates compact astrophysical objects within modified theories of gravity, focusing on neutron stars and strange stars. The work studies their internal structure, equilibrium, and stability in gravitational frameworks based on torsion and nonmetricity, which provide the foundation for theories such as f(Q) and f(T) gravity. Charged isotropic compact star models are constructed in f(Q) gravity using conformal symmetry and the MIT Bag equation of state, with matching to the Bardeen exterior spacetime. Gravitational decoupling techniques, including minimal and complete geometric deformation methods, are employed in f(T) gravity to generate anisotropic strange star models. These approaches enable the inclusion of additional gravitational sources, dark matter effects, and spacetime deformations. Exact analytical solutions are obtained under suitable physical conditions such as regularity and vanishing complexity. The models are examined using energy conditions, causality constraints, the generalized Tolman-Oppenheimer-Volkoff equation, and Herrera's cracking criterion to ensure physical viability and stability. The influence of modified gravity parameters on stellar mass, radius, compactness, and stability is analyzed in detail. A Bayesian statistical framework is applied to constrain model parameters using observational data, including NICER mass-radius measurements. Bayes factor analysis is further used to identify viable gravitational extensions consistent with astrophysical observations. The results show that modified gravity can significantly affect the maximum mass, radius, and stability of compact stars while remaining compatible with observations. This work provides a systematic theoretical and observational study of compact stars beyond general relativity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. This thesis constructs charged isotropic compact star models in f(Q) gravity via conformal symmetry and the MIT Bag EOS matched to Bardeen exterior, and anisotropic strange star models in f(T) gravity via minimal and complete geometric deformation. It derives exact solutions under regularity and vanishing complexity, verifies viability via energy conditions, causality, generalized TOV, and Herrera cracking, analyzes effects of modified-gravity parameters on mass/radius/stability, and applies Bayesian inference with NICER mass-radius data plus Bayes factors to constrain parameters, concluding that the extensions significantly alter stellar properties while remaining observationally compatible.

Significance. If the central constructions hold, the work supplies analytical interior solutions and statistical constraints for compact objects in torsion- and nonmetricity-based gravity, with explicit inclusion of additional sources and deformations. Strengths include the systematic use of standard viability tests and the application of Bayes factors for model comparison. However, the overall significance is limited because the reported effects on maximum mass and radius rest on the specific MIT Bag EOS and geometric assumptions without demonstrated robustness against alternative microphysical EOS families.

major comments (2)
  1. [Abstract] Abstract: the headline claim that f(Q) and f(T) parameters produce significant shifts in maximum mass, radius, and stability rests on the MIT Bag relation p = (ρ − 4B)/3 together with conformal symmetry (f(Q) sector) and minimal/complete geometric deformation (f(T) sector). No cross-check against stiffer or density-dependent EOS families is described, so it remains possible that the reported shifts are driven by the matter-sector simplification rather than the modified-gravity terms.
  2. [Abstract] Abstract: the Bayesian framework constrains the f(Q) and f(T) parameters directly against NICER mass-radius measurements. Because the models are constructed precisely to reproduce such data, the posteriors risk being adjustments rather than independent tests; the abstract gives no indication of external benchmarks, parameter-free predictions, or out-of-sample validation that would ground the constraints.
minor comments (1)
  1. [Abstract] The abstract refers to “vanishing complexity” without defining the complexity scalar or its relation to the field equations; a brief parenthetical or reference would clarify the condition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed report and constructive feedback on our thesis. We address each major comment point by point below, with revisions made where feasible within the scope of the work.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim that f(Q) and f(T) parameters produce significant shifts in maximum mass, radius, and stability rests on the MIT Bag relation p = (ρ − 4B)/3 together with conformal symmetry (f(Q) sector) and minimal/complete geometric deformation (f(T) sector). No cross-check against stiffer or density-dependent EOS families is described, so it remains possible that the reported shifts are driven by the matter-sector simplification rather than the modified-gravity terms.

    Authors: We acknowledge that the reported effects on stellar properties are obtained within the MIT Bag EOS framework, which is a standard choice for strange stars enabling analytical solutions under conformal symmetry and geometric deformation. The primary aim was to isolate and quantify the influence of the modified-gravity parameters on mass, radius, and stability criteria. We agree that robustness checks against alternative EOS families would strengthen the conclusions. As a partial revision, we have added a dedicated paragraph in the conclusions section explicitly stating the dependence on the MIT Bag EOS and identifying cross-checks with stiffer or density-dependent EOS as an important avenue for future research. revision: partial

  2. Referee: [Abstract] Abstract: the Bayesian framework constrains the f(Q) and f(T) parameters directly against NICER mass-radius measurements. Because the models are constructed precisely to reproduce such data, the posteriors risk being adjustments rather than independent tests; the abstract gives no indication of external benchmarks, parameter-free predictions, or out-of-sample validation that would ground the constraints.

    Authors: The Bayesian analysis provides posterior constraints on the f(Q) and f(T) parameters (as well as other model parameters) conditioned on the NICER mass-radius data, with Bayes factors used for quantitative model comparison between general relativity and the modified-gravity extensions. This follows standard practice for parameter estimation and evidence-based model selection in astrophysical contexts. We maintain that the resulting bounds and Bayes factors constitute meaningful statistical tests of the viability of the extensions. To improve clarity, we have revised the abstract to explicitly describe the use of Bayes factors for model comparison and the nature of the constraints obtained. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard model construction and external data constraints

full rationale

The provided abstract and context describe construction of exact solutions via MIT Bag EOS plus conformal symmetry (f(Q)) or geometric deformation (f(T)), followed by standard viability checks (energy conditions, TOV, cracking) and Bayesian parameter constraints against NICER observations. No quoted equation or step reduces a claimed prediction or result to its own fitted inputs by construction, nor relies on self-citation load-bearing or imported uniqueness theorems. The observational comparison uses external data and does not force the compatibility claim tautologically; the derivation remains self-contained with independent theoretical content.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central claims rest on several domain assumptions about the form of the gravity theories and the matter equation of state, plus free parameters that are fitted rather than derived; no new entities are postulated.

free parameters (2)
  • f(Q) gravity function parameter
    Extra degree of freedom in the nonmetricity-based theory adjusted to produce viable stellar models and fit NICER data
  • f(T) gravity function parameter
    Extra degree of freedom in the torsion-based theory adjusted via Bayesian analysis to match observations
axioms (3)
  • domain assumption Spacetime geometry is described by f(Q) or f(T) rather than the Einstein-Hilbert action
    Invoked at the outset to define the gravitational frameworks for all model constructions
  • domain assumption MIT Bag equation of state governs the matter inside strange stars
    Used to close the system of equations for anisotropic strange star models
  • ad hoc to paper Conformal symmetry holds for the interior metric of charged isotropic models
    Assumed to obtain exact analytical solutions in f(Q) gravity

pith-pipeline@v0.9.1-grok · 5784 in / 1631 out tokens · 54460 ms · 2026-06-30T17:02:28.945596+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

246 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Einstein,Annalen der Physik,49, 769 (1916)

    A. Einstein,Annalen der Physik,49, 769 (1916)

    1916

  2. [2]

    J. H. Jeans,Philosophical Transactions of the Royal Society of London. Series A,199, 1 (1902)

    1902

  3. [3]

    F. H. Shu, F. C. Adams, and S. Lizano,Annual Review of Astronomy and Astrophysics,25, 23 (1987)

    1987

  4. [4]

    K. D. Abhyankar,Astrophysics: Stars and Galaxies, Tata McGraw-Hill (1992)

    1992

  5. [5]

    Babusiaux,et al.,Astronomy & Astrophysics,616, A10 (2018)

    Gaia Collaboration, C. Babusiaux,et al.,Astronomy & Astrophysics,616, A10 (2018)

    2018

  6. [6]

    H. A. Bethe,Physical Review,55, 434–456 (1939)

    1939

  7. [7]

    Gamow,Physical Review,53, 595–600 (1938)

    G. Gamow,Physical Review,53, 595–600 (1938)

    1938

  8. [8]

    W. J. Luyten,Harv. Coll. Obs. Circ.243, 1 (1922)

    1922

  9. [9]

    W. J. Luyten,Harv. Coll. Obs. Circ.245, 1 (1922)

    1922

  10. [10]

    W. J. Luyten,Harv. Coll. Obs. Circ.246, 1 (1922)

    1922

  11. [11]

    Herschel,Philos

    W. Herschel,Philos. Trans. R. Soc. Lond.73, 247 (1783)

  12. [12]

    W. S. Adams,Astrophys. J.40, 385 (1914)

    1914

  13. [13]

    F. W. Bessel,Mon. Not. R. Astron. Soc.6, 136 (1844)

  14. [14]

    P. A. M. Dirac,Proc. R. Soc. A112, 661 (1926)

    1926

  15. [15]

    R. H. Fowler,Mon. Not. R. Astron. Soc.87, 114 (1926)

    1926

  16. [16]

    Chandrasekhar,Astrophys

    S. Chandrasekhar,Astrophys. J.74, 81 (1931)

    1931

  17. [17]

    Chandrasekhar,Mon

    S. Chandrasekhar,Mon. Not. R. Astron. Soc.91, 456 (1931)

    1931

  18. [18]

    Baade and F

    W. Baade and F. Zwicky,Phys. Rev.4676-77 (1934)

    1934

  19. [19]

    Chadwick,Proceedings of the Royal Society of London

    J. Chadwick,Proceedings of the Royal Society of London. Series A136(830), 692 (1932)

    1932

  20. [20]

    J. R. Oppenheimer, & G. M. Volkoff,Physical Review,55, 374–381 (1939)

    1939

  21. [21]

    I. S. Shklovsky,Astrophys. J. Lett.148L1 (1967)

    1967

  22. [22]

    Hewish, et al.,Nature,217, 709–713 (1968)

    A. Hewish, et al.,Nature,217, 709–713 (1968)

    1968

  23. [23]

    Pacini,Nature,216, 567–568 (1967)

    F. Pacini,Nature,216, 567–568 (1967). 106 References 107

    1967

  24. [24]

    B. P. Abbott et al., (LIGO Scientific Collaboration and Virgo Collaboration)Physical Review Letters,119, 161101 (2017)

    2017

  25. [25]

    Bombaci,Astronomy and Astrophysics,305, 871 (1996)

    I. Bombaci,Astronomy and Astrophysics,305, 871 (1996)

    1996

  26. [26]

    Gell-Mann,Phys

    M. Gell-Mann,Phys. Lett.,8, 214 (1964)

    1964

  27. [27]

    Zweig,CERN Report No

    G. Zweig,CERN Report No. 8182/TH.401(1964)

    1964

  28. [28]

    D. D. Ivanenko and D. F. Kurdgelaidze,Astrophysics,1, 251 (1965)

    1965

  29. [29]

    Itoh,Prog

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

    1970

  30. [30]

    A. R. Bodmer,Phys. Rev. D,4, 1601 (1971)

    1971

  31. [31]

    Witten,Phys

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

    1984

  32. [32]

    Terazawa,J

    H. Terazawa,J. Phys. Soc. Jpn.,58, 3555 (1989)

    1989

  33. [33]

    Michell, Phil

    J. Michell, Phil. Trans. R. Soc. Lond.,74, 35 (1784)

  34. [34]

    P. S. Laplace,Exposition du Systeme du Monde, (1796)

  35. [35]

    Schwarzschild, Sitzungsber

    K. Schwarzschild, Sitzungsber. Preuss. Akad. Wiss.Berlin (Math. Phys.),1916, 189 (1916)

    1916

  36. [36]

    Finkelstein,Phys

    D. Finkelstein,Phys. Rev.,110, 965 (1958)

    1958

  37. [37]

    R. P. Kerr,Phys. Rev. Lett.,11, 237 (1963)

    1963

  38. [38]

    E. T. Newman et al.,J. Math. Phys.,6, 918 (1965)

    1965

  39. [39]

    Penrose,Phys

    R. Penrose,Phys. Rev. Lett.,14, 57 (1965)

    1965

  40. [40]

    S. W. Hawking and R. Penrose,Proc. R. Soc. Lond. A,314, 529 (1970)

    1970

  41. [41]

    Penrose,Gen

    R. Penrose,Gen. Relativ. Gravit.,34, 1141 (2002)

    2002

  42. [42]

    C. T. Bolton,Nature,235, 271 (1972)

    1972

  43. [43]

    B. L. Webster and P. Murdin,Nature,235, 37 (1972)

    1972

  44. [44]

    R. A. Remillard and J. E. McClintock,Annu. Rev. Astron. Astrophys.,44, 49 (2006)

    2006

  45. [45]

    Kormendy and D

    J. Kormendy and D. Richstone,Annu. Rev. Astron. Astrophys.,33, 581 (1995)

    1995

  46. [46]

    The Event Horizon Telescope Collaboration,Astrophys. J. Lett.,875, L1 (2019)

    2019

  47. [47]

    Casares and P

    J. Casares and P. G. Jonker,Space Sci. Rev.,183, 223 (2014)

    2014

  48. [48]

    Weinberg,Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972)

    S. Weinberg,Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972)

    1972

  49. [49]

    C. M. Will,Living Reviews in Relativity,17, 4 (2014)

    2014

  50. [50]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation(W. H. Freeman, San Francisco, 1973)

    1973

  51. [51]

    J. V. Narlikar,Introduction to Cosmology, Cambridge University Press, Cambridge(2002)

    2002

  52. [52]

    Weinberg,Reviews of Modern Physics61, 1 (1989) References 108

    S. Weinberg,Reviews of Modern Physics61, 1 (1989) References 108

    1989

  53. [53]

    Padmanabhan,Physics Reports380, 235 (2003)

    T. Padmanabhan,Physics Reports380, 235 (2003)

    2003

  54. [54]

    Clifton, P

    T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis,Physics Reports513, 1 (2012)

    2012

  55. [55]

    Heisenberg, Phys

    L. Heisenberg,Review onf(Q)Gravity, arXiv:2309.15958 [gr-qc] (2023)

    work page arXiv 2023

  56. [56]

    R. P. Woodard,Lect. Notes Phys.720, 403–433 (2007)

    2007

  57. [57]

    T. P. Sotiriou and V. Faraoni,Rev. Mod. Phys.82, 451–497 (2010)

    2010

  58. [58]

    De Felice and S

    A. De Felice and S. Tsujikawa,Living Rev. Relativity13, 3 (2010)

    2010

  59. [59]

    J. D. Bekenstein,Phys. Rev. D70, 083509 (2004)

    2004

  60. [60]

    Brans and R

    C. Brans and R. H. Dicke,Phys. Rev.124, 925–935 (1961)

    1961

  61. [61]

    G. W. Horndeski,Int. J. Theor. Phys.10, 363–384 (1974)

    1974

  62. [62]

    de Rham, G

    C. de Rham, G. Gabadadze, and A. J. Tolley,Phys. Rev. Lett.106, 231101 (2011)

    2011

  63. [63]

    F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne’eman,Phys. Rep.258, 1–171 (1995)

    1995

  64. [64]

    Aldrovandi and J

    R. Aldrovandi and J. G. Pereira, Springer, Dordrecht (2013)

    2013

  65. [65]

    Beltr´ an Jim´ enez, L

    J. Beltr´ an Jim´ enez, L. Heisenberg, and T. Koivisto,Phys. Rev. D98, 044048 (2018)

    2018

  66. [66]

    Weitzenb¨ ock, Noordhoff, Groningen (1923)

    R. Weitzenb¨ ock, Noordhoff, Groningen (1923)

    1923

  67. [67]

    Beltr´ an Jim´ enez, L

    J. Beltr´ an Jim´ enez, L. Heisenberg, and T. Koivisto,Universe5, 173 (2019)

    2019

  68. [68]

    Chandrasekhar,An Introduction to the Study of Stellar Structure, University of Chicago Press (1939)

    S. Chandrasekhar,An Introduction to the Study of Stellar Structure, University of Chicago Press (1939)

    1939

  69. [69]

    Farhi and R

    E. Farhi and R. L. Jaffe,Phys. Rev. D,30, 2379 (1984)

    1984

  70. [70]

    S. H. Hendi, G. H. Bordbar, B. Eslam Panah and S. Panahiyan,JCAP,09, 013 (2016)

    2016

  71. [71]

    A. Yu. Kamenshchik, U. Moschella and V. Pasquier,Phys. Lett. B,511, 265 (2001)

    2001

  72. [72]

    Bili´ c, G

    N. Bili´ c, G. B. Tupper and R. D. Viollier,Phys. Lett. B,535, 17 (2002)

    2002

  73. [73]

    Abbott et al

    R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration),Astrophysical Journal Letters 896, L44 (2020)

    2020

  74. [74]

    J. M. Lattimer and M. Prakash,Phys. Rept.,621, 127 (2016)

    2016

  75. [75]

    H. Shen, H. Toki, K. Oyamatsu and K. Sumiyoshi,Nucl. Phys. A,637, 435 (1998)

    1998

  76. [76]

    Goriely, N

    S. Goriely, N. Chamel and J. M. Pearson,Phys. Rev. C,82, 035804 (2010)

    2010

  77. [77]

    Hebeler, J

    K. Hebeler, J. M. Lattimer, C. J. Pethick and A. Schwenk,Astrophys. J.,773, 11 (2013)

    2013

  78. [78]

    Drischler, et al.,Phys

    C. Drischler, et al.,Phys. Rev. C,103, 045808 (2021)

    2021

  79. [79]

    Akmal, V

    A. Akmal, V. R. Pandharipande and D. G. Ravenhall,Phys. Rev. C,58, 1804 (1998)

    1998

  80. [80]

    Douchin and P

    F. Douchin and P. Haensel,Astron. Astrophys.,380, 151 (2001)

    2001

Showing first 80 references.