Temperature effects on white dwarfs in modified gravity

Aneta Wojnar; Laur J\"arv; Sof\'ia Vidal

REVIEW 3 major objections 4 minor 67 references

Temperature effects on white dwarfs in modified gravity

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper shows that a white dwarf at finite temperature is larger at the same mass in three modified-gravity theories, and that at 10^8 K thermal effects can mimic or mask changes in the gravity parameters.

desk verdict A transparent finite-temperature WD study in scalar-tensor theories with a plausible central result but a surface-definition soft spot that needs addressing before the high-T radius claims can be trusted. read the letter →

arxiv 2608.12992 v1 pith:RUJPCTS3 submitted 2026-08-13 gr-qc astro-ph.SR

Sofía Vidal , Aneta Wojnar , Laur Järv This is my paper · ORCID

classification gr-qcastro-ph.SR PACS 04.50.Kd04.40.Dg97.20.Rp

keywords whitedwarfsfinitetemperatureequationofstatemass-radiusrelationmassiveBrans-Dicketheorysymmetronscreeningdilatonscalar-tensorgravityeffectivegravitationalconstant

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 asks whether a white dwarf's internal temperature changes the equilibrium size and mass predicted by modified-gravity theories, and whether temperature could be mistaken for a genuine gravitational effect. It computes white-dwarf models with a finite-temperature version of the Chandrasekhar equation of state in three scalar-tensor theories: massive Brans-Dicke, symmetron, and dilaton. The central result is that heating the star leaves its total mass almost unchanged but inflates its radius; below roughly $10^{6}$ K the effect is negligible, and above that it grows sharply. Because the high-temperature mass-radius branches of different theories overlap, the paper concludes that finite temperature creates partial degeneracies that must be accounted for when using white-dwarf observations to constrain gravity.

What carries the argument

The central object is the finite-temperature Chandrasekhar equation of state, built from relativistic Fermi-Dirac integrals $F_k(\eta,\beta)$ with $\beta=k_B T/(m_e c^2)$ and degeneracy parameter $\eta=\mu/(k_B T)$, which replaces the zero-temperature step-function occupancy of the degenerate electron gas. This EOS is coupled to the Einstein-frame scalar-tensor field equations and the hydrostatic equilibrium equation $P' = -(\rho c^2 + P)(\tilde{\varphi}' + \alpha \tilde{\phi}')$, with the scalar field governed by an effective potential set by each theory's conformal factor $A(\tilde{\phi})$ and self-interaction $V(\tilde{\phi})$. The stellar surface is fixed by $P=0$, and the effective gravitational constant is $G_{\mathrm{eff}} = A^2(\tilde{\phi}) G_N$. This machinery carries the argument because it is the temperature-dependent pressure that expands the star while the scalar field modifies the force balance.

What would settle it

Rebuild one of the paper's $10^{8}$ K models, for example the low-mass, large-radius branch near 0.75 solar masses, using a more complete finite-temperature treatment that includes non-degenerate electrons, ions, and a radiative outer envelope; if the radius at the same mass is no longer larger than the $10^{4}$ K model, or the branch disappears, the central claim is falsified.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that in all three theories a nonzero temperature shifts the mass-radius relation: at fixed total mass the equilibrium radius increases with temperature while the mass stays essentially unchanged, because thermal pressure adds to degeneracy pressure. Up to about $10^{6}$ K, deviations from zero temperature are very small; at $10^{7}$ K and $10^{8}$ K they become significant. In every theory the effective gravitational constant is weaker at the stellar center than at infinity, with the largest deviations in massive Brans-Dicke and much smaller deviations in the screened theories. At $10^{8}$ K the mass-radius curves of all theories converge at large radii and low masses, which the paper reads as a hint that thermal effects dominate modified-gravity effects in that regime, while noting that the equation of state is starting to lose validity there. The interior radial profiles of the scalar field, pressure, and metric are mostly temperature independent except near $10^{8}$ K.

Load-bearing premise

The load-bearing premise is that the finite-temperature Chandrasekhar equation of state, with energy density dominated by rest mass and electrons treated as a degenerate Fermi gas, remains valid through the entire star up to $10^{8}$ K, including the outer layers where the paper concedes the gas becomes less degenerate and the EOS starts losing validity.

Editorial extensions

If this is right

For all three theories, a white dwarf of fixed mass has a larger radius at higher temperature, with negligible change below about 10^6 K and significant change above.
White-dwarf cooling tracks from 10^8 K down to 10^6 K should not assume a constant radius, because the thermal expansion affects the relation between cooling time and observed size.
Finite temperature produces partial overlaps between different theory-parameter curves in the mass-radius plane, so parameter constraints drawn from observations must include temperature or risk being biased.
At 10^8 K the mass-radius curves for massive Brans-Dicke, symmetron, and dilaton converge at large radii and low masses, suggesting that temperature effects dominate modified-gravity effects there, subject to the paper's own caveat about equation-of-state validity.
In all three theories the central effective gravitational constant is smaller than its value at infinity, and temperature leaves this mostly unchanged except for a saturation effect at 10^8 K that the paper attributes to a possible numerical or EOS artifact.

Reading between the lines

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

Extending the paper's logic, combining mass-radius data with independent temperature or cooling-rate measurements could lift the degeneracy the paper identifies, because temperature and modified-gravity parameters affect cooling ages differently.
The high-temperature convergence of all theories at low masses suggests that any modified-gravity interpretation of an unusually large or small white dwarf should first check whether a hot standard model can reproduce the same radius; that check is not performed in the paper.
A natural next step would be to feed the same finite-temperature EOS into rotating or magnetized white-dwarf models, where thermal expansion could shift the stability boundary relevant to super-Chandrasekhar candidates.
The paper's own validity caveat implies the 10^8 K results are provisional: replacing the outer layers with a non-degenerate atmosphere and adding neutrino emission or shell burning could either sharpen or erase the apparent degeneracies.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper does something useful and honest: it takes the known finite-temperature Chandrasekhar EoS and runs it through three scalar-tensor gravity models that were previously only treated at zero temperature. The new content is the specific mass-radius relations, effective gravitational constant curves, and radial profiles at T up to 1e8 K, and the paper openly discusses the degeneracy this creates between thermal and modified-gravity signatures. The GR benchmark matches [19], the EoS formulas are standard, and the authors flag where the EoS loses validity. That is solid forward modeling, not a hidden fit.

The main soft spot is the surface definition. The radius is set by P(r_s) = 1e-10 P_c, and the paper asserts that lowering the cutoff does not change radii. But at T = 1e8 K, the outer layers are weakly degenerate and the EoS approaches an isothermal ideal-gas form with P ~ rho. In hydrostatic equilibrium, that means the radius at which P/P_c = 1e-10 shifts with the cutoff, roughly logarithmically in P_c/P_cut. The T = 1e8 K branches, including the claimed common large-radius limit, live exactly in this regime. So the central radius claim at high T is partly convention-dependent, and the convergence of all modified-gravity curves to one large radius may be more numerical than physical. The authors do warn that the EoS is losing validity there, but they still present those radii as the main temperature effect, so this is not a minor caveat.

Other issues: no convergence tests or error bars, the rest-mass-only energy-density approximation is never quantified, the dilaton parameter-conversion discrepancy is reported but left unresolved, and no code or data is released. These are addressable and the paper is transparent about the dilaton issue.

The stress-test note about the surface cutoff is the one that matters. If the authors rerun the high-T cases with the pressure cutoff varied, or use a realistic non-degenerate envelope, I would expect the T = 1e8 K radii to shift noticeably. The lower-temperature results, where the effect is small anyway, are probably robust.

Bottom line: the paper is worth a serious referee, but the referee should push on the surface-convention dependence before accepting the headline radius increase at high T. For temperatures up to ~1e6 K, the result is solid and the degeneracy point is well taken. For 1e8 K, the claims need a clearer numerical check. I would want to see that check before citing the large-radius branches.

Referee Report

3 major / 4 minor

Summary. This manuscript studies the equilibrium structure of white dwarfs at finite temperature in three scalar-tensor gravity theories: massive Brans-Dicke theory, symmetron screening, and dilaton screening. The authors derive a finite-temperature Chandrasekhar equation of state, integrate the spherically symmetric Einstein-frame field equations with a shooting method, and present mass-radius relations, effective gravitational constants, and radial profiles for temperatures up to 10^8 K. The central claim is that a non-zero temperature increases the white dwarf radius while leaving the total mass essentially unchanged, and that this thermal effect can partially mimic or mask modified-gravity signatures. The paper also reports that the T = 10^8 K branches converge to a common large radius across all theories, while repeatedly cautioning that the equation of state loses validity in precisely that regime.

Significance. If the central claim is robust, the paper provides a useful investigation of an under-explored degeneracy between thermal effects and scalar-tensor gravity modifications in white dwarfs, with potential implications for white dwarf cooling models and for interpreting mass-radius observations. The manuscript is transparent about its numerical setup, benchmarks the GR limit against Ref. [19], and explicitly flags the EoS validity limits and an unresolved dilaton parameter conversion. The main reservation is that the radius, the only temperature-sensitive diagnostic in the presented results, is defined by a pressure cutoff in a regime where the EoS is admitted to become invalid; the robustness of the central claim therefore depends on a quantitative treatment of the outer layers and of the thermal energy density that is not currently provided.

major comments (3)

[Section 4 and Section 5.1] The stellar radius is defined numerically by the pressure cutoff P(r_s) = 10^-10 P_c, with the assertion that demanding more orders of magnitude does not significantly change the radii. At T = 10^8 K the low-density outer layers become non-degenerate, as the authors themselves state in Secs. 5.1 and 6; in this regime the finite-temperature EoS approaches an isothermal ideal-gas form P ∝ ρ, for which hydrostatic equilibrium has no natural surface and r_s shifts with the arbitrary cutoff. Since the T = 10^8 K branches and their convergence to a common large radius are presented as a main result, and since the mass is nearly unchanged by construction, the radius is the only temperature-sensitive diagnostic. Please quantify the cutoff dependence of r_s at T = 10^8 K and, if possible, at T = 10^7 K, or restrict the claimed radius increase to densities and temperatures where the Chandrasekhar EoS remains valid.
[Section 2.1 and Eq. (15)] The energy density is approximated as rest-mass only, described as 'safely approximated to consist only of this term', but no estimate of the thermal energy contribution is given. The full energy density in Eq. (1b) contains a temperature-dependent part that becomes relatively important at low degeneracy and high temperature. Using only the rest-mass density in the hydrostatic equilibrium equation (15) removes a priori any direct temperature dependence of the energy density that enters the mass integral, so the conclusion that the mass is 'essentially unchanged' is partly an artifact of this approximation. Please quantify the thermal energy density relative to the rest-mass energy density over the full range of densities and temperatures used (especially ρ_c ~ 10^5-10^7 g cm^-3 at T = 10^8 K) and show the corresponding change in the inferred stellar mass.
[Section 5.1, footnote 1] The dilaton results rely on parameter values that were adopted after an unresolved factor-of-10^-3 discrepancy with the theoretical conversion from Ref. [42]. The authors state that the reported mass-radius relations are recovered only for parameters smaller by this factor than those obtained from the theoretical conversion, and that the source of the discrepancy was not identified. Since the dilaton mass-radius curves and their temperature shifts are part of the quantitative results, this unresolved conversion should be resolved or its effect on the conclusions quantified; as written, the dilaton predictions rest on an empirically adjusted parameter set.

minor comments (4)

[Abstract and Section 6] The abstract and conclusions state the finite-temperature radius increase without the important caveat, emphasized in Secs. 5.1 and 6, that at T = 10^8 K the equation of state is reaching its validity limit and that realistic models require non-degenerate outer layers. Please qualify the main claim accordingly.
[Section 4] The statement that lowering the pressure cutoff does not significantly change the radii is not supported by a convergence test. A small figure or table showing r_s as a function of P_cut/P_c for representative models, including at least one T = 10^8 K case, would make the numerical boundary treatment reproducible.
[Throughout] There are several typographical errors: Sec. 5.2 has 'it's value' instead of 'its value'; Sec. 6 has 'grativational' instead of 'gravitational'; Appendix B has 'mehtod' instead of 'method'; Sec. 5.1 has 'looses' instead of 'loses'. A careful proofreading pass is needed.
[Section 5.1] The symmetron parameters are adopted from Ref. [42] and are outside the observational bounds quoted from Ref. [44]. The paper states this is intentional for comparison and mechanism illustration, which is acceptable, but the conclusions should explicitly remind the reader that the quantitative mass-radius shifts for the symmetron are not predictions for observationally allowed parameters.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central results are forward numerical integrations from an independently derived finite-temperature Chandrasekhar EoS, with external benchmarks for the GR and dilaton cases.

full rationale

The paper's central claim, that a nonzero temperature increases the white dwarf radius at nearly fixed mass, comes from a direct numerical integration of the scalar-tensor structure equations (14a)-(14c) and (15), closed by the finite-temperature Chandrasekhar EoS (4),(6) derived from kinetic theory in Sec. 2. No parameter in the modified-gravity models is fitted to the mass-radius relations that constitute the main results: the GR benchmark is checked against the independent finite-temperature results of Ref. [19], the symmetron and dilaton parameters are taken from the external literature ([42]) or from the authors' earlier numerical setup ([43]), and the high-temperature T=10^8 K branches are explicitly flagged as approaching the validity limit of the EoS rather than being asserted as robust predictions. The self-citation [43] is limited to the numerical shooting procedure and notation conventions; it does not supply any uniqueness theorem, physical premise, or fitted quantity on which the temperature effect depends. The dilaton footnote reports an unresolved discrepancy with Ref. [42] and adopts parameter values that reproduce that external paper's curves; this is a calibration and benchmarking step, and the finite-temperature radius increase is subsequently computed from the EoS and structure equations rather than imposed by the calibration. The surface convention P(r_s)=10^-10 P_c is a numerical definition, and the paper asserts convergence with respect to it; even if that assertion failed at high temperature, the issue would be numerical robustness or EoS validity, not circularity. No equation in the paper is equivalent to its own output by construction, and no central claim reduces to a fitted parameter or a self-citation chain.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new scalar particles, forces, or entities are introduced; the scalar fields are standard elements of the cited theories. The hand-tuned inputs are the theory parameters listed above, especially the adjusted dilaton V0 values.

free parameters (4)

Brans-Dicke coupling alpha0 = 1
Chosen constant coupling in Eq. (16); the massless alpha0=1 case is not observationally viable but is included for illustration, as noted in Sec. 3.1.
Brans-Dicke scalar mass m_phi = m_phi c^2 in [1.3e-13, 2.7e-12] eV
Four values are used, within Solar System constraints from [41]; this mass sets the scalar-field range and directly shapes the M-R deviations in Sec. 5.1.
Symmetron parameters mu, Mbar_S, lambda = mu[1]=1.8, 5.4, 9.0e3; Mbar_S=1e-2; sqrt(lambda)=sqrt(2) mu M_P / M_S^2
Taken from [42] to keep a typical white dwarf screened; the authors note in Sec. 5.1 that these values violate observational bounds, so they are illustrative rather than viable.
Dilaton parameters V0 and a2 = log10(a2) in [1,4]; V0[1] in 3.3211e-3 to 3.3211
Adopted after an unresolved factor-1e-3 discrepancy relative to the theoretical conversion of [42]'s parameters; footnote 1 says the values were chosen to recover [42]'s curves.

assumptions (5)

domain assumption Spherically symmetric, static, perfect-fluid stellar model with the Einstein-frame metric of Eq. (13) and hydrostatic equilibrium Eq. (15).
Standard for this type of computation, but it excludes rotation, magnetic fields, and anisotropic pressure; introduced in Sec. 3.
domain assumption Matter is a carbon-oxygen core described by an ideal degenerate relativistic electron gas, with energy density approximated by rest mass only.
Stated in Sec. 2; the thermal kinetic-energy density and non-degenerate outer layers are neglected, a limitation the authors acknowledge in Sec. 6.
standard math The boundary value problem can be solved with the scalar field as the only shooting parameter because the temporal metric function enters only through its derivative.
Appendix B; this relies on the structure of Eqs. (14)-(15) and was already used in the authors' previous work [43].
domain assumption The chosen potentials and conformal factors define the theories: the massive Brans-Dicke quadratic potential, the symmetron symmetry-breaking potential, and the dilaton runaway potential.
Secs. 3.1-3.2; these choices define the models under study and are not derived from first principles in this paper.
ad hoc to paper The symmetron and dilaton parameter sets from [42] are accepted as representative despite being outside observational bounds or carrying an unresolved conversion issue.
Sec. 5.1 and footnote 1; the computed curves and comparisons depend on these values.

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Pith. "Pith review of Temperature effects on white dwarfs in modified gravity." pith.science (2026). https://pith.science/paper/RUJPCTS3

@misc{pith2026260812992,
  author       = {Pith},
  title        = {Pith review of: Temperature effects on white dwarfs in modified gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RUJPCTS3}},
  note         = {Machine review of arXiv:2608.12992}
}

read the original abstract

In this article we analyze the effects of a finite temperature equation of state on the equilibrium structure of white dwarfs in massive Brans-Dicke theory as well as the symmetron and dilaton screening mechanisms. We compute and present the numerically obtained mass-radius relation, effective gravitational constant as well as radial profiles of the scalar field, pressure and metric within the star. We show that assuming a non-zero temperature effectively results in a larger radius while leaving the total mass of the star essentially unchanged, and discuss the interplay between the effective gravitational constant, central density, and radius of the star.

Figures

Figures reproduced from arXiv: 2608.12992 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: b. In consistence with the scalar field profile, we observe that the field’s derivative grows to a higher maximum and converges more slowly towards zero for lower field masses. For T = 108K, the initial increase and later conversion towards zero occurs already at smal…

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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While the ﬁeld is driven to zero in high density re- gions, symmetry breaking causes it to converge towards the potential minimum at low densities

and have a Mexican hat like potential (20). While the ﬁeld is driven to zero in high density re- gions, symmetry breaking causes it to converge towards the potential minimum at low densities. In the dilaton case, it is the conformal factor (

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Equilibrium structure of white dwarfs at finite temperatures

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INTRODUCTION White dwarfs are compact stellar remnants formed after the evolution of stars with initial masses below roughly ten solar masses [ 1, 2]. Their interiors are typi- cally composed of carbon and oxygen, although low-mass white dwarfs may possess helium cores, all surrounded by thin outer envelopes of helium and hydrogen. Since thermonuclear rea...

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Temperature effects on white dwarfs in modified gravity

In Sec. 3 we introduce the relativistic ﬁeld equations for a general, conformal STT in Einstein frame together with the hydrostatic equilibrium equa- tion. Hereafter we present all considered models: mas- sive Brans-Dicke theory, symmetron and dilaton screen- ing. We proceed with a brief description of our numerical setup in Sec. 4 and a discussion of our...

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EQUATION OF STATE The matter inside a WD can be considered to be a degenerate relativistic Fermi gas which can be described analytically by the Chandrasekhar equation of state in- troduced in Ref. [ 5]. From kinetic theory, we can write the number density of a speciﬁc particle species n, energy density ε and pressure P of a system, respectively, as n = g ...

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This frame is obtained from the physical Jordan frame by a conformal transformation of the metric tensor, written as gµν = A2( ˜ϕ)˜gµν and scalar ﬁeld redeﬁnition

HYDROSTATIC EQUILIBRIUM EQUATIONS In the following, we introduce the hydrostatic equi- librium equations for scalar-tensor theories in Einstein frame. This frame is obtained from the physical Jordan frame by a conformal transformation of the metric tensor, written as gµν = A2( ˜ϕ)˜gµν and scalar ﬁeld redeﬁnition. We refer the reader to Refs. [ 21, 23, 37,...

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massive Brans-Dicke theory, symmetron and dilaton screening, at diﬀerent ﬁnite temperatures

RESULTS In this section we present and discuss the obtained mass-radius relations for each considered gravity theory, i.e. massive Brans-Dicke theory, symmetron and dilaton screening, at diﬀerent ﬁnite temperatures. These rela- tions describe the equilibrium conﬁgurations for WDs in a speciﬁc theory, meaning the conﬁguration for which the pressure exactly...

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We considered a massive Brans-Dicke theory as well as the symmetron and dilaton screening mecha- nisms

CONCLUSIONS In this article, we analyzed how a ﬁnite temperature Chandrasekhar equation of state for white dwarfs aﬀects their equilibrium and internal structure in modiﬁed grav- ity theories. We considered a massive Brans-Dicke theory as well as the symmetron and dilaton screening mecha- nisms. First, we derived the Chandrasekhar equation of state from k...

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For a more detailed description of our procedure, we refer the reader to our previous work [ 43]

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(26) We denote the eﬀective gravitational constant at the cen- ter of the star and at spatial inﬁnity by Geﬀ c := Geﬀ ( ˜ϕc) and Geﬀ ∞ := Geﬀ ( ˜ϕ∞) respectively

back to the Jordan frame, we can deﬁne an eﬀective gravitational constant that depends on the local value of the scalar ﬁeld Geﬀ( ˜ϕ) = A2( ˜ϕ)GN . (26) We denote the eﬀective gravitational constant at the cen- ter of the star and at spatial inﬁnity by Geﬀ c := Geﬀ ( ˜ϕc) and ...
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to ˜□ ˜ϕ ∝ dV ( ˜ϕ) d ˜ϕ . Thus, the asymptotic value of the scalar ﬁeld is set by the potential minimum. The radius of the star ˜rs in Einstein frame is the small- est radius that satisﬁes the condition P (˜rs) = 0, while the physical stellar radius is Rs = A[ ˜ϕ(˜rs)]˜rs. Be...
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Hence, Geﬀ c → Geﬀ ∞ and 1 − Geﬀ c /Geﬀ ∞ → 0, which is why we see a drop oﬀ to- wards lower densities for all theory parameters in Fig

At lower central densities, the star is less screened so that the central scalar ﬁeld value goes to its asymptotic value. Hence, Geﬀ c → Geﬀ ∞ and 1 − Geﬀ c /Geﬀ ∞ → 0, which is why we see a drop oﬀ to- wards lower densities for all theory parameters in Fig. 3c. On the other s...
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Before going to the modiﬁed gravity theories, we note that we also computed the mass-radius relations with a temperature dependent equation of state for GR

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and ( 17) respectively. For the theory pa- rameters, we assume α0 = 1 and dimensionless masses m ˜ϕ[1] ∈ [1 × 104, 2 × 105] which corresponds to m ˜ϕc2 [eV ] ∈ [1.3 × 10−13, 2.7 × 10−12] or equivalently m ˜ϕ [g] ∈ [2.4 × 10−46, 4.7 × 10−45]. The numerically ob- tained curves f...
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Space - Time - Matter

We observed a qualitatively consis- tent pattern for all considered theories. Deviations from the zero temperature result remain very small for tem- peratures up to ∼ 106K. For T > 106K deviations in- crease signiﬁcantly and can no longer be neglected. We note that for higher ...
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The score function is a directional measure for how far oﬀ we are from our desired target value and ∆ ˜ϕ = 0 means that we exactly hit our target

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3 ”Small/large enough” meaning that numerical results will n ot signiﬁcantly change if these values are decreased/increas ed

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˜ϕ(3) c > ˜ϕ(2) c

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correct

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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While the ﬁeld is driven to zero in high density re- gions, symmetry breaking causes it to converge towards the potential minimum at low densities

and have a Mexican hat like potential (20). While the ﬁeld is driven to zero in high density re- gions, symmetry breaking causes it to converge towards the potential minimum at low densities. In the dilaton case, it is the conformal factor (

work page

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work page Pith review arXiv

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INTRODUCTION White dwarfs are compact stellar remnants formed after the evolution of stars with initial masses below roughly ten solar masses [ 1, 2]. Their interiors are typi- cally composed of carbon and oxygen, although low-mass white dwarfs may possess helium cores, all surrounded by thin outer envelopes of helium and hydrogen. Since thermonuclear rea...

work page

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Temperature effects on white dwarfs in modified gravity

In Sec. 3 we introduce the relativistic ﬁeld equations for a general, conformal STT in Einstein frame together with the hydrostatic equilibrium equa- tion. Hereafter we present all considered models: mas- sive Brans-Dicke theory, symmetron and dilaton screen- ing. We proceed with a brief description of our numerical setup in Sec. 4 and a discussion of our...

work page Pith review arXiv 2026

[5] [3]

EQUATION OF STATE The matter inside a WD can be considered to be a degenerate relativistic Fermi gas which can be described analytically by the Chandrasekhar equation of state in- troduced in Ref. [ 5]. From kinetic theory, we can write the number density of a speciﬁc particle species n, energy density ε and pressure P of a system, respectively, as n = g ...

work page

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This frame is obtained from the physical Jordan frame by a conformal transformation of the metric tensor, written as gµν = A2( ˜ϕ)˜gµν and scalar ﬁeld redeﬁnition

HYDROSTATIC EQUILIBRIUM EQUATIONS In the following, we introduce the hydrostatic equi- librium equations for scalar-tensor theories in Einstein frame. This frame is obtained from the physical Jordan frame by a conformal transformation of the metric tensor, written as gµν = A2( ˜ϕ)˜gµν and scalar ﬁeld redeﬁnition. We refer the reader to Refs. [ 21, 23, 37,...

work page

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massive Brans-Dicke theory, symmetron and dilaton screening, at diﬀerent ﬁnite temperatures

RESULTS In this section we present and discuss the obtained mass-radius relations for each considered gravity theory, i.e. massive Brans-Dicke theory, symmetron and dilaton screening, at diﬀerent ﬁnite temperatures. These rela- tions describe the equilibrium conﬁgurations for WDs in a speciﬁc theory, meaning the conﬁguration for which the pressure exactly...

work page

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We considered a massive Brans-Dicke theory as well as the symmetron and dilaton screening mecha- nisms

CONCLUSIONS In this article, we analyzed how a ﬁnite temperature Chandrasekhar equation of state for white dwarfs aﬀects their equilibrium and internal structure in modiﬁed grav- ity theories. We considered a massive Brans-Dicke theory as well as the symmetron and dilaton screening mecha- nisms. First, we derived the Chandrasekhar equation of state from k...

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