Rotation-Induced Pressure Anisotropy in Newtonian White Dwarfs: Sequences and Applicability Criteria

Aray Muratkhan; Hernando Quevedo; Saken Toktarbay

arxiv: 2604.27956 · v1 · submitted 2026-04-30 · 🌀 gr-qc · astro-ph.SR

Rotation-Induced Pressure Anisotropy in Newtonian White Dwarfs: Sequences and Applicability Criteria

Aray Muratkhan , Saken Toktarbay , Hernando Quevedo This is my paper

Pith reviewed 2026-05-07 05:56 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.SR

keywords white dwarfsrotationpressure anisotropyChandrasekhar EOSNewtonian stellar structurelimiting masshydrostatic balancereduced models

0 comments

The pith

A one-dimensional Newtonian model encodes centrifugal support in rotating white dwarfs as pressure anisotropy, showing percent-level mass increases.

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

The authors present a reduced one-dimensional model for uniformly rotating Newtonian white dwarfs that incorporates centrifugal effects through an effective pressure anisotropy rather than solving the full two-dimensional structure equations. By averaging the centrifugal term from the Euler equation over angles with a fixed factor of 2/3, they derive a radial correction that enters the hydrostatic balance like an anisotropic pressure component. Applying this to sequences of white dwarfs using the Chandrasekhar degenerate electron equation of state across central densities from 10^6 to 10^11 g/cm³ and rotation parameters up to 0.35, they find that both maximum mass and radius grow steadily with increasing rotation. At the upper end of the rotation range the mass increase reaches a few percent. They also define diagnostics to check that the configurations remain sub-Keplerian and the anisotropy approximation stays small in the bulk interior, confirming validity within the explored domain and framing the model as a useful benchmark tool.

Core claim

We introduce a fast, one-dimensional Newtonian reduced model to capture uniform rotation in cold white dwarfs, encoding centrifugal support as an effective pressure anisotropy. Using Δ_rot(r)=(1/3)ρ(r)Ω² r² derived from the stationary Euler equation with <sin²θ>=2/3, the model incorporates rotation into hydrostatic balance without a two-dimensional solver. Applying the Chandrasekhar degenerate-electron equation of state, we compute interior structures and global sequences for ρ_c ∈ [10^6, 10^{11}] g cm^{-3} with rotation proxies f ≤ 0.35, finding monotonic increases in limiting mass and radius, with a percent-level mass gain at f = 0.35. We quantify applicability using sub-Keplerian diagonst

What carries the argument

The effective pressure anisotropy Δ_rot(r) = (1/3) ρ(r) Ω² r² with angular average <sin²θ> = 2/3 that reduces the centrifugal term to a one-dimensional correction in the hydrostatic equilibrium equation.

If this is right

Limiting mass and radius increase monotonically with rotation parameter f.
Mass gain reaches the percent level at f = 0.35.
Sub-Keplerian diagnostics max(Ω/Ω_K), max(ε) and A_{10^{-2}} stay below unity in the domain.
The model acts as a computationally efficient benchmark for slow-to-moderate rotation.

Where Pith is reading between the lines

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

This approach could support quick explorations of how rotation affects white dwarf cooling or merger rates in population models.
The anisotropy reduction might extend to models of other rotating compact objects like neutron stars in the Newtonian limit.
Validation against full multidimensional simulations at higher rotation rates would define the model's breakdown point more precisely.

Load-bearing premise

The centrifugal force can be reduced to an effective one-dimensional pressure anisotropy using a fixed angular average of two-thirds for sin squared theta, with the resulting models satisfying sub-Keplerian conditions.

What would settle it

A full two-dimensional axisymmetric computation of a white dwarf at central density 10^{11} g cm^{-3} and rotation proxy f = 0.35 yielding a mass or radius differing by more than a few percent from the one-dimensional result would show the approximation fails to capture the effects accurately.

Figures

Figures reproduced from arXiv: 2604.27956 by Aray Muratkhan, Hernando Quevedo, Saken Toktarbay.

**Figure 1.** Figure 1: FIG. 1: Normalized density profile view at source ↗

**Figure 2.** Figure 2: FIG. 2: Normalized radial pressure profile view at source ↗

**Figure 3.** Figure 3: FIG. 3: Cumulative enclosed mass fraction view at source ↗

**Figure 4.** Figure 4: FIG. 4: Rotation-induced effective anisotropy ∆ view at source ↗

**Figure 5.** Figure 5: FIG. 5: Total mass view at source ↗

**Figure 6.** Figure 6: FIG. 6: Radius view at source ↗

**Figure 7.** Figure 7: FIG. 7: Mass–radius relation view at source ↗

**Figure 8.** Figure 8: FIG. 8: Relative mass discrepancy between the one-dimensio view at source ↗

**Figure 9.** Figure 9: FIG. 9: Relative radius discrepancy between the one-dimens view at source ↗

**Figure 10.** Figure 10: FIG. 10: Normalized applicability criteria for the rotatio view at source ↗

read the original abstract

We introduce a fast, one-dimensional Newtonian {reduced model} to capture uniform rotation in cold white dwarfs, encoding centrifugal support as an effective pressure anisotropy. Using $\Delta_{\rm rot}(r)=\frac{1}{3}\rho(r)\Omega^2 r^2$ derived from the stationary Euler equation with $\langle\sin^2\theta\rangle=2/3$, the model incorporates rotation into hydrostatic balance without a two-dimensional solver. Applying the Chandrasekhar degenerate-electron equation of state, we compute interior structures and global sequences for $ \rho_c \in [10^6, 10^{11}]~{\rm g\,cm^{-3}} $ with rotation proxies $f \le 0.35$, finding monotonic increases in limiting mass and radius, with a percent-level mass gain at $f = 0.35$. We quantify applicability using sub-Keplerian diagnostics evaluated on the rotating configurations, $\max(\Omega/\Omega_K)$ and $\max(\epsilon)$, together with a bulk-interior smallness measure $A_{10^{-2}}\equiv \max_{p_r/p_c\ge 10^{-2}}(\Delta_{\rm rot}/p_r)$. Within the scanned domain these diagnostics remain below unity. The model is therefore best viewed as a reduced Newtonian benchmark for slow-to-moderate rotation, not as a replacement for fully axisymmetric calculations of rotating stars.

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.

Desk Editor's Note private letter to a colleague

A workable 1D reduction for rotating white dwarfs via averaged anisotropy, but the spherical averaging leaves an error comparable to the small reported mass gain.

read the letter

The main thing to know is that the authors reduce uniform rotation to a radially dependent pressure anisotropy Δ_rot(r) = (1/3) ρ Ω² r² by angular averaging the centrifugal term with a fixed = 2/3, then integrate standard 1D hydrostatic equilibrium with the Chandrasekhar EOS to produce sequences showing monotonic but percent-level increases in mass and radius up to their rotation proxy f = 0.35. They add three diagnostics to mark where the approximation stays plausible. This is a concrete, computationally cheap Newtonian benchmark rather than a full 2D treatment. What the paper does well is derive the anisotropy term directly from the stationary Euler equation without fitting, implement it in a transparent 1D code, and introduce the A_{10^{-2}} bulk measure that checks where Δ_rot remains small relative to central pressure. The sequences are generated cleanly and the diagnostics remain below unity across the scanned domain, which gives a practical way to decide when the model can be used. The soft spot is the self-consistency of the averaging step. The derivation fixes the 2/3 factor under the assumption of spherical isodensity surfaces and a pure monopole potential, yet inserting the anisotropy produces quadrupole deformation that should alter both the angular weighting and the gravitational field. The diagnostics bound the size of Ω/Ω_K and Δ_rot/p_r but do not recompute the average over the deformed surfaces or estimate the resulting shift in the effective coefficient. Because the headline mass gain is only a few percent, an O(10 %) change in that coefficient would affect the sequences at the same order. This paper is for people running population studies or needing a fast calibration target for more expensive rotating-star codes. It deserves a serious referee because the reduction technique is new enough and the implementation is straightforward, even though the error from the spherical assumption needs tighter control.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces a one-dimensional Newtonian reduced model for uniformly rotating white dwarfs by representing centrifugal support through an effective pressure anisotropy Δ_rot(r) = (1/3) ρ(r) Ω² r², obtained by angular averaging the centrifugal acceleration in the stationary Euler equation assuming ⟨sin²θ⟩ = 2/3. Using the Chandrasekhar degenerate electron equation of state, the authors compute interior structures and global mass-radius sequences for central densities ρ_c from 10^6 to 10^11 g cm^{-3} and rotation parameters f ≤ 0.35. They report monotonic increases in limiting mass and radius, with a percent-level mass gain at the highest f. Applicability is quantified using sub-Keplerian diagnostics max(Ω/Ω_K), max(ε), and A_{10^{-2}} = max(Δ_rot / p_r for p_r/p_c ≥ 10^{-2}), all of which remain below unity in the explored domain. The model is positioned as a fast benchmark for slow-to-moderate rotation rather than a substitute for full axisymmetric calculations.

Significance. If the central approximation holds, this provides a computationally efficient 1D framework for incorporating uniform rotation into white dwarf models, enabling rapid parameter-space exploration without 2D solvers. The reported sequences quantify that rotation at f=0.35 induces only percent-level corrections to the Chandrasekhar mass and radius, serving as a useful Newtonian benchmark. Strengths include the direct derivation of Δ_rot from the Euler equation (no data fitting), consistent numerical sequences across the ρ_c range, and the inclusion of explicit applicability diagnostics that bound the anisotropy magnitude.

major comments (1)

The fixed angular average ⟨sin²θ⟩ = 2/3 used to define Δ_rot(r) = (1/3) ρ Ω² r² (as described in the abstract and the derivation of the hydrostatic balance) assumes spherical isodensity surfaces and a purely monopolar gravitational potential. Insertion of the anisotropy term produces oblate deformations, which shift the density-weighted angular average and introduce quadrupole corrections to the potential absent from the 1D Poisson solver. The diagnostics max(Ω/Ω_K), max(ε), and A_{10^{-2}} only verify that |Δ_rot/p_r| and Ω/Ω_K remain O(1) or smaller; they do not recompute the average on the deformed geometry or bound the resulting error. Given that the reported mass increase is only a few percent at f = 0.35, an O(10 %) shift in the effective coefficient of ρ Ω² r² would alter the headline sequences at the same order. A quantitative error estimate (e.g., via comparison to a 2D axisym-m

minor comments (2)

The rotation proxy f is used throughout but its precise definition (e.g., f = Ω/Ω_K at the equator or a normalized central value) is not stated in the abstract and should be given explicitly with an equation number in §2 or §3.
The manuscript would benefit from additional references to prior 2D Newtonian and relativistic calculations of rotating white dwarfs (e.g., Ostriker & Bodenheimer 1968 and subsequent numerical work) to better situate the reduced model as a benchmark.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We appreciate the recognition of the model's utility as a computationally efficient 1D benchmark for incorporating uniform rotation. We address the major comment below, clarifying the scope of the approximations and indicating the revisions made to strengthen the discussion of limitations.

read point-by-point responses

Referee: The fixed angular average ⟨sin²θ⟩ = 2/3 used to define Δ_rot(r) = (1/3) ρ Ω² r² (as described in the abstract and the derivation of the hydrostatic balance) assumes spherical isodensity surfaces and a purely monopolar gravitational potential. Insertion of the anisotropy term produces oblate deformations, which shift the density-weighted angular average and introduce quadrupole corrections to the potential absent from the 1D Poisson solver. The diagnostics max(Ω/Ω_K), max(ε), and A_{10^{-2}} only verify that |Δ_rot/p_r| and Ω/Ω_K remain O(1) or smaller; they do not recompute the average on the deformed geometry or bound the resulting error. Given that the reported mass increase is only a few percent at f = 0.35, an O(10 %) shift in the effective coefficient of ρ Ω² r² would alter the headline sequences at the same order. A quantitative error estimate (e.g., via comparison to a 2D axisym-m

Authors: We agree that the fixed ⟨sin²θ⟩ = 2/3 average is derived under the assumption of spherical isodensity surfaces and a monopolar potential, and that the induced oblate deformation introduces higher-order corrections not captured by updating the average or including quadrupole terms in the 1D Poisson solver. However, the model is explicitly constructed as a reduced approximation whose validity is restricted to the regime where these corrections remain small. The diagnostics max(ε) and A_{10^{-2}} are designed precisely to bound the size of the anisotropy and the resulting deformation; within the scanned domain max(ε) ≪ 1, so the shift in the angular average is O(ε) while the leading centrifugal support enters at O(f). This ordering justifies retaining the spherical average to the accuracy needed for the reported percent-level mass and radius changes. We have added a dedicated paragraph in Section 4 of the revised manuscript that estimates the magnitude of the neglected quadrupole correction (scaling as ε²) and reiterates that the model is positioned only as a fast Newtonian benchmark, not a high-precision substitute for axisymmetric calculations. A direct numerical comparison against 2D solvers would furnish a sharper error bar but lies outside the intended scope of this work. revision: partial

standing simulated objections not resolved

A full quantitative error bound obtained by direct comparison of the 1D sequences against independent 2D axisymmetric integrations, as this would require developing or interfacing with a separate 2D solver and would undermine the purpose of providing a rapid 1D alternative.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The central reduction sets Δ_rot(r) = (1/3) ρ(r) Ω² r² by angular averaging of the centrifugal term in the stationary Euler equation under the explicit assumption of spherical isodensity surfaces (<sin²θ> = 2/3). This fixed functional form is inserted once into the 1D hydrostatic balance and Poisson equations; the resulting ODE system is then integrated numerically with the independent Chandrasekhar EOS for chosen ρ_c and f. The reported mass/radius sequences and the three applicability diagnostics (max(Ω/Ω_K), max(ε), A_{10^{-2}}) are direct numerical outputs of that integration and are not algebraically or statistically forced to equal the input assumptions. No parameters are fitted to the output data, no self-citation chain is invoked to justify the averaging step, and the paper explicitly frames the construction as an approximate benchmark rather than an exact or self-consistent solution. The spherical-averaging assumption is therefore an external modeling choice whose accuracy can be tested externally, not a tautology that renders the predictions equivalent to the inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 1 invented entities

The central claim rests on the Newtonian hydrostatic balance, the fixed angular average <sin²θ> = 2/3, and the Chandrasekhar EOS; the only added construct is the effective anisotropy, which is derived rather than postulated independently.

free parameters (2)

f
Dimensionless rotation proxy that scales Ω and is scanned up to 0.35; its value is chosen by the user rather than fitted to observations.
ρ_c
Central density scanned over [10^6, 10^{11}] g cm^{-3} to generate sequences.

axioms (3)

domain assumption Newtonian hydrostatic equilibrium holds with the added anisotropic pressure term Δ_rot(r).
Invoked when the centrifugal contribution is folded into the radial force balance.
domain assumption The angular average <sin²θ> = 2/3 is an adequate representation of uniform rotation for the purpose of obtaining a one-dimensional equation.
Stated explicitly in the derivation of Δ_rot from the stationary Euler equation.
standard math The Chandrasekhar equation of state for completely degenerate, non-relativistic electrons is appropriate throughout the density range considered.
Used without modification to close the hydrostatic equation.

invented entities (1)

effective pressure anisotropy Δ_rot(r) no independent evidence
purpose: To encode the centrifugal support of uniform rotation inside a one-dimensional radial structure equation.
Derived directly from the Euler equation via angular averaging; no independent observational or numerical evidence outside the model is supplied.

pith-pipeline@v0.9.0 · 5561 in / 2042 out tokens · 66749 ms · 2026-05-07T05:56:27.958269+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

In practice, we solve the dimensionless system using the variables introduced in Sec

and ( 23) outward from ( m(0) = 0 , ρ (0) = ρc). In practice, we solve the dimensionless system using the variables introduced in Sec. II C, starting at a small radius ¯r0 = 10 − 8 using a regular central expansion. The integration is terminated wh en the Chandrasekhar parameter becomes suﬃciently small, x(¯r) = xstop, x stop = 10 − 10, (26) which corresp...

work page
[2]

slow-rotation

Quantitative readout and limiting conﬁgurations Figures 5–7 quantify the impact of the rotation–anisotropy mapping on global s equences. Across the explored grid, the Newtonian Chandrasekhar sequenc e approaches a high-density saturation regime; the corresponding limiting readout at the high-d ensity edge of the scan (log10 ρc = 11) is summarized in Table...

work page 2000
[3]

The potential is determined by Poisson’s equation, ∇ 2Φ = 4 πGρ

Two-dimensional equilibrium formulation In Newtonian gravity, an axisymmetric, stationary, uniformly rota ting barotrope satisﬁes the ﬁrst integral H(ρ) + Φ − 1 2Ω 2̟ 2 = C, (32) where ̟ is the cylindrical radius, Φ is the gravitational potential, and H(ρ) ≡ ∫ ρ 0 dp ρ′ (33) is the speciﬁc enthalpy (for a barotropic Chandrasekhar EoS, p = p(ρ)) [6, 12]. T...

work page
[4]

( 34), updates the enthalpy ﬁeld using Eq

Numerical method and convergence A standard approach is a self-consistent ﬁeld (SCF) iteration on a c ylindrical grid ( ̟, z ): starting from an initial density distribution with prescribed ρc and a trial surface, one computes Φ from Eq. ( 34), updates the enthalpy ﬁeld using Eq. ( 32), and reconstructs the density via the EoS inversion ρ = ρ(H) until con...

work page
[5]

Benchmark observables and comparison method Two-dimensional equilibria provide distinct geometric radii: the equat orial radius Req and the polar radius Rp. For comparison to the one-dimensional reduced model, it is conven ient to deﬁne a volume-equivalent radius Rvol ≡ ( 3V 4π ) 1/ 3 , (35) where V is the stellar volume in the two-dimensional equilibrium...

work page
[6]

limiting

Validation grid To keep the benchmark computationally focused while spanning the r elevant regimes, we consider a small but representative set of models across logarit hmically spaced central densities (covering the non-relativistic to relativistic-degenerate transition) and multiple slow-rotation rates (e.g. Ω / Ω K ≲ 0. 3). The resulting δM , δR, and O ...

work page 2025
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J. J. Hermes et al. Kepler observations of 27 pulsating da white dwarfs (davs). The Astro- physical Journal Supplement Series , 232, 2017

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James B. Hartle and Kip S. Thorne. Slowly rotating relati vistic stars. ii. models for neutron stars and supermassive stars. The Astrophysical Journal , 153:807, 1968

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J. P. Ostriker and P. Bodenheimer. Rapidly rotating star s. i. the self-consistent-ﬁeld method. The Astrophysical Journal , 151:1075, 1968

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Boshkayev, J

K. Boshkayev, J. A. Rueda, and R. Ruﬃni. On general relati vistic uniformly rotating white dwarfs. The Astrophysical Journal , 762, 2013

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Chandrasekhar

S. Chandrasekhar. The maximum mass of ideal white dwarfs . The Astrophysical Journal , 74:81, 1931

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An Introduction to the Study of Stellar Structure

Subrahmanyan Chandrasekhar. An Introduction to the Study of Stellar Structure . University of Chicago Press, 1939

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Stuart L. Shapiro and Saul A. Teukolsky. Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects . Wiley, 1983

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Hamada and E

T. Hamada and E. E. Salpeter. Models for zero-temperatu re stars. The Astrophysical Journal, 134:683, 1961

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Theory of Rotating Stars

Jean-Louis Tassoul. Theory of Rotating Stars . Princeton University Press, 1978

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Ellipsoidal Figures of Equilibrium

Subrahmanyan Chandrasekhar. Ellipsoidal Figures of Equilibrium . Yale University Press, 1969

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Bowers and E

Richard L. Bowers and E. P. T. Liang. Anisotropic sphere s in general relativity. The Astro- physical Journal , 188:657–665, 1974

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Friedman, James R

John L. Friedman, James R. Ipser, and Rafael D. Sorkin. T urning-point method for axisym- metric stability of rotating relativistic stars. The Astrophysical Journal , 325:722–724, 1988

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Rasio, and Stuart L

Dong Lai, Frederic A. Rasio, and Stuart L. Shapiro. Elli psoidal ﬁgures of equilibrium: Com- pressible models. The Astrophysical Journal Supplement Series , 88:205–252, 1993

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Ostriker and P

Jeremiah P. Ostriker and P. J. E. Peebles. A numerical st udy of the stability of ﬂattened galaxies. The Astrophysical Journal , 186:467–480, 1973. 28

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[1] [1]

In practice, we solve the dimensionless system using the variables introduced in Sec

and ( 23) outward from ( m(0) = 0 , ρ (0) = ρc). In practice, we solve the dimensionless system using the variables introduced in Sec. II C, starting at a small radius ¯r0 = 10 − 8 using a regular central expansion. The integration is terminated wh en the Chandrasekhar parameter becomes suﬃciently small, x(¯r) = xstop, x stop = 10 − 10, (26) which corresp...

work page

[2] [2]

slow-rotation

Quantitative readout and limiting conﬁgurations Figures 5–7 quantify the impact of the rotation–anisotropy mapping on global s equences. Across the explored grid, the Newtonian Chandrasekhar sequenc e approaches a high-density saturation regime; the corresponding limiting readout at the high-d ensity edge of the scan (log10 ρc = 11) is summarized in Table...

work page 2000

[3] [3]

The potential is determined by Poisson’s equation, ∇ 2Φ = 4 πGρ

Two-dimensional equilibrium formulation In Newtonian gravity, an axisymmetric, stationary, uniformly rota ting barotrope satisﬁes the ﬁrst integral H(ρ) + Φ − 1 2Ω 2̟ 2 = C, (32) where ̟ is the cylindrical radius, Φ is the gravitational potential, and H(ρ) ≡ ∫ ρ 0 dp ρ′ (33) is the speciﬁc enthalpy (for a barotropic Chandrasekhar EoS, p = p(ρ)) [6, 12]. T...

work page

[4] [4]

( 34), updates the enthalpy ﬁeld using Eq

Numerical method and convergence A standard approach is a self-consistent ﬁeld (SCF) iteration on a c ylindrical grid ( ̟, z ): starting from an initial density distribution with prescribed ρc and a trial surface, one computes Φ from Eq. ( 34), updates the enthalpy ﬁeld using Eq. ( 32), and reconstructs the density via the EoS inversion ρ = ρ(H) until con...

work page

[5] [5]

Benchmark observables and comparison method Two-dimensional equilibria provide distinct geometric radii: the equat orial radius Req and the polar radius Rp. For comparison to the one-dimensional reduced model, it is conven ient to deﬁne a volume-equivalent radius Rvol ≡ ( 3V 4π ) 1/ 3 , (35) where V is the stellar volume in the two-dimensional equilibrium...

work page

[6] [6]

limiting

Validation grid To keep the benchmark computationally focused while spanning the r elevant regimes, we consider a small but representative set of models across logarit hmically spaced central densities (covering the non-relativistic to relativistic-degenerate transition) and multiple slow-rotation rates (e.g. Ω / Ω K ≲ 0. 3). The resulting δM , δR, and O ...

work page 2025

[7] [7]

J. J. Hermes et al. Kepler observations of 27 pulsating da white dwarfs (davs). The Astro- physical Journal Supplement Series , 232, 2017

work page 2017

[8] [8]

Cataclysmic Variable Stars

Brian Warner. Cataclysmic Variable Stars . Cambridge University Press, 1995

work page 1995

[9] [9]

James B. Hartle. Slowly rotating relativistic stars. i. equations of structure. The Astrophysical Journal, 150:1005, 1967. 27

work page 1967

[10] [10]

Hartle and Kip S

James B. Hartle and Kip S. Thorne. Slowly rotating relati vistic stars. ii. models for neutron stars and supermassive stars. The Astrophysical Journal , 153:807, 1968

work page 1968

[11] [11]

J. P. Ostriker and P. Bodenheimer. Rapidly rotating star s. i. the self-consistent-ﬁeld method. The Astrophysical Journal , 151:1075, 1968

work page 1968

[12] [12]

I. Hachisu. A versatile method for obtaining structures of rapidly rotating stars. The Astro- physical Journal Supplement Series , 61:479, 1986

work page 1986

[13] [13]

Boshkayev, J

K. Boshkayev, J. A. Rueda, and R. Ruﬃni. On general relati vistic uniformly rotating white dwarfs. The Astrophysical Journal , 762, 2013

work page 2013

[14] [14]

Chandrasekhar

S. Chandrasekhar. The maximum mass of ideal white dwarfs . The Astrophysical Journal , 74:81, 1931

work page 1931

[15] [15]

An Introduction to the Study of Stellar Structure

Subrahmanyan Chandrasekhar. An Introduction to the Study of Stellar Structure . University of Chicago Press, 1939

work page 1939

[16] [16]

Shapiro and Saul A

Stuart L. Shapiro and Saul A. Teukolsky. Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects . Wiley, 1983

work page 1983

[17] [17]

Hamada and E

T. Hamada and E. E. Salpeter. Models for zero-temperatu re stars. The Astrophysical Journal, 134:683, 1961

work page 1961

[18] [18]

Theory of Rotating Stars

Jean-Louis Tassoul. Theory of Rotating Stars . Princeton University Press, 1978

work page 1978

[19] [19]

Ellipsoidal Figures of Equilibrium

Subrahmanyan Chandrasekhar. Ellipsoidal Figures of Equilibrium . Yale University Press, 1969

work page 1969

[20] [20]

Bowers and E

Richard L. Bowers and E. P. T. Liang. Anisotropic sphere s in general relativity. The Astro- physical Journal , 188:657–665, 1974

work page 1974

[21] [21]

Friedman, James R

John L. Friedman, James R. Ipser, and Rafael D. Sorkin. T urning-point method for axisym- metric stability of rotating relativistic stars. The Astrophysical Journal , 325:722–724, 1988

work page 1988

[22] [22]

Rasio, and Stuart L

Dong Lai, Frederic A. Rasio, and Stuart L. Shapiro. Elli psoidal ﬁgures of equilibrium: Com- pressible models. The Astrophysical Journal Supplement Series , 88:205–252, 1993

work page 1993

[23] [23]

Ostriker and P

Jeremiah P. Ostriker and P. J. E. Peebles. A numerical st udy of the stability of ﬂattened galaxies. The Astrophysical Journal , 186:467–480, 1973. 28

work page 1973