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REVIEW 4 major objections 6 minor 34 references

Accuracy and Applicability of the Hartle-Thorne and Komatsu-Eriguchi-Hachisu Methods for Modeling Rotating Neutron Stars

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The Hartle-Thorne perturbative method is inaccurate for rotating neutron stars above 200 Hz, so fully general relativistic KEH modeling is indispensable; at 800 Hz radius errors reach 8% and deformation-ratio errors 27%.

desk verdict Useful HT-vs-KEH calibration for OMEG EoSs, but the claim that the OMEG family isolates L is overstated and should be fixed before publication. read the letter →

arxiv 2511.10996 v3 pith:4PX6G6RX submitted 2025-11-14 astro-ph.HE astro-ph.SRgr-qcnucl-th

Hyukjin Kwon , Kenta Yoshimura , Tsuyoshi Miyatsu , Kazuyuki Sekizawa , Myung-Ki Cheoun This is my paper
classification astro-ph.HEastro-ph.SRgr-qcnucl-th
keywords neutronstarsrotatingHartle-ThornemethodKomatsu-Eriguchi-Hachisuequationofstatesymmetryenergyslopegeneralrelativityrotationaldeformation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the standard perturbative Hartle-Thorne method, which treats rotation as a small correction to a spherical star, remains trustworthy for real neutron stars. Comparing HT against a fully general-relativistic solver (KEH) for three equations of state that share the same saturation density, effective mass, and incompressibility but differ in the symmetry-energy slope L, the authors find that the two methods already separate at 200 Hz and badly diverge by 800 Hz: for a 1.4-solar-mass star, HT underestimates the equatorial radius by about 7-8% and the deformation ratio by 15-27%. They also find that larger L makes both the rotation-induced radius growth and the HT-KEH discrepancy larger. The paper concludes that any detailed statement about the internal structure or stability of rotating neutron stars requires full general relativity, not second-order perturbation theory.

What carries the argument

The machinery is a head-to-head comparison between two schemes. The Hartle-Thorne (HT) method expands the metric and fluid equations to second order in the spin frequency around a spherical TOV solution, producing radial corrections xi0 and xi2 that give the rotationally inflated radius and the polar-to-equatorial deformation ratio. The Komatsu-Eriguchi-Hachisu (KEH) method solves the full nonlinear Einstein equations as Poisson-like integral equations for an axisymmetric star, iterated to self-consistency on a compactified radial grid. The two are compared through the mass-radius curve and the deformation ratio R_polar/R_equatorial at fixed spin frequencies, with the OMEG equations of state

What would settle it

Build a set of equations of state with S0, K0, and effective mass strictly fixed while L varies from about 20 to 70 MeV, and rerun the HT-versus-KEH comparison at 200, 400, 600, and 800 Hz. If the ordering and size of the HT-KEH radius or deformation-ratio gaps do not follow L in that clean set, the paper's central L attribution fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the second-order Hartle-Thorne approximation is not accurate enough for rotating neutron stars above roughly 200 Hz. Using the OMEG series of nuclear equations of state — three relativistic mean-field parameter sets designed to differ only in the symmetry-energy slope L, with L = 70, 45, and 20 MeV — the authors show that rotation inflates the radius of a 1.4-solar-mass star by an L-dependent amount, and that HT misses much of this inflation. At 200 Hz the HT and KEH radii agree to about 0.2-0.3%, but at 800 Hz the HT radius is 6.9-8.4% smaller than the KEH value, and the deformation ratio R_polar/R_equatorial is wrong by 15-27%, with the largest error for t

Load-bearing premise

The conclusion that larger L drives the larger rotation-induced radius increase depends on the OMEG1/2/3 family truly isolating L, yet Table 1 shows the symmetry energy S0 drifts from 35.06 to 30.00 MeV and OMEG3 required an artificial crust-core connection, so if the family is not a clean L-isolation set the attribution is weakened.

Editorial extensions

If this is right

  • At spin frequencies relevant to known millisecond pulsars (200-700 Hz), radius and ellipticity estimates obtained from Hartle-Thorne should be treated as unreliable; HT underestimates the radius by several percent at the high end.
  • Because rotational stability and mass-shedding limits are controlled by deformation, the 15-27% deformation-ratio error means HT-based stability criteria are not dependable above a few hundred hertz.
  • Because the discrepancy grows with L, attempts to constrain the symmetry-energy slope from measured pulsar radii must use fully relativistic models to avoid a stiffness-dependent bias.
  • For maximum-mass configurations the two methods nearly agree, so TOV and HT remain adequate for questions about the maximum mass and its radius even at 800 Hz.

Reading between the lines

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

  • This goes beyond the paper: because the HT-KEH gap grows with L, existing constraints on L derived from HT-based radius or ellipticity fits to millisecond pulsars may carry a stiffness-dependent bias; refitting those data with KEH could shift the inferred L.
  • This goes beyond the paper: the two schemes should also be compared on moment of inertia and quadrupole moment, since those enter pulsar timing and gravitational-wave signals and would likely inherit the same discrepancy, making the effect observable beyond radii.
  • This goes beyond the paper: if the equation-of-state dependence of the gap is real, the spin frequency at which HT becomes unreliable is not universal but scales with stellar compactness; testing that scaling across many EoS families would turn the paper's qualitative conclusion into a quantitative rule.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The manuscript presents a comparative study of the Hartle–Thorne (HT) perturbative method and the fully general-relativistic Komatsu–Eriguchi–Hachisu (KEH) method for rotating neutron stars, using three OMEG equations of state designed to have different symmetry-energy slopes L. The authors compute mass–radius relations and deformation ratios R_ratio at rotation frequencies up to 800 Hz and find that (i) HT and KEH results diverge appreciably at high frequencies, with radius discrepancies of 7–8% at 800 Hz and deformation-ratio errors of 15–27%, and (ii) the rotation-induced radius increase is larger for EoSs with larger L. The paper concludes that the HT method is inadequate for detailed studies of rapidly rotating stars and that the fully relativistic KEH method is indispensable.

Significance. If the conclusions hold, the paper would provide a useful quantitative benchmark for the accuracy of the HT approximation across a range of nuclear equations of state, and would strengthen the case that the slope of the symmetry energy L correlates with rotational deformation and the rotational enhancement of stellar radius. The central qualitative trend—that HT and KEH diverge at high rotation—is consistent with previous work (e.g., Kacskovics et al. 2023; Kwon & Sekizawa 2025) and appears robust to the specific EoS parametrization. The study uses standard, independently implemented methods (TOV, HT, and KEH), and the numerical results are presented in sufficient detail for Tables 2 and 3 to be checked. However, the paper's second objective—isolating the effect of L—is undermined by the fact that the OMEG family does not keep the symmetry energy at saturation S0 fixed, and by an artificial pressure patching for OMEG3. These confounds weaken the attribution of the observed trend to L specifically. The paper also uses a potentially misleading error metric for the deformation ratio, which overstates the agreement between HT and KEH at low frequencies.

major comments (4)
  1. [Table 1 and §2.1; §3] The claim that the OMEG series isolates L is not supported by the data. Table 1 shows S0 varying from 35.06 to 30.00 MeV across OMEG1–OMEG3, a 14% change. The text of §2.1 dismisses this as a 'minor difference in S0', but §3 and the Conclusion state that 'all other nuclear matter properties are fixed' and that the results reveal the 'pure effect of L'. Since S0 itself is a known determinant of neutron-star radii, the observed monotonic increase in rotation-induced radius growth with L cannot be unambiguously attributed to L. Please either (a) construct an EoS family in which S0 is strictly fixed, (b) quantify the sensitivity of the computed radii and deformation to the S0 variation (e.g., by a covariance analysis or by re-fitting the isovector parameters to hold S0 constant), or (c) substantially soften the language attributing the trend to L alone. As written, the second objective is no
  2. [§2.1 (OMEG3 pressure patch)] The artificial connection of the OMEG3 core EoS to the MYN13 crust is a potential source of systematic error. The paper states that the original OMEG3 pressure temporarily falls below the crust pressure, so the two segments were 'artificially connected to ensure continuity'. Such a patch can introduce a kink or a non-physical derivative in P(ε), directly affecting the computed stellar radius and its response to rotation. No demonstration is provided that the patched EoS is thermodynamically consistent (e.g., monotonic P(ε), continuous speed of sound) or that the main conclusions are insensitive to the patching procedure. This is especially problematic for OMEG3, which is the key low-L point in the trend. Please show that the patched EoS does not introduce spurious effects, or exclude OMEG3 from the L-trend analysis and replace it with an unproblematic low-L EoS.
  3. [§3, Fig. 4 and Table 3] There is an internal inconsistency in the reported R_ratio–Ω relation for the KEH method. The text states that at R_ratio = 0.5, the KEH frequency is about 800 Hz for OMEG1 and about 900 Hz for OMEG3. However, Table 3 reports R_ratio^KEH = 0.6787 (OMEG1) and 0.7635 (OMEG3) at Ω = 800 Hz. If the curves in Fig. 4 are monotonic, these two sets of numbers cannot both be correct. The discrepancy affects the quantitative claim about the L-dependence of the deformation and must be resolved. Please correct either the text or the table/figure, and re-evaluate any conclusions that rely on those numbers.
  4. [Table 3 (error metric)] The 'Error' column in Table 3 computes (R_ratio^HT − R_ratio^KEH)/R_ratio^KEH, which is a relative error in the radius ratio itself. This metric is misleading for the paper's stated goal of assessing rotational deformation. For example, for OMEG1 at 200 Hz, R_ratio^HT = 0.99218 and R_ratio^KEH = 0.98922, so the relative difference in R_ratio is only 0.30%, but the relative difference in the deformation parameter ε = 1 − R_ratio is (0.01078 − 0.00782)/0.01078 ≈ 27.5%. Thus the HT method underestimates the oblateness by about 27% even at 200 Hz, which is not 'agree within a few percent' as the table caption states. The paper should report errors in ε (or in the quadrupole moment) and discuss their implications for the claimed applicability of HT at low frequencies. This directly affects the interpretation of the abstract's statement that the two methods 'deviate from each other even for th
minor comments (6)
  1. [Abstract] Typo: 'emamine' should be 'examine'.
  2. [§2.2.2, Eq. (20)] The term 'd¯ω dr 2' is garbled; it should be (d\barω/dr)^2. Please correct the LaTeX/rendering.
  3. [§2.2.2, Eq. (17)] In Eq. (17), the scaling of \barω is described, but it is not stated that the scaled \barω must be re-integrated into the second-order equations. While this is standard, a brief comment would help readers unfamiliar with the HT method.
  4. [§3 and Fig. 4] The caption of Fig. 4 says the inset shows 'nearly identical results below 200 Hz', but Table 3 shows errors in R_ratio of 0.30–0.53% at 200 Hz. This is arguably 'nearly identical' for R_ratio itself, but in light of the deformation-error issue (major comment 4), this wording is misleading. Please clarify in terms of the deformation parameter.
  5. [§2.1] The phrase 'minor difference in the S0 value' is inconsistent with the later claims of 'pure effect of L'. Even if the authors intend to treat S0 as secondary, the manuscript should explicitly acknowledge the 5 MeV variation and discuss its potential impact.
  6. [References] The DOI for Conde-Ocazionez et al. (2025) appears malformed: '10.1103/c3jx-5487'. Please verify the correct DOI.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction: HT and KEH are independent algorithms; self-citations and the OMEG EoS are not load-bearing, though the L-isolation premise is confounded by S0 variation.

full rationale

The paper's central claims are (1) a direct numerical comparison of two independently formulated stellar-structure algorithms — the HT perturbative ODEs (Eqs. 13–21) and the KEH self-consistent field scheme (Eqs. 28–32) — and (2) a trend in rotational radius increase across the OMEG EoS family. Neither method is fitted to the other: HT is solved at fixed Ω and KEH is iterated at fixed axis ratio, with output Ω compared afterward; no parameter of one method is calibrated to reproduce the other. The EoS tables are taken from the published OMEG construction (Miyatsu et al. 2023) with tabulated nuclear properties in Table 1, and the KEH implementation follows Komatsu et al. 1989 and Cook et al. 1992/1994. Citations to the authors' prior work (Kwon & Sekizawa 2025; Miyatsu et al. 2023, 2025) are descriptive or corroborative, not invoked as a uniqueness theorem or as an ansatz that forbids alternatives. No equation reduces to another by construction. The manuscript's own caveats do flag an imperfect control: Table 1 shows S0 varying from 35.06 to 30.00 MeV while §2.1 states the properties are 'almost the same with minor difference in the S0 value', and §2.1 admits the OMEG3 core/crust match had to be 'artificially connected to ensure continuity.' These are validity/confounding concerns for attributing the trend specifically to L, not circularity: the HT-vs-KEH discrepancy is computed from the actual tabulated EoSs and would stand even if the L-isolation premise fails. Therefore the derivation is not circular; the L-attribution is a scientific-risk flag rather than a circular step.

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

The paper introduces no new physical entities. Its central claims rest on calibrated EoS inputs from the authors' own prior work, a rigid-rotation law, and the assumption that the OMEG family isolates L—an assumption partially violated because S0 also varies and OMEG3 required an artificial pressure patch.

free parameters (3)
  • OMEG meson-coupling parameters (g_σ, g_ω, g_ρ, g_δ, g2, g3, c3, Λ_σδ, Λ_ωρ) = Not listed in this paper; resulting saturation L = 70, 45, 20 MeV
    These are calibrated in Miyatsu et al. (2023) to nuclear and astrophysical constraints and are the inputs that produce OMEG1-3. The L-correlation claim inherits this calibration.
  • Artificial OMEG3 crust-core pressure patch = Unknown; one patching point in density-pressure plane
    The text says the two segments were 'artificially connected to ensure continuity' (§2.1). This hand-chosen patch is an ad hoc input affecting OMEG3 results.
  • S0 variation across OMEG sets = 35.06, 33.00, 30.00 MeV
    Not a parameter chosen in this paper, but a nuisance variation that breaks the 'only L differs' premise (Table 1), so it must be counted when interpreting the L-dependence.
assumptions (6)
  • standard math Einstein field equations with perfect-fluid stress-energy describe neutron-star spacetimes.
    §2.2, Eqs. (8)-(9): foundation of both TOV and rotating-star calculations.
  • domain assumption Relativistic mean-field approximation and non-linear meson couplings (σ, ω, δ, ρ) give a valid nuclear EoS.
    §2.1, Eqs. (1)-(6): entire EoS input rests on this effective-field-theory truncation.
  • ad hoc to paper OMEG1-3 isolate L while other saturation properties are fixed.
    §1 and Table 1 claim only L varies; Table 1 shows S0 also changes. The paper's L-attribution depends on this premise.
  • domain assumption β-equilibrium, charge neutrality, and matching to the MYN13 crust EoS are valid.
    §2.1, Fig. 1: NS EoS constructed under npeμ equilibrium; crust-core matching invoked. The OMEG3 patching shows this matching is not seamless.
  • domain assumption Rigid rotation (j(Ω) = A²(Ω-Ω_c) with A→∞) is a sufficient rotation law for the comparison.
    §2.2.3, Eq. (31): differential rotation neglected; conclusions are limited to rigid rotators.
  • domain assumption KEH self-consistent-field iterations converge to the exact stationary axisymmetric solution.
    §2.2.3: the paper provides no convergence tests; it assumes the KEH output is the 'fully relativistic' benchmark.

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Cite this review

Pith. "Pith review of Accuracy and Applicability of the Hartle-Thorne and Komatsu-Eriguchi-Hachisu Methods for Modeling Rotating Neutron Stars." pith.science (2026). https://pith.science/paper/4PX6G6RX

@misc{pith2026251110996,
  author       = {Pith},
  title        = {Pith review of: Accuracy and Applicability of the Hartle-Thorne and Komatsu-Eriguchi-Hachisu Methods for Modeling Rotating Neutron Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4PX6G6RX}},
  note         = {Machine review of arXiv:2511.10996}
}
abstract

Neutron stars, which are composed of extremely dense nuclear matter, serve as natural laboratories to study nuclear interactions beyond the terrestrial experiments. Recent researches have actively explored how the equation of state (EoS) can be constrained by observed neutron star masses and radii, and how nuclear interactions affect their macroscopic properties. Most of these studies, however, rely on the Tolman-Oppenheimer-Volkoff (TOV) equations, which assumed static, spherically symmetric neutron stars. Since neutron stars are rotating objects and thus axisymmetrically deformed, the TOV calculation may be insufficient to capture their realistic structure. In this work, we investigate the influence of nuclear matter properties on the physical quantities of rotating neutron stars using two approaches: the perturbative Hartle-Thorne (HT) method and fully general relativistic Komatsu-Eriguchi-Hachisu (KEH) method. For nuclear EoS parameter sets, we emamine the OMEG series, in which the slope of the symmetry energy $L$ is systematically varied. We find that rotational effects lead to a noticeable increase in the stellar radius, which depends sensitively on values of $L$. Additionally, focusing on the rotational deformation, we show that the results obtained by these two methods deviate each other even for the slowly rotating case such as $\Omega=200$ Hz. These results reveal that, for detailed discussions on the internal structure and stability of rotating neutron stars, the fully general relativistic method such as KEH is indispensable.

Figures

Figures reproduced from arXiv: 2511.10996 by the authors.

Figure 1
Figure 1. Equations of state calculated under the β-equilibrium and charge neutrality conditions using OMEG parameter sets. Pressure P is shown as a function of baryon number density n. Results are shown for three OMEG parameter sets: OMEG1 (red), OMEG2 (blue), OMEG3 (black) For each OMEG parameter set, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Mass-radius relations for neutron stars obtained from the TOV equation using the OMEG+MYN13 EoSs. The red, blue, and black curves correspond to OMEG1, OMEG2, and OMEG3, re￾spectively. The conservation condition of energy-momentum (9) pro￾vides the hydrostatic equilibrium condition (∇µT µν = 0) ln H + ϱ + γ 2 + 1 2 ln (1 − v 2 ) + Z j(Ω)dΩ = C, (29) with ln H = Z dP ε + P . (30) where H is the enthalpy, v is the flui… view at source ↗
Figure 3
Figure 3. Mass–radius relations for neutron stars calculated using the HT (dashed lines) and KEH (solid lines) methods at various ro￾tational frequencies (200, 400, 600, and 800 Hz) for three different EoSs: OMEG1 (a), OMEG2 (b), and OMEG3 (c). The black solid line represents the TOV result. Both methods show that the neutron star mass and radius increase with rotational frequency, and the dif￾ference between the HT and KEH r… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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