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Slowly Rotating Neutron Stars in Aether Scalar-Tensor Theory

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Pith's one-line read Slowly rotating neutron stars in Aether Scalar-Tensor theory obey nearly equation-of-state-independent moment-of-inertia versus compactness relations, and those relations differ from general relativity in a way controlled by the theory's…

desk verdict First slow-rotation neutron-star calculation in AeST with parameter-dependent I-C relations; the paper is honest about its ansatz restrictions but leaves the key error budget unquantified. read the letter →

arxiv 2505.03527 v1 pith:XGNQJ5OG submitted 2025-05-06 gr-qc astro-ph.COastro-ph.HEhep-ph

Christopher Reyes , Jeremy Sakstein This is my paper · ORCID
classification gr-qcastro-ph.COastro-ph.HEhep-ph PACS 04.40.Dg04.50.Kd
keywords AetherScalar-TensortheoryMONDneutronstarsslowrotationmomentofinertiacompactnessuniversalrelationsmodifiedgravity
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

Aether Scalar-Tensor theory (AeST) is a relativistic gravity model built to act like cold dark matter on cosmological scales and like MOND in galaxies, while passing the gravitational-wave speed constraint. This paper derives the equations for slowly rotating neutron stars in AeST to first order in the rotation rate and solves them for ten equations of state. The result is that the dimensionless moment of inertia as a function of compactness, $I/(MR^2)$ or $I/M^3$ versus $C=GM/R$, is nearly independent of the equation of state, just as in general relativity. The AeST curves, however, sit away from the general relativity curves, with the offset governed by the theory parameters $K_B$ and $\lambda_s$. If the relations hold, X-ray measurements of neutron star compactness combined with moment-of-inertia estimates can test AeST against general relativity without the usual uncertainty from nuclear physics.

What carries the argument

The machinery is the first-order-in-rotation system obtained from the $(t,\phi)$ Einstein equation and the $\phi$ vector equation: two coupled second-order equations (18) and (19) for the frame-dragging potential $\omega(r)$ and the aether perturbation $B(r)$. The background metric and matter profiles that feed these equations come from the zeroth-order static solution, so previous static neutron-star solutions are inputs. Angular momentum is extracted from the large-distance behavior $\omega(r)\to\Omega_*-2GJ/r^3$; a spurious $\propto r^2$ mode in $B(r)$ is identified and removed by combining two numerical solutions, and the constant integration freedoms are fixed by matching to the asymptotic metric. The final piece is the polynomial fitting functions, equations (26) and (28), which convert the numerical curves into parameter-dependent formulas usable for quick comparison with observations.

What would settle it

Recompute the first-order equations with $\phi(t,r)=qt+\phi(r)$ and a nonzero radial aether component; if the resulting $I/(MR^2)$ or $I/M^3$ at fixed $C$ moves by more than the reported 1.5 percent average error, the published fits are not the theory's full prediction. Observationally, a precise joint measurement of one neutron star's compactness and moment of inertia, for example by X-ray pulse-profile modeling plus pulsar timing on a $1.4\,M_\odot$ star, that falls on the GR curve while the AeST fits for all allowed $K_B$ and $\lambda_s$ lie outside the error bars would rule out the claimed relations.

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Extended reading notes

Core claim

Within the first-order slow-rotation approximation, the paper finds two approximate universal relations in AeST: the dimensionless moment-of-inertia combinations $I/(MR^2)$ and $I/M^3$ are smooth functions of compactness $C$ that are almost insensitive to the equation of state. These functions are not the general relativity ones. Both relations move away from GR in a way controlled by $K_B$ and $\lambda_s$, and the paper provides fitting polynomials, equations (26) and (28), whose coefficients are tabulated, covering $0.1<K_B<0.3$ and $1<\log_{10}(\lambda_s)<3$ with an average relative error of 1.5 percent. The physical picture is that AeST stars of a given mass are more centrally concentrated than GR stars, so the moment of inertia is smaller. The asymptotic falloff $\omega(r)\to\Omega_* - 2GJ/r^3$ fixes the stellar angular momentum $J$, and $I=J/\Omega_*$ yields the relations. The paper's stated upshot is that these relations make neutron star observations a route to distinguishing AeST from general relativity.

Load-bearing premise

The calculation assumes the scalar field around the star has no time dependence and the aether vector has no radial piece at zeroth order; if the cosmological phase $\phi(t,r)=qt+\phi(r)$ or a radial vector component contributes at neutron-star scales, the extracted angular momentum and the I-C relations will shift.

Editorial extensions

If this is right

  • A measured compactness from X-ray pulse-profile modeling can be converted through the fits into a predicted AeST moment of inertia and compared directly with pulsar-timing estimates, with equation-of-state uncertainty largely cancelled.
  • Deviations from the GR I-C relations grow with the AeST parameters in a predictable way, so a sufficiently precise set of neutron star measurements would translate into bounds on $K_B$ and $\lambda_s$ rather than just a yes/no test.
  • The relations supply the missing link between compactness measurements and the tidal-deformability plane used by gravitational-wave observatories, making a multimessenger test of AeST possible.
  • Because the relations are approximately universal, the test does not require knowing which equation of state describes neutron star matter, the main obstacle to using static stars.
  • Deriving the next-order rotation equations would yield AeST analogues of the I-Love-Q relations, extending the same measurement strategy to higher multipoles.

Reading between the lines

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

  • The paper's simplifying ansatz leaves two avenues that could shift the relations: a time-dependent scalar mode $\phi(t,r)=qt+\phi(r)$ tied to cosmology, and a radial component of the aether vector. Quantifying the size of those corrections is a natural next step before the fits are used for precision tests.
  • The AeST relations probe the strong-field, quasi-static limit of the theory, so a measured offset from GR would constrain how the MOND-inspired sector behaves at neutron-star densities, not the low-acceleration MOND regime itself.
  • A targeted falsifier is a single high-precision measurement of $I$ and $C$ for one neutron star; because the AeST and GR curves separate by more than the fit error for much of parameter space, one clean measurement already discriminates.
  • The same two-equation machinery, with the aether perturbation $B(r)$ playing the role of an extra channel, could be ported directly to tidal Love numbers; if the I-C insensitivity persists, an AeST I-Love-Q relation is plausible.
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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

3 major / 5 minor

Summary. The manuscript derives, at first order in a slow-rotation expansion, the equations governing neutron stars in Aether Scalar-Tensor theory using a Hartle-type metric, solves them numerically for ten equations of state, and extracts the moment of inertia from the asymptotic frame-dragging behavior. It proposes two approximate universal relations between the dimensionless moments of inertia and compactness, with fitting formulae (26)-(29) and coefficients in Tables I-II, covering 0.1<K_B<0.3 and 1<log10(λ_s)<3. The authors argue that AeST predicts smaller moments of inertia than GR at fixed mass and that the I-C relations deviate from GR in a parameter-dependent way, making them potentially useful for multimessenger tests. The derivation is carried out with xTensor/xCoba, and the numerical implementation is posted on Zenodo.

Significance. If the result holds, this is the first AeST prediction for slowly rotating neutron-star structure and I-C relations, and it provides testable, falsifiable signatures that differ from GR. Positive features include a transparent field-content setup, publicly archived code with a DOI, explicit recognition of the restricted field ansatz, and fitting formulae spanning a wide parameter range. However, the significance is currently conditional: the main prediction rests on a truncated zeroth-order vector configuration, on equations that are not displayed in the paper, and on fitting/universality diagnostics that are not yet quantified. These points need to be resolved before the claims can be accepted.

major comments (3)
  1. [Section III, Eq. (9)] Eq. (9) restricts the zeroth-order aether to be time-aligned with no radial component. In a static, spherically symmetric spacetime a unit-timelike vector field generically has A = a(r)dt + b(r)dr, and the field equations do not by themselves force b=0; the text states the choice is made 'to ensure consistency with our previous work.' Because the background equations (12)-(13), the first-order system (18)-(19), and the asymptotic identification of J in Eq. (22) all depend on this background, an unquantified b≠0 branch would shift all extracted I and therefore the fits (26)-(28) and the claimed GR deviation. The Discussion in Section IV lists the radial vector component and the cosmological scalar time dependence as future work but gives no error estimate. Please either prove that b=0 follows from the static, spherically symmetric field equations with the chosen boundary conditions, or quantify the change produced by a nontrivial b(r), for instance by solving the general ansatz perturbatively.
  2. [Section III.B, Eqs. (18)-(19)] The functions W(r;KB,λ_s,α) and S(r;KB,λ_s,α) are not written out; the paper says their explicit form and derivation are in the supplementary code [75]. These functions are the core of the derivation: they determine ω(r) and B(r), hence J and I, so the numerical results are not checkable from the paper text. Please include the full expressions in an appendix or as a permanent ancillary file attached to the paper, and describe the main steps of the derivation rather than only pointing to code.
  3. [Section III, fitting formulae] The claims of approximate universality and of parameter-dependent deviation from GR are supported only by a 1.5% average relative error and 0.48% standard deviation over the fitted sample. The paper does not report per-EOS residuals, leave-one-EOS-out cross-validation, a residual plot, or the number and gridding of models; nor does it show the GR curve against which the AeST fits are compared. Please add these diagnostics, and also state the numerical integration tolerances and the sensitivity of the extracted J to the subtraction of the spurious b r^2 mode described in Section III.B.
minor comments (5)
  1. [Section III, Eq. (8)] The sentence following Eq. (8) says 'ϕ1(r)P1(cosθ) is even'; P1(cosθ) is parity-odd. The conclusion that no scalar perturbation is sourced at first order is correct, because the parity-even scalar cannot be excited by the axial l=1 source, but the explanation should be corrected.
  2. [Section III, Eqs. (26)-(29)] After Eq. (26), the text says the coefficients {Ci,0, ξi, bi, di} are given in Table I, but Eq. (27) also contains gi and pi; the same omission occurs after Eq. (29) and Table II.
  3. [Section III.B, before Eq. (18)] The sentence 'we do show them here' should read 'we do not show them here.'
  4. [Section III.B, Eq. (24)] The statement that the growing b r^2 mode is 'absent when higher-order terms in the metric are included' is imprecise; in a boundary-value problem the mode is excluded by the asymptotic flatness boundary condition, and numerical noise excites it. Please clarify this point.
  5. [Figure 4] The ten equations of state are only said to be 'given in the legend'; please ensure the legend is legible in print or list the EOSs explicitly in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the I–C relations are numerical outputs of solving the AeST field equations, not inputs; self-citations to prior work are independent support.

full rationale

The paper's central result, the AeST I–C relations, is obtained by numerically integrating the first-order slow-rotation equations (18)–(19) derived from the action (1), with the angular momentum J extracted from the asymptotic coefficient in (22) and the moment of inertia defined as I=J/Ω*. The fitting functions (26)–(28) are posterior fits to that numerical output, with stated 1.5% average error; the fits are not used as inputs to the integration, so the 'fitted input called prediction' pattern does not apply. The zeroth-order background solutions are taken from the authors' previous paper [61]; while this is a self-citation, it is not circular in the sense defined here because [61] is a separate, published derivation with its own code and stated assumptions, and the present paper's new content is the first-order derivation and the resulting relations, which do not reduce to [61] by construction. No uniqueness theorem is imported, and no ansatz is smuggled in via citation: the vector ansatz (9) is explicitly stated as a choice ('to ensure consistency with our previous work'), with the non-generality acknowledged, and the discussion lists allowing a radial vector component and time-dependent scalar as future work. That is a correctness/validity caveat about the restricted ansatz, not a circularity. The paper is therefore self-contained against the external benchmarks of the 10 equations of state and the known GR I–C relations, and the central claim has independent content.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The ledger shows that the central claim inherits the AeST action from the literature, the static background from the authors' prior work, and two explicit ansatz restrictions. No new particles, forces, or entities are introduced. The only numbers fitted to data in this work are the 60 fitting coefficients of the I-C relations.

free parameters (4)
  • lambda_s (AeST strong-field coupling) = scanned over log10(lambda_s) in [1,3], not fitted here
    Appears in the strong-field action; controls deviation from GR and enters every stellar structure equation; the I-C fits are parameterized by X=log10(lambda_s).
  • K_B (aether kinetic coupling) = scanned over K_B in [0.1,0.3], not fitted here
    Second AeST parameter; stability requires 0<K_B<2; enters the stellar equations and the I-C fitting coefficients.
  • Table I fitting coefficients (C_i0, xi_i, b_i, d_i, g_i, p_i, i=0..5, 36 numbers) = listed in Table I
    Least-squares fit of the eI-C relation (Eq. 27) to numerical data for 10 equations of state; the paper quotes 1.5% average error on the fitting data.
  • Table II fitting coefficients (C_i0, xi_i, b_i, d_i, g_i, p_i, i=1..4, 24 numbers) = listed in Table II
    Least-squares fit of the Ibar-C relation (Eq. 29) to the same numerical data; same caveat as Table I.
assumptions (6)
  • domain assumption The strong-field form of F(Y,Q) reduces to (2-K_B)lambda_s Y + K_2 (Q-Q0)^2, and the K_2 mass term is negligible because mu R_NS << 1.
    Invoked in Section II to justify the static-NS equations; mu ~ Mpc^-1 comes from cosmological fits, so the error is expected small but is not quantified here.
  • domain assumption The static, spherically symmetric neutron star solutions from the authors' previous work [61] are correct and sufficient as zeroth-order input for the rotation equations.
    Same-authors prior paper, not independently reproduced in this work; the first-order equations are solved on top of those static solutions.
  • ad hoc to paper The scalar field can be treated as time-independent around neutron stars; the q t cosmological term has negligible local effect.
    Explicitly stated in Section III; a length-scale argument is given, but no quantitative estimate of the error is provided.
  • ad hoc to paper The aether vector has no radial component and is time-aligned at zeroth order; only l=1 odd perturbations are kept.
    Eq. (9); chosen for consistency with [61], not derived from the full field content of the theory.
  • domain assumption The quadratic r^2 mode in B(r) at large distances is a numerical artifact and can be removed by combining two numerical solutions.
    The Minkowski-space analysis shows such a mode exists, but the paper assumes the physical solution has b=0 and that numerical extraction of b_j is reliable.
  • standard math The Hartle-Thorne slow-rotation expansion and the identification I = J/Omega* are valid at first order in spin.
    Standard slow-rotation formalism from [70], used in all cited I-C relation papers.

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Pith. "Pith review of Slowly Rotating Neutron Stars in Aether Scalar-Tensor Theory." pith.science (2026). https://pith.science/paper/XGNQJ5OG

@misc{pith2026250503527,
  author       = {Pith},
  title        = {Pith review of: Slowly Rotating Neutron Stars in Aether Scalar-Tensor Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XGNQJ5OG}},
  note         = {Machine review of arXiv:2505.03527}
}
abstract

Aether Scalar-Tensor theory is a relativistic alternative gravity model that behaves like cold dark matter on cosmological scales while predicting the MOND force-law in astrophysical systems. The theory correctly predicts the cosmic microwave background and linear matter power spectra, and the mass discrepancies observed across the Universe. We derive and solve the equations governing neutron stars in Aether Scalar Tensor theory at first-order in slow rotation, finding that the theory predicts approximate universal relations between the moment of inertia and the compactness ($I$--$C$ relations) that differ from their general relativity counterparts. These relations may enable tests of Aether Scalar-Tensor theory using X-ray observations of pulsars and gravitational wave observations of binary neutron star mergers.

Figures

Figures reproduced from arXiv: 2505.03527 by the authors.

Figure 1
Figure 1. FIG. 1. Mass-radius relations for the AeST parameters indicated in the figure assuming the APR EOS. The left panel shows [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. I-M relations for the AeST parameters indicated in the figure assuming the APR EOS. The left panel shows the effect [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Density profile for a NS with mass of 2 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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