{"id":"e1473e09-4bce-4224-b95d-b0f2327f88e0","arxiv_id":"2505.03527","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In Aether Scalar-Tensor theory, slowly rotating neutron stars obey approximate universal moment-of-inertia versus compactness relations that deviate from general relativity and are fit with parameter-dependent formulae.","lead":"Neutron stars in the alternative gravity theory AeST are predicted to spin with moments of inertia that follow two universal curves, different from Einstein's general relativity, depending on two theory constants. If real, pulsar X-ray and gravitational wave measurements could test or rule out this MOND-style dark matter alternative.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The I-C relations assume a time-aligned aether with A_r=0 at zeroth order; if a tilted-aether branch exists, the background and all extracted J values change, and the paper gives no error estimate.","rationale":"The strongest claim is an observational discriminator: AeST I-C relations differ from GR and could be measured. That claim fails if the solutions themselves are built on an incomplete static-sector ansatz. The authors flag this limitation in Sec. IV, which is a point in their favor, but the central numerical results inherit the truncation. I would not reject or accept outright: the paper provides code and fits, and the concern is a concrete, testable incompleteness rather than an established error. I part company with the reader on one detail: the vanishing of the O(epsilon) scalar perturbation is not just an ansatz but follows from parity (axial source vs polar scalar), and the cosmological phi(t,r)=qt+phi(r) is plausibly negligible at NS scales; the unresolved piece is the zeroth-order radial aether. If the linearized test shows only b=0, the CONDITIONAL verdict can be upgraded. If a b≠0 branch exists, the I-C relations need recomputation.","tokens_in":13405,"tokens_out":28512,"duration_ms":322773,"concrete_test":"Linearize the radial component of the aether equation of motion (Eq. 5) about the time-aligned static background, using the full ansatz A=a(r)dt+b(r)dr with b treated as first order. Impose regularity at r=0 and asymptotic flatness at large r. If the only solution is b(r)=0, the ansatz is safe; if a nontrivial solution exists, solve the full static background on that branch and recompute the slow-rotation equations, the angular momentum J from Eq. (22), and the fits (26)-(28) to quantify the shift in the I-C relations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III's rotational calculation is built on the static, spherically symmetric solutions of [61], in which the aether is time-aligned. Equation (9) fixes A_r=0 in the static background, and the text says this is chosen 'to ensure consistency with our previous work,' not derived from the field equations. In static spherical symmetry the general unit-timelike aether is A=a(r)dt+b(r)dr; b(r) is not killed by the symmetry, and setting b=0 is an additional truncation. If a regular, asymptotically flat solution with b≠0 exists, the zeroth-order equations (12)-(13), the first-order equations (18)-(19), and the asymptotic coefficient used to identify J in Eq. (22) all change, so the I-C fits (26)-(28) and the claimed GR deviation would shift. The discussion in Sec. IV explicitly lists allowing a radial vector component (and the cosmological scalar phi(t,r)=qt+phi(r)) as future work; no estimate is given for the size of the resulting change. The O(epsilon) scalar perturbation is less concerning, because the rotation source is parity-odd while a scalar perturbation is parity-even, so delta phi=0 at this order is justified; the zeroth-order vector truncation is the real vulnerability.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13787,"tokens_out":10031,"duration_ms":107273,"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":[{"comment":"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.","section":"Section III, Eq. (9)"},{"comment":"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.","section":"Section III.B, Eqs. (18)-(19)"},{"comment":"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.","section":"Section III, fitting formulae"}],"minor_comments":[{"comment":"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.","section":"Section III, Eq. (8)"},{"comment":"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.","section":"Section III, Eqs. (26)-(29)"},{"comment":"The sentence 'we do show them here' should read 'we do not show them here.'","section":"Section III.B, before Eq. (18)"},{"comment":"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.","section":"Section III.B, Eq. (24)"},{"comment":"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.","section":"Figure 4"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Chris, the thing to know: this is the first slow-rotation neutron-star calculation in AeST, and it produces I-C relations that deviate from GR in a parameter-dependent way. The work is real, the code is provided, and the fitting forms are useful. The main caveat is the restricted aether ansatz, which the paper acknowledges but does not quantify.\n\nWhat is genuinely new: the authors extend their static neutron-star work to first order in rotation, derive the perturbation equations, solve them numerically for ten equations of state, and fit the resulting I-C relations across the relevant parameter space. The GR deviation is shown explicitly and the interpretation in terms of central density concentration is sensible. The paper is also transparent about what it is not doing: the discussion section explicitly lists the radial vector component and scalar time dependence as future work.\n\nThe soft spots are real but not disqualifying. The biggest is the zeroth-order aether ansatz: A_r is set to zero for consistency with prior work, not because the field equations kill it. A unit timelike vector in static spherical symmetry can have a radial piece, and if a tilted branch exists, the background, the angular-momentum extraction, and therefore the I-C relations would all shift. The paper gives no estimate of the resulting error. This does not invalidate the relations under the chosen ansatz, but it does mean the claim is narrower than \"the theory predicts\" suggests. Second, the first-order functions W and S are not displayed; they live in the supplementary code. That is acceptable for reproducibility but makes independent verification harder than it should be. Third, the removal of the spurious quadratic mode is explained but not accompanied by numerical error bars. Fourth, the universal-relation fits are not cross-validated; with ten EOS and dozens of fit coefficients, overfitting is a legitimate worry.\n\nThese are moderate concerns, not a takedown. The central argument holds for the stated ansatz, and the paper is clearly written and honest about its limitations. It will appeal to people working on alternative-gravity phenomenology, particularly AeST and related MOND theories. It deserves a serious referee: the derivation should be checked, the shown equations should appear in the text, the fit validation should be reported, and the aether-branch question should be addressed or explicitly relegated to future work with an estimate of its likely impact. I would send it to a competent referee and ask for those revisions.","headline":"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.","tokens_in":14250,"tokens_out":2000,"would_cite":false,"duration_ms":21398,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.40.Dg","04.50.Kd"],"model":"deepseek-v4-flash","headline":"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…","keywords":["Aether Scalar-Tensor theory","MOND","neutron stars","slow rotation","moment of inertia","compactness","universal relations","modified gravity"],"falsifier":"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.","tokens_in":13200,"feed_emoji":"🌟","tokens_out":10046,"duration_ms":93128,"temperature":0.7,"pith_summary":"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.","feed_headline":"Slowly spinning neutron stars separate MOND gravity from Einstein's","feed_subtitle":"The theory's spin-compactness curves deviate from general relativity across ten equations of state.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the AeST action and its strong-field limit, the theory whose neutron-star relations are computed.","marker":"[44]"},{"why":"Supplies the static, spherically symmetric neutron-star solutions used as the zeroth-order input.","marker":"[61]"},{"why":"Supplies the first-order slow-rotation metric ansatz and the matching procedure used to extract angular momentum.","marker":"[70]"},{"why":"Provides the general-relativistic universal relations that the AeST curves are compared against.","marker":"[62]"},{"why":"Provides the APR equation of state used in the solutions and figures.","marker":"[71]"},{"why":"Source of the explicit form of the first-order equations and the derivation of the asymptotic expansions used to extract $J$.","marker":"[75]"},{"why":"Supplies the method for combining two numerical solutions to impose asymptotic flatness and fix integration constants.","marker":"[76]"}],"fun_headline_variants":["MOND neutron stars: spin curves that split from Einstein","Slow-spin neutron stars reveal MOND's altered inertia","Neutron star spin-compactness: MOND vs GR different","Aether MOND stars: new universal relations for spin","Pulsar spin can test MOND against Einstein gravity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["MOND neutron stars: spin curves that split from Einstein","Slow-spin neutron stars reveal MOND's altered inertia","Neutron star spin-compactness: MOND vs GR different","Aether MOND stars: new universal relations for spin","Pulsar spin can test MOND against Einstein gravity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000224,"raw_usage":{"total_tokens":1436,"prompt_tokens":896,"completion_tokens":540,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":512,"completion_tokens_details":{"reasoning_tokens":456}},"tokens_in":512,"tokens_out":540,"duration_ms":5509,"temperature":1.0,"reasoning_tokens":456,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:49:22.257134+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Neutron Stars in Aether Scalar-Tensor Theory","cited_arxiv_id":"2406.18225","evidence_quote":"Supplies the static, spherically symmetric neutron-star solutions used as the zeroth-order input."},{"cited_title":"Reyes and J","cited_arxiv_id":null,"evidence_quote":"Source of the explicit form of the first-order equations and the derivation of the asymptotic expansions used to extract $J$."},{"cited_title":"I-Love-Q in Einstein-aether Theory","cited_arxiv_id":"2306.11930","evidence_quote":"Supplies the method for combining two numerical solutions to impose asymptotic flatness and fix integration constants."}],"review_version":1}