{"id":"d53ad7eb-be38-4380-a244-7322e670f30b","arxiv_id":"1908.08188","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"For the RR model of nonlocal gravity, orbital frequency shifts around a Kerr-like black hole are reported, but the metric is imported from prior work and no reproducible calculation is provided.","lead":"A short paper applies perturbation theory to the RR nonlocal gravity model and reports small shifts in orbital frequencies around a rotating black hole. The rotating metric is inherited from the authors' earlier work and the frequency-shift calculation is not shown in enough detail to be reproduced.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The rotating metric (10) is imported from Ref. [8] without any check that it satisfies the RR field equations; every computed frequency shift depends on this unvalidated metric.","rationale":"The reader's weakest assumption is exactly the missing validation of the rotating metric: all physical content is derived from Eq. (10), and the paper itself says the calculation is deferred. I agree with the REJECT verdict: the central claim cannot be checked from the preprint, and the load-bearing metric imported from Ref. [8] is not verified against the field equations. The recommendation is UNCHANGED because the stress-test confirms, rather than alters, the reader's assessment. The one concrete test that would settle the issue is substitution of the µ²-perturbation of metric (10) into the linearized field equations; a nonzero residual would prove that the frequency shifts are not predictions of the RR model. Even if that test passed, the paper would still need a full derivation with stated orbital parameters before the central claim could be accepted, but the present lack of verification justifies rejection as submitted.","tokens_in":3596,"tokens_out":8810,"duration_ms":89353,"concrete_test":"Take metric (10), expand it as g = g_Kerr + µ² b + O(µ⁴), linearize the field equations (2) around the Kerr background, and check whether b satisfies the resulting O(µ²) equations for the stated a and M. If the residual is nonzero, metric (10) is not a solution of the RR model and the frequency shifts are not valid predictions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is the RR-model frequency shift, computed as m δω_i = ∂⟨H1⟩/∂J_i with H1 built from bαβ, the difference between metric (10) and Kerr. The text gives no derivation of (10): it is 'obtained by applying Demianski-Janis-Newman algorithm ... in [8]'. The NJA procedure is not generally a solution generator for modified gravity; a stationary metric produced this way need not solve Eq. (2). The paper never substitutes (10) into the field equations, gives no explicit bαβ, no gauge fixing, no averaging details, and Sec. III explicitly defers the calculation to future work. Figure 1 is unreproducible because no orbital parameters or µ value are stated. If (10) is not a vacuum solution, the plotted shifts are not predictions of nonlocal gravity. A related indication of trouble is that the weak-field potentials (9) do not reduce to Schwarzschild when µ→0, which suggests an error in the metric inputs and strengthens the need for an independent check.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies geodesic motion around a rotating black hole in the RR model of nonlocal gravity. Section II derives a weak-field rotating metric (Eq. 8) with potentials Φ and Ψ given in Eq. (9). Section III presents a Kerr-like metric (Eq. 10) obtained by applying the Demianski-Janis-Newman algorithm in the authors' Ref. [8], and claims to compute the shift in orbital frequencies using canonical perturbation theory, with numerical results shown in Fig. 1. The text explicitly states that the detailed calculation of the frequency shifts and the solution of the geodesic equations will be presented in future work.","tokens_in":3782,"tokens_out":5339,"duration_ms":51913,"significance":"If the metric (10) were a verified solution of the RR field equations and the frequency shifts were correctly computed, the paper would provide an interesting first step toward strong-field tests of nonlocal gravity using EMRIs. The topic is timely, and the use of canonical perturbation theory on a Kerr background is a standard and promising approach. However, as it stands, the central result is not derived in this manuscript: the rotating metric is imported from a preprint by the same authors without verification, and the actual frequency-shift calculation is deferred to a future publication. No code, machine-checked algebra, or reproducible numerical parameters are provided for Fig. 1. The paper is better described as a research announcement than a complete derivation.","major_comments":[{"comment":"The metric (10) is stated to be \"obtained by applying Demianski-Janis-Newman algorithm ... in [8]\", but the manuscript does not verify that this metric satisfies the RR field equations (2). This is load-bearing because all subsequent frequency-shift computations are built from the perturbation bαβ extracted from (10). Without such a check, the plotted shifts are not necessarily predictions of RR nonlocal gravity. The Newman-Janis algorithm is not a general solution-generating technique in modified gravity, so the paper should either demonstrate that (10) solves Eq. (2) or explicitly label it as a conjecture pending verification.","section":"Section III, Eq. (10)"},{"comment":"The text states that \"The detailed discussion on calculation of shift in orbital frequencies and solution of geodesic equations ... will be done in our future work.\" This directly contradicts the abstract and conclusion, which claim that the shift has been calculated. The manuscript omits the explicit form of H1, the averaging procedure ⟨H1⟩, the action-angle variables used, and the numerical parameters (p, e, θmin, a, µ) behind Fig. 1. Consequently, Fig. 1 is not reproducible and the central claim of the paper is not substantiated within the manuscript itself.","section":"Section III, paragraph after Eq. (10)"},{"comment":"In the limit µ→0, the potentials in Eq. (9) reduce to Φ(r) ≈ −GM/(3r) and Ψ(r) ≈ −5GM/(3r). With Eq. (8), the weak-field metric then does not reduce to the standard weak-field Schwarzschild/Newtonian limit (g_tt ≈ −(1 − 2GM/r), g_rr ≈ 1 + 2GM/r in isotropic coordinates). This is a concrete internal inconsistency in a solution that is presented as a derivation from the field equations. It suggests an error in the metric input and must be resolved before the weak-field result can be trusted.","section":"Section II, Eq. (9)"},{"comment":"Equation (6) uses the symbol M in the nonlocal terms (e.g., 2M²□^{-1}) where the model's mass scale is µ, introduced after Eq. (1). If M here denotes the central mass, the equation is dimensionally or physically ambiguous because the nonlocal correction should be governed by µ. If it is a typo for µ², please correct it throughout the equation.","section":"Section II, Eq. (6)"}],"minor_comments":[{"comment":"The title and affiliations contain typographical errors: \"Grav ity\" on the arXiv title line and \"Isra el\" in the first affiliation should be corrected.","section":"Title and affiliations"},{"comment":"Reference [7] spells the author's name as \"Demiaski\"; the standard spelling is \"Demianski\" as used in the text.","section":"References"},{"comment":"Figure 1 does not state the values of the orbital parameters (p, e, θmin), the mass ratio a/M, or the nonlocal scale µ. Without these, the numerical curves cannot be reproduced or compared with other work. The caption should define the units of p and the convention for Ω_i.","section":"Figure 1"},{"comment":"The dφ² term in Eq. (10) is written in a dense form with nested parentheses; adding a clarifying line or an explicit comparison with the standard Kerr metric would improve readability.","section":"Section III, Eq. (10)"},{"comment":"The Conclusion repeats the claim that the frequency shifts were calculated, but no equation for δω_i appears anywhere in the paper; please number and include the final result or explicitly reference a companion paper.","section":"Concluding remarks"}],"recommendation":"reject","confidential_remarks":"The manuscript reads as a brief proceedings contribution rather than a self-contained journal paper. The main issues are not stylistic: the central derivation is explicitly deferred to future work, the imported rotating metric is unverified against the field equations, and the weak-field limit contains a possible inconsistency. These problems cannot be fixed by local edits; they would require a substantially new manuscript. I recommend rejection, while noting that the intended program — frequency shifts for EMRIs in nonlocal gravity — is worthwhile if pursued with a complete derivation and reproducible numerics."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe one thing to know: this is a conference-style announcement, not a complete derivation. The genuinely new bit is the application of Vigeland-Hughes canonical perturbation theory to the RR-model metric, producing the first (if correct) EMRI dephasing curves for that model. That is a legitimate idea, and the authors correctly identify the right tool for it. The weak-field rotating metric in Sec. II is also a concrete attempt to solve the linearized equations. So the paper is not empty.\n\nBut the load-bearing part does not hold up as written. The rotating black-hole metric (10) is simply imported from the authors' own Ref. [8], with no check that it satisfies the RR field equations (2). The Newman-Janis algorithm is not a solution generator in modified gravity; a metric that looks Kerr-like need not solve the actual EOM. Every computed frequency shift is built from the perturbation bμν extracted from this metric, so if (10) is not a true solution, the plotted curves are not predictions of the model. The text explicitly defers the details to future work.\n\nThere is also a concrete internal red flag: the weak-field potentials in (9) do not reduce to Schwarzschild when μ→0. Plugging μ=0 gives Φ = -GM/(3r) and Ψ = -5GM/(3r), not the standard linearized Schwarzschild values. Since the action reduces to Einstein-Hilbert in that limit, this suggests an error in the potential derivation or in the metric. At minimum, the authors should address this. The figure is likewise unreproducible: no orbital parameters (p, e, θ_min) or μ value are stated, and the curves are plotted in arbitrary units. The shifts are tiny (10^-9), which makes the lack of parameter specification even more frustrating.\n\nThe citation pattern is narrow but not abusive; they build on their own prior work and the standard Kerr perturbation literature. The μ value is a cosmological fit, so the numerical magnitude is not parameter-free—a limitation the paper does not state.\n\nWho is this for? A reader who wants a preview of the authors' ongoing program might skim it, but a referee cannot verify the central claim. The framework idea is worth developing, and the future paper might be good. As it stands, however, this preprint is too thin for a serious journal. I would not send it to peer review in its current form; I'd suggest the authors complete the derivation, check the metric against the field equations, fix the weak-field limit, and state the orbit parameters.","headline":"A short research announcement built on an unvalidated rotating metric; the frequency-shift idea is plausible but the paper as written is not independently checkable.","tokens_in":4348,"tokens_out":4821,"would_cite":false,"duration_ms":41985,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.70.-s","04.50.Kd"],"model":"deepseek-v4-flash","headline":"The paper claims that in the RR nonlocal gravity model, the orbital frequencies of a test particle around a rotating black hole are Kerr values plus calculable nonlocal shifts.","keywords":["nonlocal gravity","RR model","rotating black hole","geodesic motion","orbital frequencies","extreme mass ratio inspirals","canonical perturbation theory","Kerr-like metric"],"falsifier":"Substitute metric (10) into the vacuum RR field equations (2) and check whether the residual tensor vanishes at order $\\mu^2$; if it does not, the plotted frequency shifts are not predictions of the RR model. Independently, integrate the geodesic equation numerically in metric (10) and compare the resulting fundamental frequencies with the canonical-perturbation values shown in Fig. 1.","tokens_in":3367,"feed_emoji":"🌀","tokens_out":13974,"duration_ms":125833,"temperature":0.7,"pith_summary":"The paper aims to set up a strong-field test of the RR nonlocal gravity model using extreme mass ratio inspirals (EMRIs), where a small compact object orbits a supermassive black hole. It constructs a Kerr-like metric for a rotating black hole in this model, treats the nonlocal correction as a small perturbation, and computes the shift in the three fundamental orbital frequencies of a test particle. The weak-field limiting metric for a rotating object is also derived. If the rotating metric is a genuine solution, the plotted frequency shifts are what EMRI gravitational-wave templates would need to incorporate.","feed_headline":"Nonlocal gravity shifts orbital frequencies near spinning black holes","feed_subtitle":"Paper computes the shift via a perturbed Kerr metric; the effect is ~10^-9 but accumulates over many orbits.","key_machinery":"The load-bearing object is the RR action $S=\\frac{1}{2\\kappa^2}\\int d^4x\\sqrt{-g}\\,[R+\\frac{\\mu^2}{3}R\\,\\Box^{-2}R]$, whose nonlocal term generates the perturbation $b_{\\alpha\\beta}$ in the rotating metric $g_{\\alpha\\beta}=g^{\\rm Kerr}_{\\alpha\\beta}+b_{\\alpha\\beta}$. The argument runs through canonical perturbation theory: for bound Kerr geodesics the unperturbed motion separates in action-angle variables, and the first-order frequency shift is $\\delta\\omega_i = \\frac{1}{m}\\frac{\\partial\\langle H_1\\rangle}{\\partial \\hat J_i}$, with $H_1=-(m^2/2)b_{\\alpha\\beta}u^\\alpha u^\\beta$ averaged over one unperturbed orbit. The right-hand panel of Fig. 1 is the numerical evaluation of these three shifts from the explicit $b_{\\alpha\\beta}$ extracted from metric (10).","core_discovery":"The central claim is that in the RR model, the spacetime around a rotating black hole is Kerr plus a small nonlocal perturbation, metric (10), and that geodesic orbital frequencies are the Kerr frequencies plus calculable shifts $\\delta\\omega_i$ obtained from the averaged perturbing Hamiltonian. The magnitude of the shift is controlled by the nonlocal mass scale $\\mu$, fixed by cosmology to $\\mu \\simeq 0.283 H_0$. The paper reports the resulting shifts in the observable frequencies as functions of the orbital semilatus rectum and finds them negative, of order $10^{-9}$ in the plotted range. This is the ingredient needed to build waveform templates in which nonlocal gravity leaves an imprint on EMRI signals.","pith_inferences":["The absent field-equation check leaves a concrete computational task: substitute metric (10) into the vacuum field equations (2); until that is done, Fig. 1 should be read as a prediction of the metric ansatz rather than of the RR action itself.","The same canonical-perturbation pipeline applies to any nearly-Kerr metric, so it offers a cheap way to compare alternative modified-gravity black-hole models before full waveform generation is attempted.","Because the per-orbit shift is small but the number of orbits in an EMRI is large, the dephasing acts as a natural amplifier, making a Hubble-scale parameter potentially testable by future space-based gravitational-wave detectors.","The weak-field rotating metric (8) provides an independent, nearer-term test of the same model in regimes where the effective potentials can be measured directly."],"forward_implications":["EMRI waveform templates built on pure Kerr will carry a systematic nonlocal correction; the paper's shifts give the leading piece of that correction.","The plotted shifts are negative and as large as several parts in $10^9$ in the displayed range, so over the many cycles of an EMRI the accumulated phase difference can become observable.","The weak-field rotating metric (8) predicts nonlocal modifications to frame-dragging and to the effective potentials $\\Phi$ and $\\Psi$, which can be checked in weaker-field observations.","The same Hamilton-Jacobi and averaging machinery remains valid, so analytic templates for nonlocal-gravity EMRIs do not require abandoning Kerr-based methods."],"supporting_citations":[{"why":"Defines the RR nonlocal gravity action and fixes the model whose black-hole metric and frequencies the paper computes.","marker":"[1]"},{"why":"Supplies the rotating black-hole metric (10) obtained by the rotation algorithm from the static RR solution; this is the central input to the perturbation calculation.","marker":"[8]"},{"why":"Provides the canonical perturbation theory for geodesic frequency shifts in almost-Kerr spacetimes, yielding the formula the paper evaluates.","marker":"[4]"},{"why":"Gives the relativistic action-angle formalism for computing fundamental orbital frequencies in Kerr, used here as the unperturbed background.","marker":"[10]"},{"why":"Establishes separability of Kerr geodesic motion and supplies the constants of motion used in the averaging.","marker":"[9]"},{"why":"Supplies the weak-field potentials used in the rotating weak-field metric (8) for the RR model.","marker":"[5]"}],"fun_headline_variants":["Nonlocal gravity shifts orbital frequencies near spinning black holes","Tiny nonlocal gravity effect alters black hole orbits","Nonlocal gravity leaves imprint on EMRI orbital frequencies","Kerr-like black holes show nonlocal gravity frequency shifts","Nonlocal gravity modifies geodesic frequencies around rotating black holes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire frequency-shift calculation rests on the unverified assumption that metric (10), obtained by rotating the spherical RR solution with a standard solution-generating trick, is an actual solution of the RR field equations; if that assumption fails, the frequency shifts are not predictions of the model.","fun_headline_variants_meta":{"raw":{"variants":["Nonlocal gravity shifts orbital frequencies near spinning black holes","Tiny nonlocal gravity effect alters black hole orbits","Nonlocal gravity leaves imprint on EMRI orbital frequencies","Kerr-like black holes show nonlocal gravity frequency shifts","Nonlocal gravity modifies geodesic frequencies around rotating black holes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000602,"raw_usage":{"total_tokens":2740,"prompt_tokens":805,"completion_tokens":1935,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":421,"completion_tokens_details":{"reasoning_tokens":1857}},"tokens_in":421,"tokens_out":1935,"duration_ms":15387,"temperature":1.0,"reasoning_tokens":1857,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:52:39.075405+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Substitute metric (10) into the vacuum RR field equations (2) and check whether the residual tensor vanishes at order $\\mu^2$; if it does not, the plotted frequency shifts are not predictions of the RR model. Independently, integrate the geodesic equation numerically in metric (10) and compare the resulting fundamental frequencies with the canonical-perturbation values shown in Fig. 1.","supporting_citations":[{"cited_title":"Kumar, S","cited_arxiv_id":null,"evidence_quote":"Supplies the rotating black-hole metric (10) obtained by the rotation algorithm from the static RR solution; this is the central input to the perturbation calculation."},{"cited_title":"Metric for Rotating object in Infrared Corrected Nonlocal Gravity Model","cited_arxiv_id":"1808.04569","evidence_quote":"Supplies the weak-field potentials used in the rotating weak-field metric (8) for the RR model."}],"review_version":1}