{"id":"b94098e2-1ba9-4363-9899-ba13300ca581","arxiv_id":"2607.15324","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"In a rotating LQG-corrected black hole model, the polymeric parameter P lowers scalar quasinormal-mode frequencies, while spin raises them.","lead":"This paper computes scalar quasinormal-mode frequencies and ringdown signals for a rotating black hole spacetime built by applying the Newman–Janis trick to a loop-quantum-gravity-corrected Schwarzschild metric. It claims the LQG 'polymeric' parameter P lowers the oscillation frequency, leaving a possible imprint for future gravitational-wave detectors.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Effective potential Eq. (17)/(24)/(31) is asserted, not derived, with M(r) undefined; all QNM results are therefore untethered from the claimed spacetime.","rationale":"The stress-test identifies the same load-bearing assumption as the reader. Because the manuscript provides no derivation for Eq. (17), no code/data, and no benchmark against Kerr, the central claim cannot be evaluated as a property of the spacetime. The slow-rotation violation is a supporting symptom, not the root cause. I agree with the rejection and recommend no change to the verdict.","tokens_in":12806,"tokens_out":7458,"duration_ms":62213,"concrete_test":"Derive the scalar Klein-Gordon equation for metric (7) under the same slow-rotation expansion used in the paper (keep terms through O(a), and if feasible O(a^2)), separate variables, and reduce to a Schrödinger form; then compare with Eq. (17) and identify M(r). As a minimal independent check, set P=a_0=0 (Kerr), take a=0.5, and compute the l=2, m=0 and l=2, m=1 scalar QNMs from the derived potential; they should match known Kerr results from Leaver or a Teukolsky code. If Eq. (17) does not reproduce the Kerr spectrum, the P-trend in Fig. 5/Fig. 7 is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Every WKB frequency and time-domain signal in this paper is computed from the effective potential V_l(r) given by Eq. (17) (restated as (24) and (31)). This potential is not derived from the Klein-Gordon equation (13) in the rotating metric (7). The function M(r) is never defined; the paper only says 'M(r) denotes the effective mass function induced by the loop quantum gravity corrections through the revised Newman–Janis construction' (Sec. 3). In the classical limit P=a_0→0, the metric reduces to Kerr, but Eq. (17) is independent of the azimuthal number m and of aω; the actual scalar perturbation equation for Kerr includes m a ω and additional a^2 corrections at this order. Moreover, the stated slow-rotation assumption aω≪1 is contradicted by the parameter values used later (a up to 0.99 with Re(ω)~0.5), so the approximation is applied outside its regime. If Eq. (17) is not the correct reduction of Eq. (13), then all reported QNM shifts—including the headline result that P reduces Re(ω)—are properties of an undefined function, not of the claimed LQG-corrected Kerr spacetime.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript computes scalar quasinormal modes (QNMs) and ringdown waveforms for a rotating loop-quantum-gravity black hole obtained by a revised Newman–Janis algorithm. The spacetime depends on the polymeric parameter P and a minimal-area parameter a0 and reduces to Kerr when both vanish. Using a sixth-order WKB approximation and time-domain integration, the authors report that increasing P lowers Re(ω), while increasing the spin a raises Re(ω), and conclude that future gravitational-wave detectors might constrain LQG parameters through ringdown spectroscopy.","tokens_in":13220,"tokens_out":3270,"duration_ms":32582,"significance":"If the underlying perturbation calculation were correct, the paper would supply a concrete, falsifiable ringdown prediction for a class of LQG-inspired rotating black holes. The claimed parameter trends could motivate searches for anomalous spin-dependence in black-hole spectroscopy. The paper does not fit data, so the P-dependence is not circular; it is an internal consequence of the assumed metric and effective potential. However, the reliability of the entire numerical output depends on an effective potential that is asserted rather than derived, and on a slow-rotation expansion that is applied outside its stated domain. For that reason the central claim is currently unsupported.","major_comments":[{"comment":"The effective potential V_l(r) is stated without derivation from the Klein–Gordon equation for the metric (7). The function M(r) is never defined; Eq. (31) silently replaces it with a constant M. Every WKB frequency and time-domain signal follows from this potential, so the headline result that P reduces Re(ω) is a property of an undefined function unless the reduction from Eq. (13) to Eq. (15) is supplied. In particular, the Kerr limit should reproduce the well-known scalar-field potential including the m a ω and a^2 corrections; Eq. (17) does not contain m or aω, so it is not the standard slow-rotation reduction of the rotating wave equation.","section":"Section 3, Eqs. (17)/(24)/(31)"},{"comment":"The stated slow-rotation condition aω ≪ 1 is contradicted by the parameter range used. Figure 8 varies a from 0 to 0.99 while Re(ω) ~ 0.5 and M=1, giving aω ~ 0.5 even for moderate a and aω > 1 near a=0.99. Table 1 lists Re(ω) ~ 0.52 without stating the a, P, a0 values used. The approximation is therefore applied outside its regime, and the quoted high-spin trends — including the 'turnover' in Im(ω) — are not trustworthy.","section":"Section 3 and Figs. 4–8"},{"comment":"Table 1 reports six-digit QNM frequencies with no statement of a, P, a0, nor a Kerr (P=0) benchmark for comparison. This makes the numerical results irreproducible and prevents the reader from checking whether the P-induced shift is larger than the WKB error. Additionally, the text of Section 5.3 lists P = 0.1, 0.3, 0.5, 0.7 while the caption of Fig. 8 lists P = 0.01, 0.05, 0.1, 0.2; this inconsistency further obscures which results are being reported.","section":"Table 1 and Section 5.3"},{"comment":"The time-domain analysis claims to show the dependence of the ringdown on the overtone index n, but n is imposed by adding an oscillatory modulation to the initial Gaussian packet rather than extracted from the evolution (e.g., by Prony analysis). The resulting waveforms therefore do not demonstrate the physical overtone structure of the black hole, and the statement that 'higher overtone modes decay more rapidly' is asserted from artificially excited initial data rather than from the QNM spectrum.","section":"Section 6.5"}],"minor_comments":[{"comment":"The notation oscillates between V_l(r) and V(r), and between l and ℓ; Eqs. (15)/(17) and (22)/(24) repeat the same derivation verbatim. Eq. (29) is introduced but never used; it can be removed.","section":"General"},{"comment":"The function F_LQG(r;P) in Eq. (32) is undefined. If it is meant to be F(r) from Eq. (4), that should be stated explicitly.","section":"Section 5, Eq. (31)"},{"comment":"Figure captions do not always specify fixed parameters (e.g., Fig. 4 and Fig. 5); Fig. 5 uses a logarithmic P-axis without mentioning it in the caption. Several panels in Figs. 2 and 3 appear to have dense axis labels that would be illegible in print.","section":"Figures"},{"comment":"There are typographical issues, including 'Schr\"odinger' in Section 3 and inconsistent spacing in 'a 0'. The reference list contains at least one questionable entry (Ref. [29], 'A. Sakharov, Quantum gravity black hole models', JETP Lett. 81, 167 (2005)) that should be checked.","section":"Text"}],"recommendation":"reject","confidential_remarks":"The central derivation is missing: the effective potential that generates all numerical results is assumed, not derived, and M(r) is undefined. The slow-rotation approximation is violated in exactly the high-spin regime that anchors the paper's main figures. These are not cosmetic issues; they undermine the connection between the reported QNM shifts and the claimed LQG-corrected Kerr spacetime. I do not see a path to acceptance without a substantially new derivation and validation against a Kerr benchmark."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Liang, two things up front. First, the headline result—polymeric parameter P lowers Re(ω), spin a raises it—is consistent across the plots, and the WKB/time-domain machinery is standard. Second, the whole computation rests on an effective potential, Eq. (17), that is stated, not derived, and contains an undefined function M(r). That is load-bearing, not cosmetic.\n\nWhat is new: the paper extends refs. [37] and [39] with more systematic parameter scans (a0 dependence, ℓ-n hierarchy) and time-domain ringdown. The classical limit correctly reduces to Kerr. The figures presumably show a coherent picture: P smooths and broadens the barrier, lowering Re(ω); a raises the peak and shifts it inward. Those trends are plausible for any LQG-corrected Kerr model.\n\nThe soft spots: (1) The potential is not derived from the Klein-Gordon equation in the rotating metric. The slow-rotation approximation is invoked, but the potential has no m a ω or a² corrections, which is suspicious. (2) M(r) is never defined; in Eq. (31) it becomes a bare M. Without M(r), the tables and figures are not reproducible. (3) The stated condition aω ≪ 1 is violated: the plots go to a = 0.99 with ω ~ 0.5, so aω ~ 0.5. (4) Table 1 gives six-digit frequencies with no parameter values or a Kerr benchmark. (5) Prior work (refs. 37, 39) already covers rotating LQG QNMs; this paper does not state a new result beyond more numbers.\n\nThe central trend may survive a more careful derivation—that is plausible. But as it stands, the frequencies are properties of an undefined function, not of the claimed spacetime. There is no code, no data, no benchmark to check.\n\nWho is this for? A specialist in LQG phenomenology might extract intuition about parameter dependencies, but they would have to trust the unstated potential. I would not bring it to the reading group. As for peer review: I would desk-reject this version and ask the authors to derive the potential, define M(r), and restrict to the slow-rotation regime. If they can do that, the paper becomes refereeable. Right now it is not.","headline":"The parameter trends are clean, but the effective potential is asserted with an undefined mass function, so every reported frequency is untethered from the claimed spacetime.","tokens_in":13594,"tokens_out":10164,"would_cite":false,"duration_ms":81309,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that loop-quantum-gravity corrections systematically lower black-hole ringdown frequency, while spin raises it.","keywords":["loop quantum gravity","rotating black holes","quasinormal modes","ringdown signals","gravitational waves","polymeric parameter","scalar perturbations","Newman–Janis algorithm"],"falsifier":"Solving the scalar perturbation equation for the metric of Eq. (7) exactly (e.g., by separating the angular and radial equations without the slow-rotation approximation) and checking whether Re(ω) still decreases monotonically with P at fixed a would directly test the claim. Alternatively, deriving the true radial potential from the full Klein–Gordon equation and showing it differs from Eq. (24) would falsify the analysis.","tokens_in":12728,"feed_emoji":"🕳️","tokens_out":7859,"duration_ms":69016,"temperature":0.7,"pith_summary":"This paper sets out to show that quantum corrections from loop quantum gravity produce a characteristic, measurable shift in the quasinormal-mode spectrum of a rotating black hole. Starting from a static self-dual LQG black hole, the authors build a rotating metric with the revised Newman–Janis algorithm and compute the effective potential for scalar perturbations. Solving the resulting wave equation with sixth-order WKB and time-domain integration, they find that the polymeric parameter P always reduces the oscillation frequency Re(ω), while the spin parameter a increases it, and the minimal-area parameter a0 gives a milder but similar shift. If the prediction is right, future gravitational-wave detectors could search for this systematic frequency drop as a direct probe of quantum geometry.","feed_headline":"Quantum gravity parameter lowers black hole ringdown tone","feed_subtitle":"The paper predicts a systematic frequency drop that gravitational-wave detectors could one day measure.","key_machinery":"The load-bearing object is the effective potential for scalar perturbations, Vℓ(r) = Δ(r)/(r²+a²)² [ℓ(ℓ+1) + 2M(r)r/(r²+a²)], with Δ(r) = r² F_LQG(r;P) + a². The quantum deformation enters through the radial function F_LQG(r;P) inherited from the static LQG metric via the revised Newman–Janis construction; the potential's peak height, width, and location control the quasinormal frequencies through the sixth-order WKB condition. Spin enters through a in Δ and in the tortoise coordinate dr* = (r²+a²)/Δ dr, shifting the peak inward. Here P is the polymeric parameter, a dimensionless quantum-geometry deformation, and a0 is the minimal-area scale.","core_discovery":"On the paper's own terms, the central discovery is that the quasinormal spectrum of the rotating LQG black hole separates into opposite trends: quantum deformation (P and, weakly, a0) lowers the real part of the frequency and broadens the effective potential barrier, whereas rotation a raises the frequency and at high spin reverses the spin-dependence of the damping rate. This is obtained by reducing the scalar Klein–Gordon equation, under the slow-rotation approximation, to a Schrödinger-like radial equation with effective potential Vℓ(r) = Δ(r)/(r²+a²)² [ℓ(ℓ+1) + 2M(r)r/(r²+a²)], where Δ(r) = r²F_LQG(r;P)+a² encodes the quantum-deformed radial sector. The authors compute complex frequencie","pith_inferences":["If the monotonic P-induced frequency drop holds beyond the slow-rotation approximation and in gravitational perturbations, it would mean the effect is not a scalar-field artifact; this is testable by computing the fully separable angular equation for the metric of Eq. (7).","The same Newman–Janis construction could be applied to charged or higher-dimensional LQG metrics; if the direction of the shift is universal, the ringdown-frequency drop becomes a generic marker of nonclassicality rather than a model-dependent detail.","Since the paper's own parameter choices reach a=0.99 with ω≈0.5, violating the stated aω≪1 condition, a direct numerical integration of the full wave equation at high spin would settle whether the predicted trend survives or is an artifact of the effective potential approximation.","The frequency shift at fixed spin is equivalent to a redshift of the photon-sphere angular frequency; comparing the eikonal-limit relation ω≈ℓΩ_c across ℓ could separate the quantum contribution from a pure mass rescaling."],"forward_implications":["For fixed spin, the fundamental scalar ringdown frequency decreases monotonically as P grows, giving a clean, monotonic quantum-gravity signature.","Because spin a raises the frequency while P lowers it, a measurement that ignores rotation would misinterpret a quantum shift as a spin effect (or vice versa).","Higher multipoles ℓ ring at higher frequency and higher overtones decay faster in the time-domain signals, so mode separation can isolate the quantum shift from geometric effects.","If the shifts are as computed, future gravitational-wave detectors could in principle constrain the LQG parameters by measuring the real part of the ringdown frequency of a stellar-mass or intermediate-mass black hole.","The results suggest a partial separation of roles: P mainly softens and broadens the potential barrier, while a mainly raises its peak and pulls it inward."],"fun_headline_variants":["LQG parameter reduces black hole ringdown frequency","Quantum correction lowers black hole oscillation tone","Rotating LQG black hole shifts quasinormal modes","Polymeric parameter drops black hole ringdown pitch"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The paper's central claim rests on the assumption that Eq. (24)'s effective potential is the correct slow-rotation scalar perturbation potential for the rotating LQG metric — a point the paper states but does not derive, and one that its own parameter range (aω≪1 with a up to 0.99) appears to violate.","fun_headline_variants_meta":{"raw":{"variants":["LQG parameter reduces black hole ringdown frequency","Quantum correction lowers black hole oscillation tone","Rotating LQG black hole shifts quasinormal modes","Polymeric parameter drops black hole ringdown pitch"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000222,"raw_usage":{"total_tokens":1265,"prompt_tokens":691,"completion_tokens":574,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":435,"completion_tokens_details":{"reasoning_tokens":515}},"tokens_in":435,"tokens_out":574,"duration_ms":6047,"temperature":1.0,"reasoning_tokens":515,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T01:06:10.171230+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Solving the scalar perturbation equation for the metric of Eq. (7) exactly (e.g., by separating the angular and radial equations without the slow-rotation approximation) and checking whether Re(ω) still decreases monotonically with P at fixed a would directly test the claim. Alternatively, deriving the true radial potential from the full Klein–Gordon equation and showing it differs from Eq. (24) would falsify the analysis.","supporting_citations":[],"review_version":1}