{"id":"f2d24e3c-2ba2-48a1-bec4-ddd55bea77eb","arxiv_id":"2607.08619","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"In shift-symmetric Horndeski gravity, scalar field QNM contamination of black hole ringdowns appears at the same perturbative order as frequency shifts, and can dominate them if scalar amplitude suppression is relaxed.","lead":"When black holes ring down after merging, any hidden scalar fields would imprint their own frequencies on the gravitational wave signal, not just shift the expected frequencies. This matters because current tests of General Relativity only look for frequency shifts, missing a potentially dominant contamination effect.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"No significant objection identified. The perturbative structure is sound and the central claims follow directly from the derived equations.","rationale":"The reader correctly identifies the single-scale assumption as the weakest link, but this is a standard EFT assumption that is explicitly stated and does not threaten the paper's conditional claims. I looked for a more structural concern—particularly in the perturbative counting, the operator hierarchy, or the claim about which couplings survive at each order—and could not find one. The logic tracing from Eqs. (14)-(21) to the ansatz in Eq. (31) is internally consistent: each source term is correctly attributed to specific couplings, the vanishing of ϕ^(0,2) by the no-hair theorem is properly invoked, and the distinction between frequency-shift terms (carrying metric QNM frequencies) and contamination terms (carrying scalar QNM frequencies) is maintained throughout. The paper does not compute numerical QNM values, but its claims are structural and do not require them. The main limitation is that the practical detectability of contamination depends on unknown amplitudes (B_n, D_n, H_n) set by initial data, but the paper is appropriately modest about this. The verdict of ACCEPT at HIGH confidence is appropriate.","tokens_in":14316,"tokens_out":4290,"duration_ms":307538,"concrete_test":"Independently re-derive Eq. (21) from the full shift-symmetric Horndeski action including the O(X²) terms suppressed in Eq. (9), and verify that none of these higher-order kinetic terms contribute at O(ϵq²). The paper claims this check was performed but does not show it explicitly. If any O(X²) term survives at this order, the conclusion that only α and τ₄ are relevant would need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"I examined the perturbative logic carefully and could not identify a load-bearing concern that threatens the central claims. The key structural result—that the background d'Alembertian (for the scalar) and linearized Einstein tensor (for the metric) act as the operators at each perturbative order—is consistent: metric corrections at O(q²) only feed back into dynamical equations through the explicitly included -2δ²G_μν[h^(1,0), h^(0,2)] term in Eq. (21), and higher-order corrections to these operators are beyond O(ϵq²). The claim that only α and τ₄ contribute at O(ϵq²) follows directly from tracing which source terms in Eq. (21) survive: S^(1,2)[h^(1,0)] and S^(1,2)[ϕ^(1,1)] involve only α (since ϕ^(1,1) is itself sourced only by α through Eq. 17), while S^(1,2)[ϕ^(1,0)] introduces τ₄ but vanishes when ϕ^(1,0)=0. The reader's identified concern (single-scale assumption forcing τ_i scaling) is a real assumption but is standard EFT practice, explicitly stated, and the paper's claims are conditional on it. The paper honestly presents both the ϕ^(1,0)=0 and ϕ^(1,0)≠0 cases. No hidden circularity or internal inconsistency was found.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"This paper studies black hole ringdown perturbations in shift-symmetric Horndeski gravity, focusing on how massless scalar fields affect quasinormal mode (QNM) frequencies. The authors employ a double perturbative expansion in dynamical perturbations ($ϵ$) and scalar charge per unit mass ($q$), extending prior work to $O(ϵq^2)$. The central result is that, under the assumption that the scalar amplitude is suppressed by $q$ (i.e., $ϕ^{(1,0)}=0$), the linear coupling $αϕG$ between the scalar and the Gauss-Bonnet invariant is the only interaction contributing to both frequency shifts and contamination at $O(ϵq^2)$, with both effects appearing at the same perturbative order. If this suppression assumption is relaxed, contamination appears at $O(ϵq)$ and can dominate over frequency shifts, with subleading corrections from the quartic coupling $τ_4$. The perturbative framework is systematic: the hierarchical field equations (Eqs. 18–21) are derived step by step, and the ringdown ansatz (Eq. 31) is constructed by tracing which source terms survive at each order. The key structural simplification—that the background d'Alembertian (scalar sector) and linearized Einstein tensor (metric sector) serve as operators at each perturbative order—is consistent, and the claim that only $α$ and $τ_4$ contribute at $O(ϵq^2)$ follows directly from the source term structure in Eq. (21).","tokens_in":14861,"tokens_out":1018,"duration_ms":253346,"significance":"The paper addresses a timely and important question in gravitational-wave physics: whether the standard black hole spectroscopy program, which models beyond-GR effects purely as frequency shifts, is systematically biased by missing contamination from additional field modes. The result that contamination and frequency shifts generically appear at the same perturbative order (under standard assumptions) provides concrete theoretical backing for the theory-agnostic claims of Ref. [37] and motivates updating ringdown search templates. The identification of exactly which Horndeski couplings ($α$ and $τ_4$) are relevant at $O(ϵq^2)$ is a useful simplification for EFT-based modeling. The falsifiable prediction that contamination can dominate over shifts when $ϕ^{(1,0)}≠0$ is a concrete, testable claim that could be checked with numerical relativity simulations of mergers. The framework is parameter-efficient: only two coupling constants need to be constrained at this order.","major_comments":[],"minor_comments":[{"comment":"§IV, Eq. (31): The relabeling of the shift-term coefficient from $G_n$ in Eq. (30) to $ẽA_n$ in Eq. (31) is explained, but the notation $ẽA_n$ (with a tilde over 'eA') is unusual and could be confused with a derivative or operator. Consider using a more standard notation such as $A_n^{(2)}$ or $Ã_n$ to improve readability.","section":null},{"comment":"§II.A, paragraph after Eq. (9): The statement that $O(X^2)$ terms do not contribute at the perturbative orders considered is confirmed later (end of §III), but it would help the reader to briefly note already at this point that this will be verified a posteriori, to avoid apparent inconsistency with the claim that all second-order-equation interactions are included.","section":null},{"comment":"§IV, Eq. (29): The statement that the spatial mode function shift can be absorbed into amplitudes when evaluating at null infinity is reasonable, but a brief justification or reference for why this absorption is valid specifically for QNM mode functions (which are not normalizable) would strengthen this point.","section":null},{"comment":"§V: The discussion of when $ϕ^{(1,0)}≠0$ might arise (nonlinearities during merger, spontaneous scalarization) is interesting but speculative. A brief mention of whether any existing numerical relativity results in shift-symmetric Horndeski already provide evidence one way or the other would contextualize this, even if the answer is currently unknown.","section":null},{"comment":"The abstract in the manuscript appears to be cut off mid-sentence ('...from an additional coupling constant'). This is likely a formatting artifact but should be checked.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is a solid, well-executed calculation that fills a clear gap between theory-agnostic ringdown analyses and specific beyond-GR theories. The overlap in authorship with Refs. [37, 49, 56] is transparent and does not raise concerns about circularity, as the key scaling result (Eq. 5) is derived from first principles in the cited work. The single-scale EFT assumption is standard and honestly stated. I see no reason this should not be published after minor revisions."},"author_rebuttal":null,"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper takes the theory-agnostic result from Lestingi et al. [37] that scalar QNM contamination appears alongside frequency shifts in beyond-GR ringdowns, and instantiates it in shift-symmetric Horndeski gravity. The concrete payoff is identifying exactly which couplings matter at each perturbative order and showing that contamination can appear at O(εq) — one order lower than frequency shifts at O(εq²) — if you relax the assumption that the scalar amplitude is suppressed by q. That's a real structural result with direct implications for how ringdown data analysis is done, since current searches only model frequency shifts and would miss a contaminating signal that could be the dominant beyond-GR effect for lower-mass black holes or merger scenarios that amplify the scalar field. The perturbative framework is systematic and well-laid-out. The double expansion in ε (dynamical perturbations) and q (scalar charge per unit mass) is clean, the hierarchical field equations (Eqs. 18–21) are derived step by step, and the ansatz construction in §IV follows logically from the source terms. The key simplification — that the background d'Alembertian and linearized Einstein tensor are the operators at each order — checks out. Tracing which terms survive in Eq. (21) confirms the claim that only α (Gauss-Bonnet coupling) and τ₄ (quartic Horndeski) contribute at O(εq²), with τ₃ and τ₅ dropping out entirely. The stress-test concern about the single-scale assumption forcing τ_i ~ q is a real but standard EFT assumption, explicitly stated, and the paper's claims are conditional on it. The paper honestly presents both the ϕ^(1,0) = 0 and ϕ^(1,0) ≠ 0 cases and acknowledges where its assumptions break down (two-scale theories, spontaneous scalarization). The main limitation is the absence of actual QNM frequency computations — the paper gives the structural framework but no numerical predictions. That's fine for what the paper is trying to do, but it means the practical impact depends on follow-up work computing the actual frequencies and amplitudes. This is for gravitational-wave theorists and data analysts who need a concrete theoretical framework for interpreting ringdown tests of GR. It's a solid, carefully done calculation that extends prior work to a specific, well-motivated theory and clarifies what ringdown signals can actually probe. It deserves a serious referee.","headline":"Clean perturbative calculation showing scalar QNM contamination can dominate over frequency shifts in Horndeski ringdowns — deserves a serious referee.","tokens_in":15301,"tokens_out":599,"would_cite":true,"duration_ms":137027,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"Scalar fields can dominate black hole ringdowns before frequency shifts appear","keywords":[],"falsifier":"A ringdown signal from a black hole with known mass and spin that shows no evidence of extra frequencies beyond the Kerr quasinormal mode spectrum, at a sensitivity level where the predicted contamination amplitude should be detectable, would constrain the scalar-Gauss-Bonnet coupling alpha and the charge q to be below the threshold where contamination is observable.","tokens_in":14589,"feed_emoji":"🌊","tokens_out":1072,"duration_ms":236816,"temperature":0.7,"pith_summary":"When a black hole rings down after a merger, its signal is a sum of characteristic frequencies called quasinormal modes. The standard approach to testing General Relativity (GR) with these signals looks for small shifts in the expected frequencies. This paper argues that if a new massless scalar field exists and couples to gravity, the ringdown signal will also be contaminated by the scalar field's own frequencies, which are generically different from the gravitational ones. Working within shift-symmetric Horndeski gravity, the most general theory coupling a massless scalar to gravity at second order, the authors show that under the standard assumption that the scalar amplitude is suppressed by the charge parameter q, both the frequency shift and the contamination appear at the same order in the perturbative expansion, order q squared. The only coupling that drives both effects at that order is the linear coupling between the scalar and the Gauss-Bonnet invariant, a topological quantity built from curvature. If the suppression assumption is relaxed, contamination enters at order q, one step earlier than the frequency shift, and can dominate the beyond-GR signal. In that case a second coupling, from the quartic Horndeski sector, also contributes subleading corrections to the contamination.","feed_headline":"Scalar fields can dominate black hole ringdowns before frequency shifts appear","feed_subtitle":"Beyond-GR ringdown signals may carry the scalar field's own frequencies as contamination, which can outrank the frequency shifts that tests ","key_machinery":"The central mechanism is a double perturbative expansion: a linear expansion in dynamical perturbations (parameter epsilon) and an expansion in the scalar charge per unit black hole mass (parameter q). The scalar charge q is not free but is set by the black hole mass and the theory's coupling constants, with the linear scalar-Gauss-Bonnet coupling alpha being the dominant contributor. The perturbation hierarchy separates cleanly because the operator acting on each perturbation order is always a background quantity: the d'Alembertian for the scalar and the linearized Einstein tensor for the metric. At each order, one can trace which coupling constants source which parts of the ringdown ansatz","core_discovery":"In shift-symmetric Horndeski gravity, the ringdown signal of a hairy black hole receives two distinct types of beyond-GR correction: a shift of the gravitational quasinormal mode frequencies and contamination from the scalar field's own quasinormal mode frequencies. Under the standard amplitude-suppression assumption, both effects appear at order q squared and are controlled solely by the scalar-Gauss-Bonnet coupling. Without that assumption, contamination appears at order q and dominates over the frequency shift, with subleading corrections from the quartic Horndeski coupling tau_4.","pith_inferences":["If future ringdown observations detect extra frequencies that do not match any Kerr quasinormal mode, the contamination framework provides a direct way to distinguish scalar-field signatures from other beyond-GR effects such as modified dispersion relations","The dominance of the scalar-Gauss-Bonnet coupling at leading order suggests that null results from current ringdown tests can be recast as direct bounds on alpha rather than on a generic deviation parameter, tightening the link between observation and theory","The hierarchy where contamination precedes frequency shifts when amplitudes are unsuppressed implies that early-time ringdown data, where higher overtones are more visible, might be especially sensitive to contamination since overtone amplitudes could be less suppressed than the fundamental mode"],"forward_implications":["Ringdown searches for beyond-GR physics that only model frequency shifts may carry a systematic bias if scalar contamination is present but unmodelled","If scalar amplitudes are not suppressed by q, contamination rather than frequency shifts would be the leading observable beyond-GR effect in ringdown signals","Only two coupling constants, alpha and tau_4, need to be retained to model massless scalar effects on ringdowns up to order q squared, simplifying theory-specific searches","The scaling q proportional to M inverse squared means supermassive black hole ringdowns probed by space-based detectors are poor probes of these effects, while solar-mass ringdowns probed by next-generation ground detectors are more promising","Nonlinear merger dynamics or spontaneous scalarization scenarios could amplify scalar amplitudes, making the contamination-dominated regime physically realizable"],"fun_headline_variants":["Scalar field frequencies can dominate black hole ringdowns ahead of frequency shifts","Quasinormal mode contamination from massless scalars can outrank black hole shifts","Massless scalar fields can contaminate black hole ringdowns without shifting frequencies","Scalar contamination may dominate black hole ringdowns over quasinormal frequency shifts","Beyond-GR scalar fields contaminate black hole ringdowns at leading perturbative order"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The analysis assumes a single new energy scale in the theory, which forces the Horndeski coupling constants to scale with the charge parameter q in a specific way. Theories with two widely separated scales are known to exist and would break this hierarchy, potentially changing which couplings dominate and at what perturbative order each effect appears.","fun_headline_variants_meta":{"raw":{"variants":["Scalar field frequencies can dominate black hole ringdowns ahead of frequency shifts","Quasinormal mode contamination from massless scalars can outrank black hole shifts","Massless scalar fields can contaminate black hole ringdowns without shifting frequencies","Scalar contamination may dominate black hole ringdowns over quasinormal frequency shifts","Beyond-GR scalar fields contaminate black hole ringdowns at leading perturbative order","Hairy black hole ringdowns may be dominated by scalar field quasinormal contamination"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":2463,"prompt_tokens":538,"completion_tokens":1925,"prompt_tokens_details":null},"tokens_in":538,"tokens_out":1925,"duration_ms":144415,"temperature":1.0,"reasoning_tokens":1885,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T04:10:49.970627+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"A ringdown signal from a black hole with known mass and spin that shows no evidence of extra frequencies beyond the Kerr quasinormal mode spectrum, at a sensitivity level where the predicted contamination amplitude should be detectable, would constrain the scalar-Gauss-Bonnet coupling alpha and the charge q to be below the threshold where contamination is observable.","supporting_citations":[],"review_version":1}