{"id":"fd95aa97-1252-4674-9bcb-da01ed797c65","arxiv_id":"2501.09000","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Bayesian MCMC inference over Rezzolla-Zhidenko metric parameters can recover the injected analog black hole spacetime from the full time-domain ringdown signal, at least in closed-loop simulations.","lead":"The authors propose fitting an effective black hole metric to analog gravity signals by simulating the full wave response and running Bayesian MCMC inference. The method recovers injected metric parameters in synthetic tests and avoids the need to choose quasinormal-mode start times or mode counts.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The core inference claim is only demonstrated in closed loop: data and model share the same truncated RZ family, evolution code, and resolution, so real draining-vortex data could still be biased by RZ truncation or model misspecification.","rationale":"Read charitably, this is a proof-of-principle paper and is appropriately cautious in many places. It uses an external QNM anchor from the literature, explicitly acknowledges the noiseless and same-resolution limitation, and discusses extensions to more general analog metrics. The statistical machinery is standard, and the recovery is internally self-consistent. The remaining issue is external validity: the conclusion's phrasing goes beyond what closed-loop injection and recovery can establish. A real draining vortex will not exactly lie in the truncated RZ family, and the paper does not test an experiment-specific forward model or real waveform data. Because this is exactly the risk identified by the reader, and because the conditional verdict already reflects that limitation, no adjustment to the verdict is needed.","tokens_in":18882,"tokens_out":6739,"duration_ms":70204,"concrete_test":"Generate synthetic time-series data from an independent forward model of a specific analog system, e.g., the 2+1 effective metric of a draining vortex with a concrete background flow profile, and evolve the same Gaussian initial data with a separate, higher-order code on a finer grid (delta r* < 0.05). Feed those waveforms, both noiseless and with noise realizations at SNR=250, into the paper's four-parameter RZ MCMC pipeline with the published priors. The central claim survives only if the 95% credible intervals for g_tt and g_rr over the probed radial domain contain the true metric functions and the whitened residual of the best-fit RZ model is consistent with the assumed noise level.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Sec. V's claim that the framework is capable of reconstructing analog black hole metrics from time-evolution data corresponding to a draining vortex requires that the truncated four-parameter RZ metric (a1=b1=0) adequately captures the effective spacetime of a real analog system. The paper's demonstration does not exercise this requirement. In Sec. IID the injection is defined as d=m(theta_inj), and Sec. IVA states that using the same resolution for injection and modeling avoids biases by construction. Thus every recovery in Sec. III tests only whether MCMC can find parameters within the same model family, not whether the RZ ansatz can absorb a real draining-vortex metric. The RZ continued fraction is expressive, but setting a1=b1=0 restricts A(x) and B(x) to finite polynomials; a real vortex profile typically has a different functional form, so the residual between true and best-fit RZ waveform may exceed the noise level. The QNM frequency check in Sec. IVA validates the evolution code for the canonical case, but it does not constrain the inference claim. This makes model misspecification, not MCMC convergence, the load-bearing risk for the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a Bayesian framework for reconstructing the effective spacetime metric of an analog gravity system (a draining vortex) from time-domain wave signals. The authors adapt the Rezzolla-Zhidenko (RZ) parametrized metric to 2+1 dimensions, use a staggered-leapfrog code to evolve scalar-field perturbations on this background, and sample the four RZ parameters (r0, a0, b0, epsilon) with an emcee MCMC sampler using a Gaussian white-noise likelihood. They demonstrate parameter recovery for a canonical Schwarzschild-like injection and for a noncanonical injection, and they explore the dependence on signal-to-noise ratio and observer location. The paper claims this full-waveform approach avoids the need to select quasinormal-mode start/end times and the number of modes, and that it is capable of reconstructing analog black hole metrics from actual draining-vortex data.","tokens_in":19091,"tokens_out":10209,"duration_ms":95507,"significance":"If the method is validated against out-of-family data, it would be a useful proof-of-concept for analog-gravity spectroscopy: the full time-domain signal is used instead of extracted quasinormal modes, and the numerical evolution is cheap enough to be done during MCMC sampling. The strengths of the paper include an independent check of the evolution code against known quasinormal-mode frequencies (Sec. IVA, relative errors 0.0005 and 0.0003), an honest recognition of the closed-loop nature of the injection/recovery procedure (Sec. IVA), and clear statements of the assumptions behind the RZ ansatz (Secs. IIB and IIIA). The main risk is model misspecification: all injections are drawn from the same truncated RZ family with a1=b1=0, so the current results do not yet establish the claimed capability for real vortex data.","major_comments":[{"comment":"The central claim that the framework is 'capable of reconstructing analog black hole metrics from time-evolution data corresponding to a draining vortex' (Sec. V) is not supported by the present closed-loop tests. In Sec. IID the injection is defined as d = m(theta_inj), and in Sec. IVA the authors note that using the same resolution for injection and modeling avoids biases by construction. Each recovery in Sec. III therefore verifies only that the MCMC sampler can locate parameters within the same four-parameter RZ family (a1=b1=0), not that this family can absorb an exact draining-vortex effective metric. A real vortex metric has a different functional form (e.g., the metrics in Refs. [41, 77]), and the residual between the true waveform and the best-fit RZ waveform may exceed the noise level at the high SNRs considered (rho=100-500). The authors should add an out-of-family test, such as injecting waveforms from an exact vortex metric or from an RZ metric with nonzero a1,b1, and then analyzing with the truncated model; they should report the resulting bias and the waveform consistency with the noise. This test directly addresses the model-misspecification risk and is needed before the conclusion in Sec. V can be drawn.","section":"Secs. II D, IV A, and V."},{"comment":"The paper claims that the approach allows one to 'model the entire signal, including the prompt response and possible effects of late-time tails.' In the analyses presented, however, the likelihood uses only the time window t in [120,145] for r*_obs=80 (Fig. 1 and all later injections). This window captures the prompt response and the exponentially damped ringdown, but it very likely stops before any late-time power-law tail becomes the dominant signal component. To support the 'entire signal' claim, the authors should either extend t_end until the waveform has reached the numerical floor (and show the tail in the plots), or qualify the claim as applying to the prompt response and ringdown without quasinormal-mode start/end times. This is a material distinction because the ability to include tails is one of the advertised advantages over standard quasinormal-mode-based analyses.","section":"Abstract and Sec. V; see Sec. II C and Fig. 1."}],"minor_comments":[{"comment":"The sentence 'The time resolution is defined by Delta t = 1/4 Delta r*' is ambiguous; it should read Delta t = (1/4) Delta r* = 0.0375 to clarify the factor.","section":"Sec. II C."},{"comment":"The likelihood and inner product use a constant S, but the text does not specify whether S is the noise variance (per unit time) or the noise spectral density; please state the units and the relation between S and the SNR rho.","section":"Sec. II D, Eqs. (21)-(23)."},{"comment":"The prior ranges for r0, a0, b0, and epsilon are only visible in the corner plots; add a table listing the prior bounds used for each analysis, since the posterior widths for a0 and b0 are sensitive to those bounds.","section":"Sec. III A, Fig. 2."},{"comment":"The sentence reporting the quasinormal-mode comparison is syntactically ambiguous: 'we obtained the real part of the fundamental mode with relative errors of 0.0005 and 0.0003 for its imaginary part' could be misread. Please state explicitly, e.g., 'the relative error of the real part is 0.0005 and of the imaginary part is 0.0003.'","section":"Sec. IV A."},{"comment":"The caption labels the observer positions as 'r*_0 = 80, 40, 10', but the text varies r*_obs; use consistent notation.","section":"Fig. 8 caption."},{"comment":"References [36] and [38] appear to be the same paper by Clovecko et al. (same journal and volume, with [38] including an arXiv number); please merge or distinguish them.","section":"References [36] and [38]."},{"comment":"The sentence 'Since the main numerical cost consists of the wave propagation, not using it in the likelihood, it should be straightforward' is confusing; rephrase to say that because the model evolution already computes the full radial domain, including multiple observers in the likelihood is straightforward.","section":"Sec. IV C1."}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a reasonable proof-of-concept, but the main claim about reconstructing real draining-vortex metrics is not yet backed by a test with data that are not generated by the same model. I would be comfortable with acceptance after the authors add an out-of-family injection test and adjust the conclusions accordingly. The novelty claim 'first study of this kind' is plausible given the existing literature, but the authors should ensure that the related work on Bayesian RZ reconstruction for gravitational waves (Ref. [97]) and semiclassical inverse problems for analog systems (Refs. [89-91]) is sufficiently distinguished."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Plain take: this is a competent proof-of-principle, and the main result is that a full time-domain Bayesian fit with the 2+1 RZ metric is computationally feasible and recovers injected parameters. The claim that it can reconstruct real draining-vortex metrics goes a bit beyond what the tests show, but the paper is honest enough about its own limits.\n\nNew and good: adapting the RZ compactification to 2+1 dimensions is sensible; the wave equation evolved inside the MCMC loop is a genuinely different approach from the QNM-based inversion of Voelkel-Barausse and the semiclassical inverse-scattering papers. Modeling the entire signal avoids mode-counting and start/end-time choices, which is a real practical advantage in a lab where you control initial data. The leapfrog scheme is standard, the QNM check against known values (relative errors ~5e-4) is a useful external anchor for the forward code, and the SNR/observer-location scans are informative. The paper also explicitly says it uses noiseless injections and the same resolution for injection and model, which is the main caveat in plain sight.\n\nSoft spots: the recovery tests are closed-loop. Injection and model share Eq. (17), the same RZ truncation with a1=b1=0, and the same numerical resolution, so the posteriors are guaranteed to concentrate near the truth. That is a self-consistency check, not evidence that the RZ ansatz absorbs a real vortex metric. The noncanonical case is still another RZ metric, not an independent model. If the true effective metric has a different functional form, the inferred RZ parameters could be biased even at high SNR; the stress-test concern about model misspecification is on target. The authors know this--Sec. IVC3 lists applying the method to exact analog metrics as future work--so I read it as a limitation rather than a hidden flaw. The Sec. V sentence about being 'capable of reconstructing analog black hole metrics' should be softened to 'capable in principle, within the RZ family.'\n\nCitation pattern is fine; prior self-citations are relevant and not padded.\n\nWho this is for: analog gravity people planning parameter estimation from surface-wave or BEC experiments, and ringdown methodologists. It deserves a serious referee. I would recommend acceptance after minor revision, with the conclusion recalibrated and ideally one cross-model test (inject a known vortex metric, fit with RZ) or a note that it is a near-term target. Code release would help but is not essential for a proof-of-principle.","headline":"A competent proof-of-principle for full time-domain Bayesian metric reconstruction in analog gravity; the closed-loop recovery tests support feasibility but not yet real-vortex fidelity.","tokens_in":19678,"tokens_out":2867,"would_cite":true,"duration_ms":29668,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83C35","62F15","65M06"],"pacs":["04.70.-s","04.30.-w"],"model":"deepseek-v4-flash","headline":"Modeling the entire time-domain signal of a controlled perturbation can reconstruct the effective black hole metric of an analog gravity system, without any quasinormal-mode extraction.","keywords":["analog gravity","draining vortex","Rezzolla-Zhidenko metric","Bayesian inference","Markov chain Monte Carlo","quasinormal modes","ringdown","effective metric reconstruction"],"falsifier":"Take mock data from an exact draining-vortex metric known to lie outside the four-parameter RZ family and run the same Bayesian recovery; if the posterior centers on biased parameters or cannot reproduce the waveform, the assumed universality of the ansatz is refuted.","tokens_in":18609,"feed_emoji":"🌀","tokens_out":6957,"duration_ms":74308,"temperature":0.7,"pith_summary":"This paper works out a proof of principle for extracting the effective spacetime of an analog black hole from a single controlled pulse in a draining vortex. The authors adopt the Rezzolla-Zhidenko (RZ) metric, a continued-fraction parametrization of static black hole metrics, evolve scalar perturbations on that background, and use Bayesian Markov chain Monte Carlo to fit the entire time-domain waveform to simulated observer data. Unlike standard quasinormal-mode ringdown analysis, the fit never needs to choose when the mode sum starts or ends, nor how many modes are present. If the scheme carries over to real experiments, a laboratory could infer the effective metric and perturbation potential directly from wave-scattering data.","feed_headline":"Full-waveform Bayesian pipeline reconstructs analog black hole metrics","feed_subtitle":"Modeling the whole signal skips quasinormal-mode start times and still recovers the metric parameters.","key_machinery":"The central object is the RZ metric, adapted to 2+1 dimensions through the radial compactification x=1-(r0/r)^2, with free parameters r0, a0, b0, and epsilon. The scalar wave equation on this background reduces to a 1+1-dimensional wave equation in a tortoise coordinate r* with an effective potential V_m(r). The mechanism that carries the argument is that, during MCMC sampling, the same staggered-leapfrog finite-difference code used to generate the injected waveform is run for every proposed parameter set, so the whole time-domain signal is fitted at once. A Gaussian likelihood with a white-noise inner product defines the posterior, and proposals that would make g_tt or g_rr change sign are rejected to keep the time evolution well defined.","core_discovery":"The paper's central assertion is that a Bayesian analysis of the full time-domain signal from a controlled initial perturbation can reconstruct the effective metric of an analog black hole. In injection-recovery tests on the 2+1-dimensional RZ ansatz, the posterior maxima sit close to the injected values for both the canonical parameter set (r0,a0,b0,epsilon)=(1,0,0,0) and a noncanonical set (1,0.3,0.45,0); the metric functions g_tt and g_rr and the effective potential V_m(r*) are constrained, with the potential best constrained outside its peak. Varying the signal-to-noise ratio from 100 to 500 narrows the posteriors as expected, while moving the observer between tortoise radii 10, 40, and 80 has little effect on the inferred parameters. The authors present this as the first study of its kind and emphasize that the entire signal, including the prompt response and late-time tails, is modeled.","pith_inferences":["Carried further, the same full-signal likelihood could be applied to multi-observer data from a real vortex experiment; the paper notes that the time series are already computed on the full radial grid, so including all observers in the likelihood is a natural extension.","If the true analog metric has structure beyond the four RZ parameters used here, the recovered parameters would be biased; testing the pipeline with exact analog metrics that lie outside the RZ family would quantify how severe this bias is.","Because the likelihood in this paper is white noise in the time domain, applying the method to actual experimental data will require an experiment-specific noise model, likely formulated in the frequency domain."],"forward_implications":["A single Gaussian pulse and one distant observer's time series can, in principle, determine the four RZ parameters controlling the analog metric, with the injected values inside the recovered posteriors.","Increasing the signal-to-noise ratio from 100 to 500 tightens the posteriors and narrows the reconstructed metric functions and effective potential.","Moving the observer between tortoise radii 10, 40, and 80 changes the waveform shape but has almost no effect on the inferred parameters.","The noncanonical injection (r0,a0,b0,epsilon)=(1,0.3,0.45,0) is clearly distinguished from the canonical Schwarzschild-like case, so the method can detect deviations from the standard analog description.","No choice of quasinormal-mode start or end times and no mode-counting procedure are required anywhere in the analysis."],"supporting_citations":[{"why":"Supplies the continued-fraction parametrization of static black hole metrics that serves as the model ansatz.","marker":"[54]"},{"why":"Provides the effective potential for acoustic perturbations on a radial vortex that the perturbation equation reproduces.","marker":"[41]"},{"why":"Gives the effective potential and the imperfect draining-vortex model underlying the scalar perturbation setup.","marker":"[77]"},{"why":"Supplies the ensemble MCMC sampler used to draw posterior samples.","marker":"[80]"},{"why":"Provides accurate quasinormal frequencies of analog black holes used to validate the numerical time-evolution code.","marker":"[84]"},{"why":"Establishes the prior Bayesian RZ metric reconstruction from quasinormal modes that the full time-domain approach extends.","marker":"[97]"},{"why":"Developed the semiclassical inverse-problem approach to analog gravity metrics that this Bayesian time-domain method complements.","marker":"[89]"},{"why":"Describes experimental black-hole spectroscopy from a giant quantum vortex, motivating the measurable harmonics considered in the analysis.","marker":"[35]"}],"fun_headline_variants":["Bayesian full-signal fit reveals analog black hole metrics","Whole-signal Bayesian analysis pins down analog spacetime","Analog black hole metric recovered without mode-counting","Bayesian pipeline uses entire ringdown to map analog metrics","No mode counting: Bayesian fit of full wave pins metric"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole scheme depends on the four-parameter RZ metric, with the two next-order deformation coefficients set to zero, containing the true effective metric of a real draining vortex, and on the scalar wave equation being the right description of the measured surface waves; if either is false, the inferred parameters will be biased even when the MCMC looks well-behaved.","fun_headline_variants_meta":{"raw":{"variants":["Bayesian full-signal fit reveals analog black hole metrics","Whole-signal Bayesian analysis pins down analog spacetime","Analog black hole metric recovered without mode-counting","Bayesian pipeline uses entire ringdown to map analog metrics","No mode counting: Bayesian fit of full wave pins metric"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000512,"raw_usage":{"total_tokens":2484,"prompt_tokens":934,"completion_tokens":1550,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":1473}},"tokens_in":550,"tokens_out":1550,"duration_ms":12452,"temperature":1.0,"reasoning_tokens":1473,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:12:47.097673+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take mock data from an exact draining-vortex metric known to lie outside the four-parameter RZ family and run the same Bayesian recovery; if the posterior centers on biased parameters or cannot reproduce the waveform, the assumed universality of the ansatz is refuted.","supporting_citations":[{"cited_title":"The ringdown-Hawking radiation connection in real and analogue black holes","cited_arxiv_id":"2407.00448","evidence_quote":"Provides the effective potential for acoustic perturbations on a radial vortex that the perturbation equation reproduces."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the prior Bayesian RZ metric reconstruction from quasinormal modes that the full time-domain approach extends."}],"review_version":1}