standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.| relation to other work | claim_relations | how this paper stands to another: agrees, contradicts, extends, qualifies |
| claim type | claim_type | the shape of the claim: existence, mechanism, method, critique, prediction, null |
| concept edge | concept_edges | an asserted relation between two concepts, with the sentence asserting it |
| concept | concepts | an idea the paper works with, quoted where the paper uses it |
| content tag | content_tags | a finding, definition, quantity, statistic or variable named in the paper |
| contribution | contribution | what the paper claims to add |
| control | controls | an experiment run to eliminate a rival explanation |
| limitation | limitations | what the paper says its evidence cannot support |
| mechanism | mechanisms | how the reported effect is said to come about |
| method | method | how the paper produced its evidence |
| object of study | object_of_study | what the paper is about — the thing it investigates |
| phenomenon | phenomenon | the effect or regularity under study |
| research question | research_question | the question the paper sets itself |
| sense | senses | a distinct use of a term, quoted where the paper fixes it |
| transfer | transfers | a method or concept carried in from another field |
Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; 1 of 1 relation here carries that mark. The rest are the tagger’s reading of the sentence quoted beside them.
| facet | tag | field | conf. | whose words |
|---|---|---|---|---|
| object_of_study | the complex characteristic frequencies at which a perturbed black hole or relativistic star rings down, and what a detected ringdown could be made to say about the object that produced it Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | object_of_study | the paper's words | |
| research_question | which families of quasi-normal modes exist for black holes and for stars, whether they can be excited and detected, and what the perturbative approach can and cannot establish Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | research_question | the paper's words | |
| contribution | a review of the theory of quasi-normal modes from the mathematical and the astrophysical side at once - the definition via poles of an analytically continued Green function, the families of black hole and stellar modes, the numerical techniques and, unusually, what each of them cannot see Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | contribution | the paper's words | |
| claim_type | critique Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_type | the paper's words | |
| phenomenon | ringdown - a compact object losing energy to infinity oscillates at complex frequencies fixed by its own parameters and not by whatever disturbed it Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | phenomenon | the paper's words | |
| method | review Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: review | method | the paper's words | |
| mechanisms | the effective potential peaks near the unstable photon orbit at r = 3M; whatever is imposed inside that radius has to cross the peak to reach an observer, and the peak passes only the ringing. This is why the frequencies are a fingerprint of the object rather than of the disturbance, and why a crude close-limit approximation to a black hole collision predicts the waveform correctly Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[0] | 0.95 | the tagger's words |
| mechanisms | the quasi-normal frequencies are the zeros of a Wronskian in the analytic continuation of the Green function to Re(s) < 0. The corresponding functions grow exponentially at both ends and are not physical states; what is physical is that they control the late-time decay in any bounded region Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[1] | 0.95 | the tagger's words |
| mechanisms | evolving the equations in time and Fourier-transforming the result recovers the modes still present in the signal - the slowest damped ones. Everything with a larger imaginary part has decayed before the window opens, so the method's reach is set by its own arithmetic and not by the spectrum Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[2] | 0.95 | the tagger's words |
| mechanisms | linearised perturbation theory gives no built-in indication of how good it is; the only quantitative check is to compute the next order and take the difference. So the accuracy of a first-order result is not a property the calculation can report about itself Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[3] | 0.95 | the tagger's words |
| limitations | whether the late-time solution can be expanded pointwise in quasi-normal modes is unresolved, and has been shown only for one particular potential Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[0] | 0.95 | the tagger's words |
| limitations | no spectral theorem applies, so the completeness that normal modes enjoy cannot be expected for QNMs Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[1] | 0.95 | the tagger's words |
| limitations | properties of quasi-normal modes cannot decide stability; only the appearance of a normal mode settles the question, and then only in the direction of instability Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[2] | 0.95 | the tagger's words |
| limitations | the stability of Kerr is made very plausible but is not established as conclusively as for Schwarzschild, and it is not known whether all solutions stay bounded in time Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[3] | 0.95 | the tagger's words |
| limitations | the Kerr-Newman spectrum has not been calculated at all, because the perturbation equations do not separate Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[4] | 0.95 | the tagger's words |
| limitations | time-domain evolution cannot return the complete spectrum - at most the two slowest damped frequencies survive into the signal Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[5] | 0.95 | the tagger's words |
| limitations | WKB is accurate for low-lying modes and fails for higher-order ones Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[6] | 0.95 | the tagger's words |
| limitations | the continued-fraction method reaches very high mode numbers and, being purely numerical, gives no intuition about the spectrum's properties Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[7] | 0.95 | the tagger's words |
| limitations | direct numerical integration for stars cannot reach the w-modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[8] | 0.95 | the tagger's words |
| limitations | the detectors are sensitive in the f-mode band while the p- and w-modes carrying the rest of the information sit above it, and the authors call for detectors in that range Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[9] | 0.95 | the tagger's words |
| limitations | which modes are excited, and by how much, is not determined by the theory - it depends on initial data that are themselves arbitrary until a full nonlinear calculation supplies them Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[10] | 0.95 | the tagger's words |
| limitations | the energy released as gravitational radiation in stellar collapse is basically unknown, as is its distribution among the modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[11] | 0.95 | the tagger's words |
| limitations | linearised perturbation theory carries no built-in indication of its own accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[12] | 0.95 | the tagger's words |
| limitations | trapped modes require a star more compact than any realistic equation of state produces, so that family is of no observational relevance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[13] | 0.95 | the tagger's words |
| limitations | whether the algebraically special purely imaginary frequencies are QNMs at all is still questioned Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[14] | 0.95 | the tagger's words |
| transfers | resonance theory from quantum mechanics - alpha decay, poles of a continued Green function, the Bohr-Sommerfeld rule and WKB scattering off a barrier - carried into the calculation of black hole oscillation frequencies Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[0] | 0.95 | the tagger's words |
| transfers | the asteroseismological programme of inferring stellar interiors from an oscillation spectrum, carried from classical astrophysics to neutron stars where the spectrum includes modes of the spacetime Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[1] | 0.95 | the tagger's words |
| controls | perturbation-theory waveforms compared against fully nonlinear numerical relativity for the head-on collision of two black holes and for collapse to a Kerr hole Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the linearised treatment being an artefact of linearisation - the comparison is against a calculation that makes none of its approximations, on the same physical problem · outcome: held | controls[0] | 0.95 | the tagger's words |
| controls | second-order perturbation theory proposed as the quantitative error estimate for a first-order calculation, since the difference between the orders is the only available measure Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: a first-order result being reported without any indication of its accuracy - the method has no internal one and the authors say so before proposing this · outcome: partial | controls[1] | 0.95 | the tagger's words |
| controls | five independent numerical routes to the same frequencies - time evolution, integration of the time-independent equation, WKB and phase-integral, continued fractions, and resonance searching - each reported with the part of the spectrum it cannot reach Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: any one method's blind spot being mistaken for a property of the spectrum; the modes WKB loses are the ones continued fractions find, and vice versa · outcome: held | controls[2] | 0.95 | the tagger's words |
| controls | Nollert's continued-fraction calculation carried to mode number 100,000, on a method whose convergence for quasi-normal modes is not obvious because the relevant solution grows exponentially Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the asymptotic mode distribution being an extrapolation from the few modes the other methods reach · outcome: held | controls[3] | 0.95 | the tagger's words |
| controls | the potential barrier at r = 3M treated as a filter on initial data, which is why different initial conditions give the same observed ringing Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the initial data as an explanation of the ringing - the potential barrier at r = 3M filters whatever is imposed, which is why different initial conditions give the same modes · outcome (stated by the tagger, no quotation): absent-declared-unreported | controls[4] | 0.95 | the tagger's words |
| controls | the Cowling approximation, which freezes the spacetime to isolate the fluid modes, and the inverse Cowling approximation, which freezes the fluid to isolate the spacetime modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the coupling between fluid and spacetime - the Cowling approximation freezes the spacetime to leave the fluid modes alone, and the inverse freezes the fluid to leave the spacetime modes · outcome (stated by the tagger, no quotation): absent-declared-unreported | controls[5] | 0.95 | the tagger's words |
| concepts | quasi-normal modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: quasi-normal modes | concepts[0] | 0.95 | the paper's words |
| concepts | normal modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: normal modes | concepts[1] | 0.95 | the paper's words |
| concepts | w-modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: w-modes | concepts[2] | 0.95 | the paper's words |
| concepts | f-mode Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: f-mode | concepts[3] | 0.95 | the paper's words |
| concepts | trapped modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: trapped modes | concepts[4] | 0.95 | the paper's words |
| concepts | r-modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: r-modes | concepts[5] | 0.95 | the paper's words |
| concepts | Kerr Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Kerr | concepts[6] | 0.95 | the paper's words |
| concepts | completeness Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: completeness | concepts[7] | 0.95 | the paper's words |
| concepts | potential barrier Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: potential barrier | concepts[8] | 0.95 | the paper's words |
| concepts | evolution schemes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: evolution schemes | concepts[9] | 0.95 | the paper's words |
| concepts | quadrupole formula Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: quadrupole formula | concepts[10] | 0.95 | the paper's words |
| concepts | radiative tail Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: radiative tail | concepts[11] | 0.95 | the paper's words |
| senses | the QNM spectrum of a potential - FOR ANY POSITIVE MULTIPLE OF THE REGGE-WHEELER POTENTIAL: an infinite number of modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[0] | 0.95 | the tagger's words |
| senses | the QNM spectrum of a potential - AT MULTIPLIER EXACTLY ZERO: no QNM at all. The count is discontinuous and no precision on the multiplier removes the jump Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[1] | 0.95 | the tagger's words |
| senses | the spectrum you obtain - BY EVOLVING THE TIME-DEPENDENT EQUATIONS: at most two frequencies, the slowest damped, whatever the initial data Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[2] | 0.95 | the tagger's words |
| senses | the spectrum you obtain - BY CONTINUED FRACTIONS: mode numbers up to 100,000, and no intuition about the spectrum's properties, because the method is purely numerical Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[3] | 0.95 | the tagger's words |
| senses | stellar QNM information - AS THE THEORY OFFERS IT: mass, radius and equation of state to about 10%, IF the f-mode and the first w-mode are both observed Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[4] | 0.95 | the tagger's words |
| senses | stellar QNM information - AS THE DETECTORS CAN TAKE IT: the f-mode band only; the w-modes sit at 5-12 kHz where the interferometers are not sensitive Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[5] | 0.95 | the tagger's words |
| senses | what QNM properties settle about stability - AGAINST INSTABILITY: nothing. They cannot decide the issue Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[6] | 0.95 | the tagger's words |
| senses | what QNM properties settle about stability - FOR INSTABILITY: everything. The appearance of a normal mode proves it Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[7] | 0.95 | the tagger's words |
| claim_relations | critiques → the quadrupole formula as the route to radiated energy - it accounts only for fluid deformations and misses the emission carried by the spacetime modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[0] | 0.95 | the tagger's words |
| claim_relations | critiques → fully relativistic simulation taken on its own - it gives numerical answers without indicating which principles govern the process, and can be simply incorrect or misleading Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[1] | 0.95 | the tagger's words |
| claim_relations | qualifies → the perturbative approach itself - the agreement with nonlinear collision calculations proves its power and indicates its limits in the same sentence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[2] | 0.95 | the tagger's words |
| claim_relations | qualifies → the prospect of neutron-star asteroseismology - the empirical relations recover mass and radius to about 10%, and require observing a mode outside the detectors' band Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[3] | 0.95 | the tagger's words |
| claim_relations | extends → helioseismology and asteroseismology, whose programme of reading a star's interior from its oscillation spectrum is carried here to objects whose oscillations are of the spacetime as well as the matter Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[4] | 0.95 | the tagger's words |
| concept_edges | quasi-normal modes —distinct-from→ completeness Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: whether a general solution can be written as a sum of the modes · the relation itself is separately evidenced · strength of the relation: 0.95 · differs in (stated by the tagger, no quotation): whether a general solution can be written as a sum of the modes · the relation stated: the spectral theorem gives normal modes a convergent expansion and no similar result can be expected here
Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span sets QNM against the completeness of normal modes; distinct-from is loose. also in: quasi-normal modes · completeness | concept_edges[2] | 0.95 | the tagger's words |
| content_tags | multiplying the Regge-Wheeler potential by any positive factor gives infinitely many QNMs, and at factor zero there are none - the count is discontinuous at zero Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[0] | 0.95 | the tagger's words |
| content_tags | quasi-normal mode properties cannot decide stability, while the appearance of a normal mode proves instability - the test is one-sided Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[1] | 0.95 | the tagger's words |
| content_tags | A black-hole evolution signal shows at most the two slowest-damped frequencies, so the rest of the spectrum is missing. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[2] | 0.95 | the tagger's words |
| content_tags | the interferometers cover the f-mode band while the p- and w-modes carrying the rest of the stellar information lie above it, and the authors ask for detectors there Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[3] | 0.95 | the tagger's words |
| content_tags | The potential barrier near r = 3M filters any initial data inside it, so an outside observer sees only the QNM ringing. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[4] | 0.95 | the tagger's words |
| content_tags | the quasi eigenfunctions grow exponentially at both ends and are not physically relevant solutions, unlike normal modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[5] | 0.95 | the tagger's words |
| content_tags | Linearized perturbation theory has no built-in indication of its accuracy; the difference from a second-order result quantifies the error. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[6] | 0.95 | the tagger's words |
| content_tags | massive scalar perturbations of Kerr are unstable, with growth times comparable to the age of the universe Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[7] | 0.95 | the tagger's words |
| content_tags | the r-mode instability slows a rapidly rotating neutron star within a year, which explains why only slowly rotating pulsars are associated with supernova remnants Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[8] | 0.95 | the tagger's words |
| content_tags | perturbations of a stellar or black hole spacetime whose frequencies are complex because energy is radiated away - real part the oscillation frequency, imaginary part the damping Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: quasi-normal modes | content_tags.definitions[0] | 0.95 | the tagger's words |
| content_tags | spacetime modes of a relativistic star: high frequency, very rapidly damped, hardly exciting any fluid motion, and closer to black hole QNMs than to the star's own fluid modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: w-modes | content_tags.definitions[1] | 0.95 | the tagger's words |
| content_tags | the first w-mode frequency for a typical neutron star - above every detector band named in the same paragraph Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[0] | 0.95 | the tagger's words |
| content_tags | the interferometers' sensitive band, which covers the f-mode and not the p- or w-modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[1] | 0.95 | the tagger's words |
| content_tags | the error with which the empirical relations recover a polytrope's mass and radius from its f-mode and first w-mode Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[2] | 0.95 | the tagger's words |
| content_tags | quasi-normal modes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: quasi-normal modes | content_tags.variables[0] | 0.95 | the tagger's words |
| content_tags | completeness Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: completeness | content_tags.variables[1] | 0.95 | the tagger's words |
Tags that could not be placed in the text:
What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.