Critical phenomena in gravitational collapse (review paper)

Carsten Gundlach (Albert Einstein Institut; Potsdam)

RECORD

Critical phenomena in gravitational collapse (review paper)

Carsten Gundlach (Albert Einstein Institut, Potsdam)

General Relativity and Quantum Cosmology · Submitted 21 Dec 1997

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar.

how it is stated · asserted 0.99 read the record →

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arXiv IDgr-qc/9712084 (version 3)

Pith ID5VQON3XE, Pith's permanent record of this paper and its review

CitationCarsten Gundlach (Albert Einstein Institut, Potsdam). "Critical phenomena in gravitational collapse (review paper)." arXiv:gr-qc/9712084 (1997). https://pith.science/paper/5VQON3XE

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,881 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity. Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term "critical phenomena". They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar. This review gives an introduction to the phenomena, tries to summarize the essential features of what is happening, and then presents extensions and applications of this basic scenario. Critical phenomena are of interest particularly for creating surprising structure from simple equations, and for the light they throw on cosmic censorship. They may have applications in quantum black holes and astrophysics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity.	background 0.98	0.03	0.12	asserted 1.00
s1	Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term "critical phenomena".	background 0.87	0.05	0.11	asserted 1.00
s2	They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar.	interpretation 0.70	0.09	0.24	asserted 0.99
s3	This review gives an introduction to the phenomena, tries to summarize the essential features of what is happening, and then presents extensions and applications of this basic scenario.	contribution 0.98	0.55	0.06	asserted 0.71
s4	Critical phenomena are of interest particularly for creating surprising structure from simple equations, and for the light they throw on cosmic censorship.	interpretation 0.67	0.06	0.12	asserted 0.92
s5	They may have applications in quantum black holes and astrophysics.	interpretation 0.45	0.05	0.05	hedged possibility 1.00

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.96.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity. Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term "critical phenomena". They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar. This review gives an introduction to the phenomena, tries to summarize the essential features of what is happening, and then presents extensions and applications of this basic scenario. Critical phenomena are of interest particularly for creating surprising structure from simple equations, and for the light they throw on cosmic censorship. They may have applications in quantum black holes and astrophysics.

Human review

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References

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Nonlinear Dynamics near the Threshold of Gravitational Collapse
gr-qc 2026-07 conditional novelty 7.0 of 10

Perturbation theory around flat space fails before black hole formation once peak luminosity exceeds ~10^-2 L_Planck; near criticality the spectrum flattens to 1/ω, matching the prediction from discrete self-similarity.
Dynamics of Primordial Black Hole Formation
astro-ph 1999-01 conditional novelty 7.0 of 10

Full general relativistic simulations put the primordial black hole formation threshold at a density contrast of about 0.7 rather than 1/3, and confirm critical-collapse mass scaling in an expanding universe.
Isolated and dynamical horizons and their applications
gr-qc 2004-07 accept novelty 4.0 of 10

Isolated and dynamical horizons give a quasi-local replacement for event horizons that supports black hole mechanics, an explicit area-growth balance law, and entropy counting, without requiring global stationarity.
Critical phenomena in gravitational collapse
gr-qc 2007-11 accept novelty 3.0 of 10

Fine-tuning initial data to the black hole threshold produces universal, scale-invariant critical solutions whose perturbation spectra fix the power-law exponents for black hole mass, charge, and angular momentum.
Ramifications of Lineland
hep-th 2006-04 unverdicted novelty 2.0 of 10

This is a non-technical review of two-dimensional dilaton gravity and its applications across string theory, black hole physics, and integrable models.

Show 1 more citing papers

Dilaton Gravity in Two Dimensions
hep-th 2002-04 accept novelty 2.0 of 10

Two-dimensional dilaton gravity can be quantized exactly in its geometric sector, with matter handled perturbatively, and this review assembles the supporting results into a coherent framework.

How the literature uses it

8 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar.

Critical phenomena in gravitational collapse - Living Reviews · 1.00

Papers citing it · 3 sentences without a confident label

Cites it as background 5 papers

The problem of critical collapse has received significant attention in the past three decades, extending to different matter fields and beyond spherical symmetry [ref] .

Nonlinear Dynamics near the Threshold of Gravitational Collapse · Introduction · 0.91
Imploding scalar solutions have found application in models of gravitational collapse [ref] .

Hybrid imploding scalar and ads spacetime · Introduction · 0.95
For more information on critical collapse we refer to the review paper by Gundlach [ref] .

The Einstein-Vlasov System/Kinetic Theory · Numerical studies on critical collapse · 1.00

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