An exact solution for 2+1 dimensional critical collapse

David Garfinkle

RECORD

An exact solution for 2+1 dimensional critical collapse

David Garfinkle

General Relativity and Quantum Cosmology · Submitted 9 Aug 2000

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

The authors' main claim We find an exact solution in closed form for the critical collapse of a scalar field with cosmological constant in 2+1 dimensions.

how it is stated · asserted 1.00 read the record →

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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,228 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We find an exact solution in closed form for the critical collapse of a scalar field with cosmological constant in 2+1 dimensions. This solution agrees with the numerical simulation done by Pretorius and Choptuik of this system.

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	We find an exact solution in closed form for the critical collapse of a scalar field with cosmological constant in 2+1 dimensions.	result 0.56	0.96	0.89	asserted 1.00
s1	This solution agrees with the numerical simulation done by Pretorius and Choptuik of this system.	result 0.80	0.24	0.15	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

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

We find an exact solution in closed form for the critical collapse of a scalar field with cosmological constant in 2+1 dimensions. This solution agrees with the numerical simulation done by Pretorius and Choptuik of this system.

Human review

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References

Forward citations

Cited by 5 Pith papers

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

Quantum critical collapse in the large $D$ limit
gr-qc 2026-10 conditional novelty 7.0 of 10

Quantum vacuum polarization with Lyapunov exponent D−2 creates a finite-radius trapped surface (quantum wall) in both continuously and discretely self-similar critical collapse at large D.
Critical spacetime crystals in continuous dimensions
gr-qc 2026-02 unverdicted novelty 7.0 of 10

Numerical construction of a one-parameter family of discretely self-similar critical spacetimes for massless scalar collapse in continuous D>3, giving echoing period Delta(D) and Choptuik exponent gamma(D) with a maxi...
Unveiling horizons in quantum critical collapse
gr-qc 2025-09 unverdicted novelty 7.0 of 10

Semiclassical quantum corrections in critical collapse yield a finite mass gap and transition from classical Type II to quantum Type I behavior, providing a quantum enforcement of weak cosmic censorship.
Quantum fate of the Choptuik naked singularity
gr-qc 2026-06 unverdicted novelty 6.0 of 10

Quantum backreaction generates horizons that cloak the Choptuik naked singularity, reducing its predictability violation to the standard black hole evaporation problem.
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.

How the literature uses it

7 arXiv papers cite this in 14 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

We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution.

Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model · 0.91

Papers citing it · 11 sentences without a confident label

Contests it 1 paper

However, by examining further its global structure and the classical perturbation modes [ref] , the Garfinkle solution cannot be the true critical spacetime for the following reasons: * The surface $x=0$, which corresponds to the past light cone of the naked singularity, is a marginally outer-trapped surface.

Unveiling horizons in quantum critical collapse · The critical Garfinkle spacetime in $2+1$ dimensions · contest 0.88

Cites it as background 2 papers

The first numerical studies of gravitational collapse in AdS spacetime appeared in [ref] for the 2+1 dimensional case (see also [ref] ).

Moving Closer to the Collapse of a Massless Scalar Field in Spherically Symmetric Anti-de Sitter Spacetimes · Introduction · 0.98
Looking for the critical solution in closed form, Garfinkle [ref] found a countable family of exact spherically symmetric CSS solutions for a massless scalar field with $Λ=0$, but his results remain inconclusive.

Critical phenomena in gravitational collapse · Scalar field collapse in 2+1 · 0.82

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