Perturbations of an exact solution for 2+1 dimensional critical collapse

Carsten Gundlach; David Garfinkle

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Perturbations of an exact solution for 2+1 dimensional critical collapse

David Garfinkle, Carsten Gundlach

General Relativity and Quantum Cosmology · Submitted 24 May 2002

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

The authors' main claim Our results are compared to the numerical simulations of Pretorius and Choptuik and are inconclusive: We find a CSS solution with exactly one unstable mode, which suggests that it may be the critical solution, but another CSS solution which has three unstable modes fits the numerically found critical solution better.

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arXiv IDgr-qc/0205107 (version 2)

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CitationCarsten Gundlach, David Garfinkle. "Perturbations of an exact solution for 2+1 dimensional critical collapse." arXiv:gr-qc/0205107 (2002). https://pith.science/paper/22RHOXTT

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.66 · compares with prior results 0.97 · mentions code or data availability 0.02.

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We find the perturbation spectrum of a family of spherically symmetric and continuously self-similar (CSS) exact solutions that appear to be relevant for the critical collapse of scalar field matter in 2+1 spacetime dimensions. The rate of exponential growth of the unstable perturbation yields the critical exponent. Our results are compared to the numerical simulations of Pretorius and Choptuik and are inconclusive: We find a CSS solution with exactly one unstable mode, which suggests that it may be the critical solution, but another CSS solution which has three unstable modes fits the numerically found critical solution better.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We find the perturbation spectrum of a family of spherically symmetric and continuously self-similar (CSS) exact solutions that appear to be relevant for the critical collapse of scalar field matter in 2+1 spacetime dimensions.	contribution 0.96	0.94	0.09	asserted 0.74
s1	The rate of exponential growth of the unstable perturbation yields the critical exponent.	interpretation 0.45	0.57	0.10	asserted 1.00
s2	Our results are compared to the numerical simulations of Pretorius and Choptuik and are inconclusive: We find a CSS solution with exactly one unstable mode, which suggests that it may be the critical solution, but another CSS solution which has three unstable modes fits the numerically found critical solution better.	result 0.64	0.94	0.82	hedged possibility 0.82

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.95.

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The paper

Original abstract

We find the perturbation spectrum of a family of spherically symmetric and continuously self-similar (CSS) exact solutions that appear to be relevant for the critical collapse of scalar field matter in 2+1 spacetime dimensions. The rate of exponential growth of the unstable perturbation yields the critical exponent. Our results are compared to the numerical simulations of Pretorius and Choptuik and are inconclusive: We find a CSS solution with exactly one unstable mode, which suggests that it may be the critical solution, but another CSS solution which has three unstable modes fits the numerically found critical solution better.

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References

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 23 citations worldwide. 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.
Weak cosmic censorship for the circularly symmetric Einstein-scalar field system in $2+1$ dimensions
gr-qc 2026-05 unverdicted novelty 7.0 of 10

Proves weak cosmic censorship for circularly symmetric Einstein-scalar field system in 2+1D with Λ<0: maximal developments of generic C^k initial data (k≥2) contain no naked singularities.
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.

Show 3 more citing papers

Quantum Critical Collapse Abhors a Naked Singularity
gr-qc 2025-09 unverdicted novelty 6.0 of 10

One-loop quantum vacuum polarization in Einstein-scalar critical collapse generates a horizon and finite mass gap, enforcing black hole formation even under arbitrary fine-tuning.
Critical Phenomena in Gravitational Collapse
gr-qc 2025-07 unverdicted novelty 3.0 of 10

An authoritative review of critical collapse, updated with results on nonspherical vacuum collapse and rigorous PDE blowup.
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 16 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 citing it · 10 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

Uses its method or tool 1 paper

Here, we find it clear to work first in the coordinates $(u, w)$ used in [ref] , in which the reduced Garfinkle system [ref] takes the form ds^2=2 e^2ρ du dw, ϕ=-1/2 ln[1/2(-u-w^2n)].

Unveiling horizons in quantum critical collapse · The Weyl-Garfinkle spacetime · 0.82

Uses its data or values 1 paper

A full treatment must also include the classical growing mode $(p-p^∗)e^ω_c T$, arising from deviations off the critical point, where the exponent $ω_c$ for each $n$ has been worked out in [ref] .

Quantum Critical Collapse Abhors a Naked Singularity · Introduction · 0.89

Cites it as background 3 papers

Fortunately, the classical growing modes in Garfinkle spacetime have already been analyzed in detail [ref] .

Unveiling horizons in quantum critical collapse · Setting up the horizon-tracing problem · 0.86
In $2+1$ dimensions, the scalar critical solution observed numerically is CSS [ref] , and the Garfinkle family gives an analytic description of this critical behavior in the self-similar regime [ref] .

Quantum fate of the Choptuik naked singularity · Introduction · 0.98
We consider the Einstein-scalar field system of equations with a negative cosmological constant $Λ<0$: [equation] In $2+1$ dimensions, the system [ref] has been studied extensively in the physics and numerical relativity literature [ref] .

Weak cosmic censorship for the circularly symmetric Einstein-scalar field system in $2+1$ dimensions · The Einstein-scalar field system in $2+1$ dimensions with $Λ<0$ · 1.00

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