Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour

Patrick R Brady

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Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour

Patrick R Brady

General Relativity and Quantum Cosmology · Submitted 16 Sep 1994

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

The authors' main claim The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes.

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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, 6,000 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions. The first consists of solutions with a non-singular origin in which the scalar field collapses and disperses again. There is a singularity at one point of these solutions, however it is not visible to observers at finite radius. The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes. The properties of these solutions are discussed in detail. The paper also contains some speculation about the significance of self-similarity in recent numerical studies.

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	Homothetic scalar field collapse is considered in this article.	background 0.55	0.55	0.02	asserted 0.88
s1	By making a suitable choice of variables the equations are reduced to an autonomous system.	method 1.00	0.89	0.02	asserted 1.00
s2	Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions.	result 0.56	0.94	0.21	asserted 1.00
s3	The first consists of solutions with a non-singular origin in which the scalar field collapses and disperses again.	result 1.00	0.84	0.10	asserted 1.00
s4	There is a singularity at one point of these solutions, however it is not visible to observers at finite radius.	result 0.91	0.79	0.07	asserted 1.00
s5	The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes.	result 1.00	0.85	0.56	asserted 1.00
s6	The properties of these solutions are discussed in detail.	contribution 0.91	0.71	0.04	asserted 0.77
s7	The paper also contains some speculation about the significance of self-similarity in recent numerical studies.	interpretation 0.78	0.42	0.03	speculative 0.93

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from simulation or computation 0.76.

What was examined, and what was not

sources read

arXiv listing abstract v1

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

Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions. The first consists of solutions with a non-singular origin in which the scalar field collapses and disperses again. There is a singularity at one point of these solutions, however it is not visible to observers at finite radius. The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes. The properties of these solutions are discussed in detail. The paper also contains some speculation about the significance of self-similarity in recent numerical studies.

Human review

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References

Forward citations

Cited by 4 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.
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.
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.

How the literature uses it

5 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 citing it · 11 sentences without a confident label

Cites it as background 3 papers

The Roberts solution provides a useful analytic substitute: it is a closed-form CSS solution of the same Einstein-scalar system, supported by a massless scalar field, and captures several structural features of near-critical scalar collapse [ref] .

Quantum fate of the Choptuik naked singularity · The Roberts interior and its quantum horizon · 0.81
This analytic CSS spacetime is closely related to the DSS solution first identified by Choptuik [ref] .

Quantum Critical Collapse Abhors a Naked Singularity · Introduction · 0.90
Second, while we have focused on CSS-type spacetimes in $2+1$ and $3+1$ dimensions (i.e., the Garfinkle and Roberts solutions), many other exact solutions conjectured to model critical collapse exist in spherical symmetry [ref] .

Unveiling horizons in quantum critical collapse · Outlook · 0.88

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