Critical phenomena in perfect fluids

David W. Neilsen; Matthew W. Choptuik

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Critical phenomena in perfect fluids

David W. Neilsen, Matthew W. Choptuik

General Relativity and Quantum Cosmology · Submitted 16 Dec 1998

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

The authors' main claim In addition, we find strong evidence that globally regular critical solutions do exist for 1.89 < Gamma <= 2$, that the sonic point for Gamma_dn = 1.8896244 is a degenerate node, and that the sonic points for Gamma >Gamma_dn are nodal points rather than focal points as previously reported.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.97 · mentions code or data availability 0.02.

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We investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P = (Gamma -1)rho. We restrict attention to the ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where black hole formation is anticipated to turn on at infinitesimal black hole mass (Type II behavior). Critical solutions (those which sit at the threshold of black hole formation in parametrized families of collapse) are found by solving the system of ODEs which result from a self-similar ansatz, and by solving the full Einstein/fluid PDEs in spherical symmetry. These latter PDE solutions (``simulations'') extend the pioneering work of Evans and Coleman (Gamma = 4/3) and verify that the continuously self-similar solutions previously found by Maison and Hara et al for $1.05 < Gamma < 1.89 are (locally) unique critical solutions. In addition, we find strong evidence that globally regular critical solutions do exist for 1.89 < Gamma <= 2$, that the sonic point for Gamma_dn = 1.8896244 is a degenerate node, and that the sonic points for Gamma >Gamma_dn are nodal points rather than focal points as previously reported. We also find a critical solution for Gamma = 2, and present evidence that it is continuously self-similar and Type II. Mass-scaling exponents for all of the critical solutions are calculated by evolving near-critical initial data, with results which confirm and extend previous calculations based on linear perturbation theory. Finally, we comment on critical solutions generated with an ideal-gas equation of state.

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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 investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P = (Gamma -1)rho.	contribution 0.83	0.88	0.03	asserted 0.87
s1	We restrict attention to the ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where black hole formation is anticipated to turn on at infinitesimal black hole mass (Type II behavior).	limitation 0.43	0.40	0.05	hedged possibility 0.86
s2	Critical solutions (those which sit at the threshold of black hole formation in parametrized families of collapse) are found by solving the system of ODEs which result from a self-similar ansatz, and by solving the full Einstein/fluid PDEs in spherical symmetry.	method 0.97	0.93	0.07	asserted 1.00
s3	These latter PDE solutions (``simulations'') extend the pioneering work of Evans and Coleman (Gamma = 4/3) and verify that the continuously self-similar solutions previously found by Maison and Hara et al for $1.05 < Gamma < 1.89 are (locally) unique critical solutions.	result 0.72	0.81	0.15	asserted 1.00
s4	In addition, we find strong evidence that globally regular critical solutions do exist for 1.89 < Gamma <= 2$, that the sonic point for Gamma_dn = 1.8896244 is a degenerate node, and that the sonic points for Gamma >Gamma_dn are nodal points rather than focal points as previously reported.	result 1.00	0.96	0.26	asserted 0.71
s5	We also find a critical solution for Gamma = 2, and present evidence that it is continuously self-similar and Type II.	result 0.94	0.97	0.17	asserted 0.94
s6	Mass-scaling exponents for all of the critical solutions are calculated by evolving near-critical initial data, with results which confirm and extend previous calculations based on linear perturbation theory.	result 0.86	0.96	0.10	asserted 1.00
s7	Finally, we comment on critical solutions generated with an ideal-gas equation of state.	contribution 0.38	0.43	0.04	unclear 0.89

What kind of paper the classifier reports this is: simulation study 0.98 · evidence from simulation or computation 1.00.

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The paper

Original abstract

We investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P = (Gamma -1)rho. We restrict attention to the ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where black hole formation is anticipated to turn on at infinitesimal black hole mass (Type II behavior). Critical solutions (those which sit at the threshold of black hole formation in parametrized families of collapse) are found by solving the system of ODEs which result from a self-similar ansatz, and by solving the full Einstein/fluid PDEs in spherical symmetry. These latter PDE solutions (``simulations'') extend the pioneering work of Evans and Coleman (Gamma = 4/3) and verify that the continuously self-similar solutions previously found by Maison and Hara et al for $1.05 < Gamma < 1.89 are (locally) unique critical solutions. In addition, we find strong evidence that globally regular critical solutions do exist for 1.89 < Gamma <= 2$, that the sonic point for Gamma_dn = 1.8896244 is a degenerate node, and that the sonic points for Gamma >Gamma_dn are nodal points rather than focal points as previously reported. We also find a critical solution for Gamma = 2, and present evidence that it is continuously self-similar and Type II. Mass-scaling exponents for all of the critical solutions are calculated by evolving near-critical initial data, with results which confirm and extend previous calculations based on linear perturbation theory. Finally, we comment on critical solutions generated with an ideal-gas equation of state.

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References

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Cited by 14 Pith papers

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

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From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back)
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Using numerical relativity thresholds, cosmological perturbation theory, and peak theory, the authors derive updated upper limits on the small-scale primordial curvature power spectrum from primordial black hole abund...
Self-similar collapse with elasticity
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Continuous self-similar collapse solutions exist for a scale-invariant elastic matter model, and regularity imposes bounds on the elasticity parameters.

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Quantum Critical Collapse Abhors a Naked Singularity
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Primordial black hole formation during the QCD phase transition: threshold, mass distribution and abundance
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Polarisation and Temperature Dependence of Er$^{3+}$:CaWO$_4$ -- Towards a Solid-State Rare-Earth Ion-Doped Quantum Memory
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Primordial black holes through preheating instabilities in $\alpha$-attractor models
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In alpha-attractor models, preheating self-resonance can form primordial black holes of 10^2 to 10^7 g, with the Khlopov-Polnarev collapse formalism staying viable and the Press-Schechter formalism overproducing.
Primordial Black Holes as Dark Matter
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Effects of Critical Collapse on Primordial Black-Hole Mass Spectra
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Applying the critical-collapse scaling law to four primordial-black-hole production scenarios shifts their mass spectra to lower masses, broadens them, and lowers their abundance, with a model-dependent size that a co...
Critical Phenomena in Gravitational Collapse
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An authoritative review of critical collapse, updated with results on nonspherical vacuum collapse and rigorous PDE blowup.
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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

19 arXiv papers cite this in 29 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 · 21 sentences without a confident label

Contests it 2 papers

As Ori and Piran before [ref] , he claimed that there are no regular CSS solutions for $k>0.89$, but Neilsen and Choptuik [ref] have found CSS critical solutions for all values of $k$ right up to 1, both in collapse simulations and by making a CSS ansatz.

Critical phenomena in gravitational collapse · Spherical symmetry · contest 0.80
As [ref] before, he claimed that there are no regular CSS solutions for $k>0.89$, but [ref] have found CSS critical solutions for all values of $k$ right up to 1, both in collapse simulations and by making a CSS ansatz.

Critical Phenomena in Gravitational Collapse · The asymptotically flat case · contest 0.84

Uses its method or tool 1 paper

Finally, we compute the PBH masses using the critical scaling method [ref] for both formalisms.

Revisiting primordial black holes formation from preheating instabilities: the case of Starobinsky inflation · Numerical characterization of PBH formation · 0.99

Uses its data or values 1 paper

The PBH mass $M_PBH(ν)$ is proportional to the horizon mass at horizon-crossing time, $M_H(t_m)$, according to the relation [ref] [equation] In this equation the horizon mass at horizon-crossing time is given by the equation $M_H(t_m) = 1/2H_m$ while the factor $(ν-ν_c)^γ$ is the scaling law for critical collapse (extracted from numerical simulation, and with $γ̃≃0.36$ in the case of radiation [ref] ) while $𝒦 = O(1)$.

Solving peak theory in the presence of local non-gaussianities · Threshold for gravitational collapse into black holes · 0.85

Cites it as support 1 paper

Numerical general relativistic simulations [ref] have demonstrated that the scaling of black hole mass with the proximity to the formation threshold, known to occur in near-critical gravitational collapse, also applies to PBH formation.

Primordial black holes through preheating instabilities in $\alpha$-attractor models · PBH mass · 0.96

Cites it as background 3 papers

Since Choptuik's discovery, this framework has been generalized to a wide variety of matter models in spherical symmetry [ref] , revealing extremely rich phase structures depending on the number of dimensions and the type of matter content.

Unveiling horizons in quantum critical collapse · Introduction · 0.85
Imploding scalar solutions have found application in models of gravitational collapse [ref] .

Hybrid imploding scalar and ads spacetime · Introduction · 0.95
For example, the previous work has been extended to massive scalar fields [ref] , the gravitational collapse of radiation [ref] and perfect fluid [ref] , a complex scalar field with angular momentum [ref] , K-essence models [ref] , the Einstein-Massless-Dirac system [ref] , and massive vector field [ref] , to mention some of the many investigations carried out to date.

Critical collapse for the Starobinsky $R^2$ model · Introduction · 0.80

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