Scalar field collapse in three-dimensional AdS spacetime

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2+1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the n = 4 Garfinkle solution, matched at the lightcone to a Vaidya-like solution, and corrected to leading order for the effect of Λ < 0. This approximation is only C 3 at the lightcone and has three growing modes. We conjecture that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of γ = 8/7 and a mass-scaling exponent of δ = 16/23, compatible with our numerical experiments. CONTENTS

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“…7. This value is roughly similar to the value δ 0.81 of [10] (but different from the δ = 2γ 2.50 of [9]). …”

Section: Apparent Horizon Mass Scalingsupporting

confidence: 67%

“…The first numerical simulations of critical collapse of a spherically symmmetric scalar field in 2+1 dimensions with a negative cosmological constant were carried out by Pretorius and Choptuik [9] and Husain and Olivier [10].…”

Section: Previous Workmentioning

confidence: 99%

Scalar field critical collapse in2+1dimensions

2015

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“…Analytic and numerical work on spherically symmetric collapse has commonly modeled the fluid accreted by the black hole as a massless scalar field, usually taken to be uncharged [7,9,11,12,13,14,15,24,27,32,33,38,50,56], but sometimes charged [26,46,48,49,61,71]. A key property of a massless scalar field is that it allows waves to counter-stream relativistically through each other, which allows the phenomenon of mass inflation on the Cauchy horizon to occur.…”

Section: Introductionmentioning

confidence: 99%

Inside charged black holes. I. Baryons

Hamilton

Pollack²

2005

Phys. Rev. D

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An extensive investigation is made of the interior structure of self-similar accreting charged black holes. In this, the first of two papers, the black hole is assumed to accrete a charged, electrically conducting, relativistic baryonic fluid. The mass and charge of the black hole are generated selfconsistently by the accreted material. The accreted baryonic fluid undergoes one of two possible fates: either it plunges directly to the spacelike singularity at zero radius, or else it drops through the Cauchy horizon. The baryons fall directly to the singularity if the conductivity either exceeds a certain continuum threshold κ∞, or else equals one of an infinite spectrum κn of discrete values. Between the discrete values κn, the solution is characterized by the number of times that the baryonic fluid cycles between ingoing and outgoing. If the conductivity is at the continuum threshold κ∞, then the solution cycles repeatedly between ingoing and outgoing, displaying a discrete self-similarity reminiscent of that observed in critical collapse. Below the continuum threshold κ∞, and except at the discrete values κn, the baryonic fluid drops through the Cauchy horizon, and in this case undergoes a shock, downstream of which the solution terminates at an irregular sonic point where the proper acceleration diverges, and there is no consistent self-similar continuation to zero radius. As far as the solution can be followed inside the Cauchy horizon, the radial direction is timelike. If the radial direction remains timelike to zero radius (which cannot be confirmed because the selfsimilar solutions terminate), then there is presumably a spacelike singularity at zero radius inside the Cauchy horizon, which is distinctly different from the vacuum (Reissner-Nordström) solution for a charged black hole.

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“…Birmingham and Sen found the same exponent at the threshold of formation in the case of colliding particles. Husain and Olivier have also studied the massless scalar field in 2+1 dimensions using a double null formalism, and have formed black holes with their code [11].…”

mentioning

confidence: 99%

Gravitational collapse in 2+1 dimensional AdS spacetime

2000

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We present results of numerical simulations of the formation of black holes from the gravitational collapse of a massless, minimally-coupled scalar field in 2+1 dimensional, axially-symmetric, anti de-Sitter (AdS) spacetime. The geometry exterior to the event horizon approaches the BTZ solution, showing no evidence of scalar 'hair'. To study the interior structure we implement a variant of black-hole excision, which we call singularity excision. We find that interior to the event horizon a strong, spacelike curvature singularity develops. We study the critical behavior at the threshold of black hole formation, and find a continuously self-similar solution and corresponding mass-scaling exponent of approximately 1.2. The critical solution is universal to within a phase that is related to the angle deficit of the spacetime.

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Scalar field collapse in three-dimensional AdS spacetime

Cited by 69 publications

References 16 publications

Scalar field critical collapse in2+1dimensions

Scalar field critical collapse in2+1dimensions

Inside charged black holes. I. Baryons

Gravitational collapse in 2+1 dimensional AdS spacetime

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