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Scalar field critical collapse in 2+1 dimensions

Scalar field critical collapse in 2+1 dimensions
Scalar field critical collapse in 2+1 dimensions
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 light cone to a Vaidya-like solution, and corrected to leading order for the effect of ?<0. This approximation is only C3 at the light cone 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 ?=8/7 and a mass-scaling exponent of ?=16/23, compatible with our numerical experiments.
1550-7998
1-27
Jałmużna, Joanna
2600ccc1-f088-40b3-99c8-b1861e3b9990
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Chmaj, Tadeusz
9bba1d70-dbba-4038-9a50-942deba287d5
Jałmużna, Joanna
2600ccc1-f088-40b3-99c8-b1861e3b9990
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Chmaj, Tadeusz
9bba1d70-dbba-4038-9a50-942deba287d5

Jałmużna, Joanna, Gundlach, Carsten and Chmaj, Tadeusz (2015) Scalar field critical collapse in 2+1 dimensions. Physical Review D, 92 (124044), 1-27. (doi:10.1103/PhysRevD.92.124044).

Record type: Article

Abstract

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 light cone to a Vaidya-like solution, and corrected to leading order for the effect of ?<0. This approximation is only C3 at the light cone 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 ?=8/7 and a mass-scaling exponent of ?=16/23, compatible with our numerical experiments.

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Published date: 21 December 2015
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 405145
URI: https://eprints.soton.ac.uk/id/eprint/405145
ISSN: 1550-7998
PURE UUID: 5e87b9ba-89e1-476b-8c73-5019101c45f3
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

Catalogue record

Date deposited: 31 Jan 2017 13:49
Last modified: 20 Jul 2018 00:34

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