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2015

Scalar field critical collapse in 2+1 dimensions

Jałmużna, Joanna, Gundlach, Carsten, Chmaj, Tadeusz

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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 $\Lambda<0$.
This approximation is only $C^3$ at the lightcone and has three growing modes.
We {\em 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).

Scalar field critical collapse in 2+1 dimensions · Around

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Original
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Abramowitz and Stegun, Handbook of Mathematical Functions, accessed in an online version, http://people.math.sfu.ca/~cbm/aands , page 559
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Then

C. Gundlach and J. M. Martín-García, Living Rev. Relativity, 2007
2007
Later among the works it cites.
P. Bizoń and A. Rostworowski, Phys. Rev. Lett. 107
2011
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J. Jałmużna, A. Rostworowski and P. Bizoń, Phys. Rev. D 84
2011
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M. Maliborski and A. Rostworowski, Phys. Rev. Lett. 111
2013
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P. Bizoń and J. Jałmużna, Phys. Rev. Lett. 111
2013
Later among the works it cites.

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