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arXiv · 1510.02592

Scalar field critical collapse in 2+1 dimensions

Joanna Jałmużna·Carsten Gundlach·Tadeusz Chmaj
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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 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 {\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). 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.

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Joanna Jałmużna, Carsten Gundlach, Tadeusz Chmaj. 2015-10-09. Scalar field critical collapse in 2+1 dimensions. https://doi.org/10.1103/physrevd.92.124044

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