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arxiv: 1510.02592 · v1 · pith:SBBTE6PHnew · submitted 2015-10-09 · 🌀 gr-qc · hep-th

Scalar field critical collapse in 2+1 dimensions

Joanna Ja{\l}mu\.zna , Carsten Gundlach , Tadeusz Chmaj This is my paper
classification 🌀 gr-qc hep-th
keywords solutioncriticalapproximationcollapseconjecturedimensionsexperimentsexponent
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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). With this conjecture, we predict a Ricci-scaling exponent of $\gamma=8/7$ and a mass-scaling exponent of $\delta=16/23$, compatible with our numerical experiments.

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