Weak cosmic censorship for the circularly symmetric Einstein-scalar field system in $2+1$ dimensions

Abstract

We prove the weak cosmic censorship conjecture in $2+1$ spacetime dimensions for the circularly symmetric Einstein-scalar field system in the presence of a negative cosmological constant $\Lambda <0$. More precisely, we show that for any integer $k\ge 2$, the maximal development of generic $C^k$ initial data does not contain naked singularities. An essential step of the proof is establishing the presence of a mass gap. In particular, this implies that all naked singularities have infinite blueshift, which represents the main instability mechanism.

arXiv comment62 pages + references, 4 figures