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

TL;DR

This paper proves the weak cosmic censorship conjecture for a specific Einstein-scalar field system in 2+1 dimensions with negative cosmological constant, showing generic initial data do not lead to naked singularities.

Contribution

It establishes the weak cosmic censorship in 2+1 dimensions for the Einstein-scalar system with a negative cosmological constant, including the presence of a mass gap.

Findings

Maximal development of generic initial data lacks naked singularities.

Naked singularities exhibit infinite blueshift, indicating instability.

Presence of a mass gap is crucial for the proof.

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 $k\geq2$, 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.