Spherically symmetric scalar field collapse

TL;DR

This paper demonstrates that scalar fields minimally coupled to gravity can undergo collapse even when energy conditions are violated, with implications for dark energy clustering and black hole formation.

Contribution

It shows collapsing modes of scalar fields exist under energy condition violations and analyzes their horizon formation and singularity characteristics.

Findings

Apparent horizons form before singularities.

Singularities are shell focusing with diverging density.

Ricci scalar diverges at the singularity.

Abstract

It is shown that a scalar field, minimally coupled to gravity may have collapsing modes even when the energy condition is violated, that is, for $(\rho+3p)<0$. This result may be useful in the investigation of the possible clustering of dark energy. All the examples dealt with have apparent horizons which form before the formation of the singularity. The singularities formed are shell focusing in nature. The density of the scalar field distribution is seen to diverge at singularity. The Ricci scalar also diverges at the singularity. The interior spherically symmetric metric is matched with exterior Vaidya metric at the hypersurface and the appropriate junction conditions are obtained.