Collapsing Scalar Field with Kinematic Self-Similarity of the Second Kind in 2+1 Gravity

TL;DR

This paper classifies all 2+1-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind in Einstein-massless-scalar field equations, revealing that some solutions describe scalar field collapse leading to black hole formation.

Contribution

It provides a complete set of solutions with this symmetry in 2+1 gravity and analyzes their properties, including black hole formation during scalar field collapse.

Findings

Some solutions describe gravitational collapse leading to black holes.

All solutions exhibit kinematic self-similarity of the second kind.

The global properties of these solutions are characterized.

Abstract

All the 2+1-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.