Kink Stability of Self-Similar Solutions of Scalar Field in 2+1 Gravity

TL;DR

This paper investigates the stability of self-similar scalar field solutions in 2+1 gravity, finding that while they are unstable to certain perturbations along the sonic line, considering external perturbations limits this instability, preserving the critical nature of the solutions.

Contribution

It demonstrates that the critical solutions in scalar collapse are stable against kink perturbations when external perturbations are included, refining previous stability analyses.

Findings

Unstable against kink perturbations along the sonic line.

External perturbations restrict unstable modes.

Critical solutions remain stable after considering kink perturbations.

Abstract

The kink stability of self-similar solutions of a massless scalar field with circular symmetry in 2+1 gravity is studied, and found that such solutions are unstable against the kink perturbations along the sonic line (self-similar horizon). However, when perturbations outside the sonic line are considered, and taking the ones along the sonic line as their boundary conditions, we find that non-trivial perturbations do not exist. In other words, the consideration of perturbations outside the sonic line limits the unstable mode of the perturbations found along the sonic line. As a result, the critical solution for the scalar collapse remains critical even after the kink perturbations are taken into account.