Gravitational Instability of a Kink

TL;DR

This paper investigates the stability and evolution of a self-gravitating scalar field kink outside a reflecting barrier, revealing a bifurcation between stable and unstable equilibria and the potential for black hole formation.

Contribution

It introduces a new analysis of gravitational kinks with a potential difference, highlighting the degenerate static equilibria and their stability properties.

Findings

Small kinks decay to a static solution.

Large kinks exhibit degenerate equilibria with stable and unstable states.

Unstable kinks can collapse into black holes.

Abstract

We study the equilibria of a self-gravitating scalar field in the region outside a reflecting barrier. By introducing a potential difference between the barrier and infinity, we create a kink which cannot decay to a zero energy state. In the realm of small amplitude, the kink decays to a known static solution of the Einstein-Klein-Gordon equation. However, for larger kinks the static equilibria are degenerate, forming a system with two energy levels. The upper level is unstable and, under small perturbations, decays to the lower energy stable equilibrium. Under large perturbations, the unstable upper level undergoes collapse to a black hole. The equilibrium of the system provides a remarkably simple and beautiful illustration of a turning point instability.