Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field

TL;DR

This paper explores the gravitational collapse of a non-linear scalar field, identifying self-similar solutions, their stability, and bifurcation phenomena related to black hole formation.

Contribution

It introduces a family of self-similar solutions parameterized by coupling constants and analyzes their stability and bifurcation behavior in gravitational collapse.

Findings

Identification of self-similar solutions in scalar field collapse

Discovery of a Hopf bifurcation leading to instability

Calculation of critical exponents for black hole formation

Abstract

We examine the gravitational collapse of a non-linear sigma model in spherical symmetry. There exists a family of continuously self-similar solutions parameterized by the coupling constant of the theory. These solutions are calculated together with the critical exponents for black hole formation of these collapse models. We also find that the sequence of solutions exhibits a Hopf-type bifurcation as the continuously self-similar solutions become unstable to perturbations away from self-similarity.