Multiply Unstable Black Hole Critical Solutions

TL;DR

This paper investigates the stability and critical solutions in gravitational collapse of a complex scalar field, revealing multiple unstable solutions and explaining their occurrence through parameter space analysis.

Contribution

It demonstrates the coexistence of multiple unstable critical solutions and proposes an explanation based on parameter space behavior.

Findings

Identification of parameter regions with different critical solutions.

Existence of initial data families that lead to CSS as critical solution despite multiple instabilities.

Explanation of the stability change between DSS and CSS solutions.

Abstract

The gravitational collapse of a complex scalar field in the harmonic map is modeled in spherical symmetry. Previous work has shown that a change of stability of the attracting critical solution occurs in parameter space from the discretely self-similarity critical (DSS) solution originally found by Choptuik to the continuously self-similar (CSS) solution found by Hirschmann and Eardley. In the region of parameter space in which the DSS is the attractor, a family of initial data is found which finds the CSS as its critical solution despite the fact that it has more than one unstable mode. An explanation of this is proposed in analogy to families that find the DSS in the region where the CSS is the attractor.