Non-Abelian Black Holes and Catastrophe Theory I : Neutral Type

TL;DR

This paper classifies neutral non-Abelian black holes into two types based on their non-Abelian field mass and analyzes their stability using catastrophe theory, revealing universal stability structures.

Contribution

It provides a unified classification of neutral non-Abelian black holes and applies catastrophe theory to analyze their stability structures.

Findings

Type I black holes have a fold catastrophe stability structure.

Type II black holes exhibit both fold and cusp catastrophe structures.

High-entropy Type II black holes are stable and nearly neutral.

Abstract

We re-analyze the globally neutral non-Abelian black holes and present a unified picture, classifying them into two types; Type I (black holes with massless non-Abelian field) and Type II (black holes with ``massive" non-Abelian field). For the Type II, there are two branches: The black hole in the high-entropy branch is ``stable" and almost neutral, while that in the low entropy branch, which is similar to the Type I, is unstable and locally charged. To analyze their stabilities, we adopt the catastrophe theoretic method, which reveals us a universal picture of stability of the black holes. It is shown that the isolated Type II black hole has a fold catastrophe structure. In a heat bath system, the Type I black hole shows a cusp catastrophe, while the Type II has both fold and cusp catastrophe.