Non-Abelian Black Holes and Catastrophe Theory II: Charged Type

TL;DR

This paper reexamines charged non-Abelian black holes in Einstein-Yang-Mills-Higgs theory, revealing their stability patterns through catastrophe theory and identifying conditions for instability and thermodynamic behavior changes.

Contribution

It demonstrates that stability of these black holes can be systematically understood via swallow tail catastrophe theory and explores their thermodynamic properties.

Findings

Stability linked to swallow tail catastrophe structure.

Reissner-Nordström solution becomes unstable with monopole black hole emergence.

Monopole black hole's specific heat can change sign in a small parameter range.

Abstract

We reanalyze the gravitating monopole and its black hole solutions in the Einstein-Yang-Mills-Higgs system and we discuss their stabilities from the point of view of catastrophe theory. Although these non-trivial solutions exhibit fine and complicated structures, we find that stability is systematically understood via a swallow tail catastrophe. The Reissner-Nordstr\"{o}m trivial solution becomes unstable from the point where the non-trivial monopole black hole appears. We also find that, within a very small parameter range, the specific heat of a monopole black hole changes its sign .