# On the stability of soliton and hairy black hole solutions of ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant

- Authors
- Type
- Preprint
- Publication Date
- Jan 25, 2016
- Submission Date
- Jan 29, 2015
- Identifiers
- DOI: 10.1063/1.4940694
- Source
- arXiv
- License
- Yellow
- External links

## Abstract

We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda $. These solutions are described by $N-1$ magnetic gauge field functions $\omega _{j}$. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any $N$, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions $\omega _{j}$ have no zeros, and satisfy a set of $N-1$ inequalities. In the gravitational sector, we are able to prove that there are solutions which have no instabilities in a neighbourhood of stable embedded ${\mathfrak {su}}(2)$ solutions, provided the magnitude of the cosmological constant $\left| \Lambda \right| $ is sufficiently large.