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

Baxter, J. Erik; Winstanley, Elizabeth

doi:10.1063/1.4940694

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

Jan 29, 2015

32 pages

Published in:

J.Math.Phys. 57 (2016) 2, 022506

Published: Feb 3, 2016

e-Print:

1501.07541 [gr-qc]

DOI:

10.1063/1.4940694

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Abstract: (AIP)

We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N − 1 magnetic gauge field functions ωj. 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 ωj have no zeros and satisfy a set of N − 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant Λ is sufficiently large.

Note:

43 pages, 4 figures, minor changes, discussion expanded and references updated. Matches version accepted for publication in J. Math. Phys

cosmological constant: negative
symmetry: rotation
soliton: stability
black hole: hair
dimension: 4
Einstein-Yang-Mills theory
gauge field theory
perturbation
gravitation
decoupling

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