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

Baxter, J. Erik; Winstanley, Elizabeth

doi:10.1088/0264-9381/25/24/245014

Cited by 23 publications

(144 citation statements)

References 61 publications

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“…The details of this power series can be found in Ref. 30 (following the analysis of Ref. 33 for the asymptotically flat case).…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…The N − 1 initial parameters ω j (r h ), together with the cosmological constant Λ and event horizon radius r h , completely determine the solution of the field equations in a neighbourhood of the horizon. 30 c. Infinity. As r → ∞, the field variables have the form 26) where M,ω j,∞ , and c j are constants.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…, N − 1 then gauge field strength tensor (2.10) does not vanish as F θφ has a contribution from nonzero matrix D (2.15). In this case, we obtain the magnetically charged Reissner-Nordström black hole solution with 30) where the magnetic charge Q is fixed to be…”

Section: Embedded Solutionsmentioning

confidence: 99%

“…From the argument in Subsection III E, there are embedded su(2) soliton and black hole solutions such that the values of the gauge field functions lie in R for all r. From Proposition 9 of Ref. 30, there are genuinely (that is, non-embedded) su(N) soliton and black hole solutions whose initial parameters (either near the origin or the event horizon, see Section II B 2 for details) lie in a neighbourhood of the initial parameters for the embedded su(2) solitons and black holes. Propositions 3 and 6 of Ref.…”

Section: F Existence Of Static Solutions With No Sphaleronic Sector mentioning

confidence: 99%

“…Providing we have chosen r 1 sufficiently large, for r > r 1 , we are in the asymptotic large r regime discussed in Section 4.2 of Ref. 30. The upshot of that analysis is that, by taking r 1 sufficiently large, the change in the gauge field functions as r → ∞ from r = r 1 can be made arbitrarily small.…”

Section: F Existence Of Static Solutions With No Sphaleronic Sector mentioning

confidence: 99%

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

Baxter

Winstanley

2016

Journal of Mathematical Physics

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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 ω 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 ω j 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. C 2016 AIP Publishing LLC. [http://dx

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“…The details of this power series can be found in Ref. 30 (following the analysis of Ref. 33 for the asymptotically flat case).…”

Section: Boundary Conditionsmentioning

confidence: 99%

Section: Boundary Conditionsmentioning

confidence: 99%

Section: Embedded Solutionsmentioning

confidence: 99%

Section: F Existence Of Static Solutions With No Sphaleronic Sector mentioning

confidence: 99%

Section: F Existence Of Static Solutions With No Sphaleronic Sector mentioning

confidence: 99%

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

Baxter

Winstanley

2016

Journal of Mathematical Physics

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A Menagerie of Hairy Black Holes

Winstanley

2018

Springer Proceedings in Physics

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According to the no-hair conjecture, equilibrium black holes are simple objects, completely determined by global charges which can be measured at infinity. This is the case in Einstein-Maxwell theory due to beautiful uniqueness theorems. However, the no-hair conjecture is not true in general, and there is now a plethora of matter models possessing hairy black hole solutions. In this note we focus on one such matter model: Einstein-Yang-Mills (EYM) theory, and restrict our attention to four-dimensional, static, non-rotating black holes for simplicity. We outline some of the menagerie of EYM solutions in both asymptotically flat and asymptotically anti-de Sitter space. We attempt to make sense of this black hole zoo in terms of Bizon's modified no-hair conjecture.

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Black holes with s u N $$ \mathfrak{s}\mathfrak{u}(N) $$ gauge field hair and superconducting horizons

Shepherd¹,

Winstanley²

2017

J. High Energ. Phys.

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We present new planar dyonic black hole solutions of the su(N ) Einstein-Yang-Mills equations in asymptotically anti-de Sitter space-time, focussing on su(2) and su(3) gauge groups. The magnetic part of the gauge field forms a condensate close to the planar event horizon. We compare the free energy of a non-Abelian hairy black hole with that of an embedded Reissner-Nordström-anti-de Sitter (RN-AdS) black hole having the same Hawking temperature and electric charge. We find that the hairy black holes have lower free energy. We present evidence that there is a phase transition at a critical temperature, above which the only solutions are embedded RN-AdS black holes. At the critical temperature, an RN-AdS black hole can decay into a hairy black hole, and it is thermodynamically favourable to do so. Working in the probe limit, we compute the frequency-dependent conductivity, and find that enlarging the gauge group from su(2) to su(3) eliminates a divergence in the conductivity at nonzero frequency.

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

Cited by 23 publications

References 61 publications

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

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

A Menagerie of Hairy Black Holes

Black holes with s u N $$ \mathfrak{s}\mathfrak{u}(N) $$ gauge field hair and superconducting horizons

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