Exact classical solutions of yang-mills sourceless equations

Ramírez

2017

We construct and study stationary, asymptotically flat multicenter solutions describing regular black holes with non-Abelian hair (colored magnetic-monopole and dyon fields) in two models of N = 2, d = 4 Super-Einstein-Yang-Mills theories: the quadratic model CP 3 and the cubic model ST [2,6], which can be embedded in 10-dimensional Heterotic Supergravity. These solutions are based on the multicenter dyon recently discovered by one of us, which solves the SU(2) Bogomol'nyi and dyon equations on E 3 . In contrast to the well-known Abelian multicenter solutions, the relative positions of the non-Abelian black-hole centers are unconstrained. We study necessary conditions on the parameters of the solutions that ensure the regularity of the metric. In the case of the CP 3 model we show that it is enough to require the positivity of the "masses" of the individual black holes, the finiteness of each of their entropies and their superadditivity. In the case of the ST [2, 6] model we have not been able to show that analogous conditions are sufficient, but we give an explicit example of a regular solution describing thousands of non-Abelian dyonic black holes in equilibrium at arbitrary relative positions. We also construct non-Abelian solutions that interpolate smoothly between just two aDS 2 ×S 2 vacua with different radii (dumbbell solutions).

Section: Jhep10(2017)066mentioning

confidence: 99%

“…[54]. The BPS limit of the 't HooftPolyakov monopole [50][51][52], the SU(2) Wu-Yang monopole [53] and the so-called colored monopoles considered in refs.…”

Section: Setting Up the Problemmentioning

confidence: 99%

Dyonic black holes at arbitrary locations

Ramírez

2017

“…After Prasad and Sommerfield [76] found the solution describing the 't Hooft-Polyakov monopole in the BPS limit, Protogenov [77] classified all spherically symmetric solutions to the SU(2) Bogomol'nyi equations: the ones that can be used to generate BH-like spacetimes are a 2-parameter family (f µ,s , h µ,s ) plus a 1-parameter family (f λ , h λ ) given by…”

Section: The Hedgehog Ansatzmentioning

confidence: 99%

N = 2 $$ \mathcal{N}=2 $$ Einstein-Yang-Mills’ static two-center solutions

Bueno

et al. 2014

“…This solution corresponds to the coloured solution found by Protogenov in ref. [27] and which was used in refs. [2,7,8] to construct coloured black hole solutions to various N = 2 EYM theories; the parameter λ is a hair parameter that doesn't show up in the coloured black hole's asymptotic nor near-horizon behaviour.…”

Section: Su(2)'s Coloured Solution Revisitedmentioning

confidence: 99%

N = 2 $$ \mathcal{N}=2 $$ super-EYM coloured black holes from defective Lax matrices

2015

We construct analytical supersymmetric coloured black hole solutions, i.e. non-Abelian black hole solutions that have no asymptotic non-Abelian charge but do have non-Abelian charges on the horizon that contribute to the Bekenstein-Hawking entropy, to two SU(3)-gauged N = 2 d = supergravities. The analytical construction is made possible due to the fact that the main ingredient is the Bogomol'nyi equation, which under the assumption of spherical symmetry admits a Lax pair formulation. The Lax matrix needed for the coloured black holes must be defective which, even though it is the non-generic and less studied case, is a minor hindrance.