N=2 Super-EYM coloured black holes from defective Lax matrices

TL;DR

This paper constructs analytical supersymmetric coloured black hole solutions in SU(3)-gauged N=2 supergravity, revealing non-Abelian horizon charges that influence entropy, using a defective Lax matrix approach.

Contribution

It introduces a novel analytical method for constructing coloured black holes with non-Abelian horizon charges via defective Lax matrices in supergravity.

Findings

Black hole solutions with non-Abelian horizon charges are explicitly constructed.

The use of defective Lax matrices is essential for the analytical solution.

Non-Abelian charges contribute to the black hole entropy.

Abstract

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.