(Super-)renormalizable hairy meronic black holes

TL;DR

This paper constructs new analytical black hole solutions in Einstein-Maxwell-Yang-Mills theory with conformal scalar fields, generalizing known solutions and exploring their properties with non-Abelian gauge fields.

Contribution

It introduces a class of (super-)renormalizable hairy meronic black holes and extends conformal scalar field theories to include charged solutions with Yang-Mills fields.

Findings

Derived a generalized charged black hole solution with non-Abelian gauge fields.

Extended conformal scalar field theories to include non-Noetherian, second-order invariant solutions.

Showed static black holes can be charged with Yang-Mills fields in extended scalar theories.

Abstract

We construct an analytical black hole solution in the Einstein-Maxwell-Yang-Mills theory with a conformally coupled scalar field in four dimensions, which generalizes the charged Mart\'inez-Troncoso-Zanelli (MTZ) black hole in the presence of self-gravitating non-Abelian gauge fields. The internal gauge group is determined by the horizon curvature, becoming $SU(N)$ in the case of positive curvature and $SU(N-1,1)$ when the curvature is negative. Moreover, this solution is employed as a conformal seed to obtain new meronic spacetimes dressed with all (super-)renormalizable contributions of the scalar field, which provides the generalization of the Anabal\'on-Cisterna (AC) solution when self-gravitating non-Abelian gauge fields are included. Finally, we consider the non-Noetherian extension of the conformal scalar fields, which still yields a second-order conformally invariant scalar equation, even though the action is not. In that case, we show that static black hole solutions can also be charged with Yang-Mills fields.