Exact meron Black Holes in four dimensional SU(2) Einstein-Yang-Mills theory

TL;DR

This paper constructs an exact non-Abelian black hole solution in four-dimensional SU(2) Einstein-Yang-Mills theory, featuring a meron gauge field and a metric similar to Reissner-Nordström, with unique non-Abelian properties affecting field excitations.

Contribution

It presents a novel exact black hole solution with a meron gauge field in SU(2) Einstein-Yang-Mills theory, highlighting its non-Abelian characteristics and implications for fermionic behavior.

Findings

Solution features a meron gauge field with non-Abelian properties.

The metric resembles Reissner-Nordström but with a non-constant coefficient.

Field excitations exhibit fermionic behavior due to the gauge field structure.

Abstract

In this paper an intrinsically non-Abelian black hole solution for the SU(2) Einstein-Yang-Mills theory in four dimensions is constructed. The gauge field of this solution has the form of a meron whereas the metric is the one of a Reissner-Nordstr\"om black hole in which, however, the coefficient of the $1/r^2$ term is not an integration constant. Even if the stress-energy tensor of the Yang-Mills field is spherically symmetric, the field strength of the Yang-Mills field itself is not. A remarkable consequence of this fact, which allows to distinguish the present solution from essentially Abelian configurations, is the Jackiw, Rebbi, Hasenfratz, 't Hooft mechanism according to which excitations of bosonic fields moving in the background of a gauge field with this characteristic behave as Fermionic degrees of freedom.