New Black Hole Solutions with Axial Symmetry in Einstein-Yang-Mills Theory

TL;DR

This paper introduces new static, axially symmetric black hole solutions in Einstein-Yang-Mills theory, characterized by additional parameters, expanding the known family of solutions and confirming theoretical mass relations.

Contribution

The authors construct novel black hole solutions with axial symmetry and multiple parameters, extending previous spherically symmetric solutions and exploring their properties and mass relations.

Findings

New solutions exist for k>1, with properties depending on n.

Solutions form two branches merging at a maximal horizon radius.

Mass differences align with the isolated horizon framework.

Abstract

We construct new black hole solutions in Einstein-Yang-Mills theory. They are static, axially symmetric and asymptotically flat. They are characterized by their horizon radius and a pair of integers (k,n), where k is related to the polar angle and n to the azimuthal angle. The known spherically and axially symmetric EYM black holes have k=1. For k>1, pairs of new black hole solutions appear above a minimal value of n, that increases with k. Emerging from globally regular solutions, they form two branches, which merge and end at a maximal value of the horizon radius. The difference of their mass and their horizon mass equals the mass of the corresponding regular solution, as expected from the isolated horizon framework.