Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: II.Black Hole Solutions

TL;DR

This paper presents a new class of static, axially symmetric black hole solutions in Einstein-Yang-Mills-dilaton theory, characterized by unique geometric and physical properties, including angle-dependent matter fields and specific relations among physical quantities.

Contribution

It introduces a novel family of black hole solutions with axial symmetry, characterized by two integers, expanding understanding of Einstein-Yang-Mills-dilaton configurations.

Findings

Solutions are asymptotically flat with regular horizons.

Event horizon slightly elongated along the symmetry axis.

Sequences of solutions approach known Einstein-Maxwell-dilaton and Reissner-Nordström solutions.

Abstract

We discuss the new class of static axially symmetric black hole solutions obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory. These black hole solutions are asymptotically flat and they possess a regular event horizon. The event horizon is almost spherically symmetric with a slight elongation along the symmetry axis. The energy density of the matter fields is angle-dependent at the horizon. The static axially symmetric black hole solutions satisfy a simple relation between mass, dilaton charge, entropy and temperature. The black hole solutions are characterized by two integers, the winding number $n$ and the node number $k$ of the purely magnetic gauge field. With increasing node number the magnetically neutral black hole solutions form sequences tending to limiting solutions with magnetic charge $n$, corresponding to Einstein-Maxwell-dilaton black hole solutions for finite dilaton coupling constant and to Reissner-Nordstr\o m black hole solutions for vanishing dilaton coupling constant.