Dyon Solution in Einstein-Yang-Mills Theory on a Cylindrical Symmetric Space Time with Cosmological Constant

Abstract

We investigated numerically dyon-like solutions of the SU(2) Einstein-Yang-Mills system on a cylindrically symmetric space time with a cosmological constant. We find a new kind of behaviour not found in the spherically symmetric models. For positive values of $\Lambda$ we have an oscillatory behaviour of the magnetic component of the YM field around the r-axis, so there is an arbitrary number of nodes. For increasing positive $\Lambda$, the frequency increases also and the solution breaks down at finite radius, indicating a singularity. The electric component, however, approaches a constant value. After further increasing $\Lambda$, this global behaviour repeats itself at a larger r while the former singular behaviour disappears. For increasing negative $\Lambda$, the oscillatory behaviour disappears and the magnetic and electric components behave like the scalar and gauge field in the Abelian cosmic string model.