Axially symmetric, static self-dual SU(3) gauge fields and stationary Einstein-Maxwell metrics

Abstract

The stationary axially symmetric (AS) Einstein-Maxwell equations are shown to be a special case of the static AS self-dual SU(3) Yang-Mills equations; they can become identical by imposing certain functional relations on the Yang-Mills fields. Certain techniques developed for the Einstein-Maxwell equations are translated into the SU(3) Yang-Mills equations, and a linear eigenvalue problem for the stationary AS Einstein-Maxwell equations is formulated.