On vacuum solutions of scalar, su2 Yang-Mills and gravitation theories

In this letter it is shown that a) classical Yang-Mills solutions on Minkowsky space, generated via the Corrigan-Fairlie-'t Hooft-Wilczek ansatz, corresponding to a vanishing energy-momentum tensor, and b) conformally flat solutions of vacuum Einstein field equations with a nonzero cosmological constant are completely determined by the solutions of the massless scalar field equation whose improved energy-momentum tensor vanishes. The scalar functions depend on the Lorentz invariants u=x2 or u=ksub(lambda) xsup(lambda), k being a constant and uniform four-vector