Abstract
We show thata) classical Yang-Mills solutions on Minkowski space, generated via the Corrigan-Fairlie-'t Hooft-Wilczek ansatz, corresponding to a vanishing energy-momentum tensor, andb) 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. Our scalar functions depend on the Lorentz invariantsu=x 2 oru=k λ x λ,k being a constant and uniform four-vector.
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