Wavelike solutions to the Einstein equations coupled to neutrino and gauge fields

Starting from the plane-wave metric, solutions to the Einstein field equations coupled to a Weyl neutrino field and to a Yang-Mills field are found. These solutions can be superposed to yield a solution with both sources if the direct interaction between them is neglected. A solution to the coupled Einstein-Yang-Mills-Weyl equations that represents a multiplet of neutrino fields interacting with the gauge field and the gravitational field is also found. All these solutions contain arbitrary functions