Some solutions of stationary, axially-symmetric gravitational field equations

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Abstract
Stationary, axially‐symmetric solutions of the gravitational field equations for vacuum, perfect fluid, and massless scalar field are considered. For the vacuum case, a similiar formulation to the one introduced by Ernst is presented by use of quarternions. Null dust solutions are found, and it is shown that they match with the van Stockum exterior solutions. An extension of the theorem by Eriş and Gürses is given which enables one to construct solutions to the gravitational field equations coupled with a charged dust and a massless scalar field from the solutions of the field equations coupled only with a charged dust.