Abstract
AbstractIn a stationary axisymmetric vacuum gravitational field, the conformal structure of the 3‐space is determined by the symmetric, trace free and divergence‐less tensor Yir. Using the Killing vector Ki of the axisymmetry, the conformal potential U can be defined by U,i = εijkKjYkrKr. Conversely, the tensor Yik is given algebraically in terms of the gradient U,i of the conformal potential. An attempt is made here to re‐formulate the field equations Rλμ = 0 in terms of the conformal potential. Introducing the Ernst potential as a complex coordinate, the cylindrical radius can be eliminated from the field equations.
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