| Abstract: | In 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. |
