Ernst coordinates

Abstract

Ernst coordinates can be introduced in space-times in which the complex Ernst potential exists with functionally independent real and imaginary parts. The real part of the Ernst potential is the norm and the imaginary part is the curl scalar of a Killing vector. As yet only stationary space-times have been investigated by this approach. Some special limiting types must be excluded from the discussion such as the static, the Papapetrou class and Petrov-type N metrics. The Poynting vector of the gravitational field is required to be surface-forming, a mild condition satisfied by most exact solutions of the gravitational equations. As an illustration of the procedure, we discuss axisymmetric vacuum space-times with conformally flat 3-spaces.