Weyl–Lewis–Papapetrou coordinates

Summary

Weyl–Lewis–Papapetrou coordinates are coordinates adapted to a stationary and axisymmetric spacetime. In them the metric depends on only two coordinates $\rho$ and $z$ and is described by three functions. For vacuum, the Einstein equations reduce to equations on flat three-dimensional space, which is the starting point of the Ernst equation. The Kerr metric and all static axisymmetric vacuum solutions can be written in this form.