Ernst equation

Summary

The Ernst equation is a single nonlinear partial differential equation for one complex function, the Ernst potential. It is equivalent to the vacuum Einstein equations for stationary axisymmetric spacetimes, written in Weyl–Lewis–Papapetrou coordinates. It was introduced by Frederick J. Ernst in 1968. The equation is integrable, and solution-generating techniques based on it produce many exact solutions, including the Kerr metric.