Ernst equation

In mathematics, the Ernst equation (named after Frederick J. Ernst) is the non-linear partial differential equation

\displaystyle \Re(u)(u_{rr}+u_r/r+u_{zz}) = (u_r)^2+(u_z)^2.

It is used to produce exact solutions of Einstein's equations.

References

Zwillinger, Daniel (1989), Handbook of differential equations, Boston, MA: Academic Press, ISBN 978-0-12-784390-2, MR 977062