Christian Klein

Christian Klein
(MPI for Mathematics in the Sciences, Germany)

Riemann-Hilbert problem for the Ernst equation

We study the Riemann-Hilbert problem for the Ernst equation which is equivalent to the stationary axisymmetric Einstein equations in vacuum. Using a gauge freedom of the associated linear system we show that the Riemann-Hilbert problem can be solved explicitly in terms of hyperelliptic theta functions for rational jump data. Properties of these solutions are discussed.