Numerical study of the Kerr solution in rotating coordinates
  The Kerr solution in coordinates corotating with the horizon is studied as a testbed for a spacetime with a helical Killing vector in the Ernst picture. The solution is numerically constructed by solving the Ernst equation with a spectral method and a Newton iteration. We discuss convergence of the iteration for several initial iterates and different values of the Kerr parameters. 
S. Bai, G. Izquierdo, and C. Klein
gr-qc