Complex variables for separation of Hamilton-Jacobi equation on   three-dimensional Minkowski space
  The real coordinates separating geodesic Hamilton-Jacobi equation on three-dimensional Minkowski space in several cases cannot be defined in the whole space. We show through an example how to naturally extend them to complex variables defined everywhere (excluding the singular surfaces of each coordinate system only) and still separating the same equation. 
Luca Degiovanni, Giovanni Rastelli