Separation of variables and exact solution of the Klein-Gordon and Dirac   equations in an open universe
  We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary time-dependence of the field, we discuss the asymptotic behavior of the solutions with the help of the relativistic Hamilton-Jacobi equation. 
Victor M. Villalba, E. Isasi