Godel´s metric is a solution to the Einstein field equations, with cosmological constant, in the presence of an incoherent matter distribution.Godel´s universe is then the total space of a principal bundle over a 3-dimensional non-degenerate CR manifold. Invariant wave maps in the universe are precisely the vertical lifts of subelliptic harmonic maps of the manifold. For every such wave map we solve the L2 Dirichlet problem for the (degenerate elliptic) Jacobi operator J and prove that J has a discrete spectrum.