  We find solutions of the Dirac equation in curved spacetime. In particular,
we consider 1+1 dimensional sections of several exotic metrics: the Alcubierre
metric, which describes a scenario that allows faster-than-light (FTL)
velocity; the G\"odel metric, that describes a universe containing closed
timelike curves (CTC); and the Kerr metric, which corresponds to the spacetime
of a rotating black hole. Moreover, we also show that the techniques that we
use in these cases can be extended to nonstatic metrics.
