  On a compact globally hyperbolic Lorentzian spin manifold with smooth
spacelike Cauchy boundary the (hyperbolic) Dirac operator is known to be
Fredholm when Atiyah-Patodi-Singer boundary conditions are imposed. In this
paper we investigate to what extent these boundary conditions can be replaced
by more general ones and how the index then changes. There are some differences
to the classical case of the elliptic Dirac operator on a Riemannian manifold
with boundary.
