  We consider a hyperbolic Dirac-type operator with growing potential on a a
spatially non-compact globally hyperbolic manifold. We show that the
Atiyah-Patodi-Singer boundary value problem for such operator is Fredholm and
obtain a formula for this index in terms of the local integrals and the
relative eta-invariant introduced by Braverman and Shi. This extends recent
results of B\"ar and Strohmaier, who studied the index of a hyperbolic Dirac
operator on a spatially compact globally hyperbolic manifold.
