  We give a relativistic generalization of the Gutzwiller-Duistermaat-Guillemin
trace formula for the wave group of a compact Riemannian manifold to globally
hyperbolic stationary space-times with compact Cauchy hypersurfaces. We
introduce several (essentially equivalent) notions of trace of self-adjoint
operators on the null-space $\ker \Box$ of the wave operator and define $U(t)$
to be translation by the flow $e^{t Z}$ of the timelike Killing vector field
$Z$ on $\Box$. The spectrum of $Z$ on $\ker \Box$ is discrete and the
singularities of $\rm{Tr}\;e^{t Z} |_{\ker \Box}$ occur at periods of periodic
orbits of $\exp t Z$ on the symplectic manifold of null geodesics. The trace
formula gives a Weyl law for the eigenvalues of $Z$ on $\ker \Box$.
