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 of the wave operator and define U(t) to be translation by the flow etZ of the timelike Killing vector field Z on. The spectrum of Z on ker is discrete and the singularities of TretZ|ker occur at periods of periodic orbits of exp tZ on the symplectic manifold of null geodesics. The trace formula gives a Weyl law for the eigenvalues of Z on ker.
|Original language||English (US)|
|State||Published - Aug 25 2018|
ASJC Scopus subject areas