A GUTZWILLER TRACE FORMULA FOR STATIONARY SPACE-TIMES

ALEXANDER STROHMAIER, STEVE ZELDITCH

Research output: Contribution to journalArticlepeer-review

Abstract

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 languageEnglish (US)
JournalUnknown Journal
StatePublished - Aug 25 2018

ASJC Scopus subject areas

  • General

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