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Strohmaier, A orcid.org/0000-0002-8446-3840 and Zelditch, S (2021) A Gutzwiller trace formula for stationary space-times. Advances in Mathematics, 376. 107434. ISSN 0001-8708
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□.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Elsevier Inc. All rights reserved. This is an author produced version of a paper published in Advances in Mathematics. Uploaded in accordance with the publisher's self-archiving policy. This manuscript version is made available under the Creative Commons CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Oct 2020 15:16 |
Last Modified: | 13 Oct 2021 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aim.2020.107434 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:166170 |
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A Gutzwiller trace formula for stationary space-times. (deposited 02 Oct 2020 15:15)
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