An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
- We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.
Author details: | Christian BärORCiDGND, Alexander StrohmaierORCiD |
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DOI: | https://doi.org/10.1353/ajm.2019.0037 |
ISSN: | 0002-9327 |
ISSN: | 1080-6377 |
Title of parent work (English): | American Journal of Mathematics |
Publisher: | Johns Hopkins Univ. Press |
Place of publishing: | Baltimore |
Publication type: | Article |
Language: | English |
Year of first publication: | 2019 |
Publication year: | 2019 |
Release date: | 2020/11/04 |
Volume: | 141 |
Issue: | 5 |
Number of pages: | 35 |
First page: | 1421 |
Last Page: | 1455 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access |
Open Access / Green Open-Access |