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 |
|---|---|
| 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 |
