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An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
journal contributionposted on 2019-09-20, 11:11 authored by Christian Baer, Alexander Strohmaier
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.
- Mathematical Sciences
Published inAmerican Journal of Mathematics
Pages1421 - 1455
CitationBÄR, C. and STROHMAIER, A., 2018. An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. American Journal of Mathematics, In Press.
PublisherJohns Hopkins University Press
- AM (Accepted Manuscript)
Rights holder© the Authors
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
Notes© 2017. This is an author produced version of a paper accepted for publication in American Journal of Mathematics.