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An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary

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journal contribution
posted on 20.09.2019, 11:11 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

American Journal of Mathematics

Volume

141

Issue

5

Pages

1421 - 1455

Citation

BÄR, C. and STROHMAIER, A., 2018. An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. American Journal of Mathematics, In Press.

Publisher

Johns Hopkins University Press

Version

AM (Accepted Manuscript)

Rights holder

© the Authors

Publisher statement

This 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/

Acceptance date

11/10/2017

Publication date

2019

Notes

© 2017. This is an author produced version of a paper accepted for publication in American Journal of Mathematics.

ISSN

0002-9327

Language

en

Depositor

Dr Alexander Strohmaier

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