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Title: An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
Authors: Baer, Christian
Strohmaier, Alexander
Issue Date: 2015
Publisher: arXiv.org
Citation: BAER, C. and STROHMAIER, A., 2015. An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. arXiv:1506.00959v1 [math.DG], 25pp.
Abstract: 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.
Description: This pre-print was submitted to arXiv on 2 June 2015.
Version: Submitted for publication
URI: https://dspace.lboro.ac.uk/2134/20035
Publisher Link: http://arxiv.org/abs/1506.00959
Appears in Collections:Pre-prints (Maths)

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