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arXiv · 1506.00959

An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary

Christian Baer·Alexander Strohmaier
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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.

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Christian Baer, Alexander Strohmaier. 2015-06-02. An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. https://doi.org/10.1353/ajm.2019.0037

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