%0 Journal Article
%T An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
%A Christian Baer
%A Alexander Strohmaier
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1506.00959v1