The squared Lorentzian Dirac operator on small Minkowski perturbations has real spectrum plus isolated resonances, and a zeta-function residue equals the scalar curvature plus twisting curvature.
Cauchy Problem for the Dirac operator on spatially non-compact spacetimes
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Let $M$ be a globally hyperbolic manifold with complete spacelike Cauchy hypersurface $\Sigma$. We prove well-posedness of the Cauchy problem for the Dirac operator on globally hyperbolic manifolds with complete Cauchy hypersurfaces. This result is needed as preparation in showing a Fredholmness result in the manner, provided by B\"ar and Strohmaier, for certain non-compact Cauchy hypersurfaces in future work. The results already have been published for a simpler setting in arxiv:2107.08532. This version is only focused on the Cauchy problem for a slightly modified setting.
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Dirac operators and local invariants on perturbations of Minkowski space
The squared Lorentzian Dirac operator on small Minkowski perturbations has real spectrum plus isolated resonances, and a zeta-function residue equals the scalar curvature plus twisting curvature.