Cauchy Problem for the Dirac operator on spatially non-compact spacetimes

Orville Damaschke

Cauchy Problem for the Dirac operator on spatially non-compact spacetimes

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arxiv 2409.17344 v2 pith:FSUTTK3K submitted 2024-09-25 math.DG math.AP

Orville Damaschke This is my paper · ORCID

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keywords cauchyproblemcompletediracgloballyhyperbolichypersurfacesnon-compact

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abstract

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
math.AP 2024-12 conditional novelty 7.0 of 10

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.

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