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arXiv · 2409.17344

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

Orville Damaschke
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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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Orville Damaschke. 2024-09-25. Cauchy Problem for the Dirac operator on spatially non-compact spacetimes. https://arxiv.org/abs/2409.17344

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