On pp-waves with lightlike parallel spinors

Bernd Ammann; Jonathan Glöckle; Klaus Kroencke

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arXiv · 2602.14821

On pp-waves with lightlike parallel spinors

Bernd Ammann·Jonathan Glöckle·Klaus Kroencke

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Abstract

We parametrize pp-wave spacetimes with compact codimension 2 hypersurfaces. In the vacuum case, we show that these spacetimes are locally in one-to-one correspondence with smooth curves of Riemannian Ricci-flat metrics modulo smooth curves of diffeomorphisms. We also prove that this one-to-one correspondence extends to pp-waves with prescribed null Ricci curvature. Moreover, the pp-wave spacetime carries a lightlike parallel spinor if and only if one (and hence all) of the Ricci-flat metrics carries a parallel spinor.

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Bernd Ammann, Jonathan Glöckle, Klaus Kroencke. 2026-02-16. On pp-waves with lightlike parallel spinors. https://arxiv.org/abs/2602.14821

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