On pp-waves with lightlike parallel spinors
by
Bernd Ammann, Jonathan Glöckle, Klaus Kröncke
On pp-waves with lightlike parallel spinors,
Preprint version (pdf)
Arxiv version arxiv:2602.14821
Abstract
We parametrize pp-wave spacetimes with compact codimension 2 submanifolds. 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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Last update of this page 03.08.2026
The paper was originally written on 19.2.2026