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arXiv · 2409.19682

Unique Carrollian manifolds emerging from Einstein spacetimes

S. Blitz·D. McNutt·P. Nurowski
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Abstract

We explicitly determine all shear-free null hypersurfaces embedded in an Einstein spacetime, including vacuum asymptotically flat spacetimes. We characterize these hypersurfaces as oriented 3-dimensional manifolds where each is equipped with a coframe basis, a structure group and a connection. Such manifolds are known as null hypersurface structures (NHSs). The coframe and connection one-forms for an NHS appear as solutions to the projection of the Cartan structure equations onto the null hypersurface. We then show that each NHS corresponds to a Carrollian structure equipped with a unique pair of Ehresmann connection and affine connection.

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S. Blitz, D. McNutt, P. Nurowski. 2024-09-29. Unique Carrollian manifolds emerging from Einstein spacetimes. https://doi.org/10.1088/1361-6382/adbb4e

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