Unique Carrollian manifolds emerging from Einstein spacetimes
Mar 19, 202520 pages
Published in:
- Class.Quant.Grav. 42 (2025) 7, 075006
- Published: Mar 19, 2025
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Abstract: (IOP)
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.- null hypersurfaces
- Einstein spacetimes
- Carrollian geometry
- asymptotically flat spacetimes
- vacuum spacetimes
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