Differential Invariants of Carrollian Spacetimes
Abstract
We compute invariants of Carrollian spacetimes, deriving them from the geometry of the screen bundle. For generic Carrollian structures we specify how to generate the entire algebra of differential invariants, with emphasis on dimension 3, which has special physical relevance. Then, in the framework of jet-spaces, we compute the numerology behind these invariants: the Hilbert and Poincaré functions that govern their numbers according to order. Finally, we compute the Spencer cohomology behind the Carrollian geometry that, in particular, contains the spaces of intrinsic torsion and intrinsic curvature, which are fundamental invariants, important in the equivalence problem and symmetry analysis. Thus, we also discuss symmetry sizes of Carrollian spacetimes.
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BibTeX
@misc{kruglikov2026differential,
title = {{Differential Invariants of Carrollian Spacetimes}},
author = {Boris Kruglikov and Eivind Schneider and Wijnand Steneker},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.30274},
eprint = {2606.30274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30274},
}
RIS
TY - UNPB
TI - Differential Invariants of Carrollian Spacetimes
AU - Boris Kruglikov
AU - Eivind Schneider
AU - Wijnand Steneker
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2606.30274
UR - https://arxiv.org/abs/2606.30274
AB - We compute invariants of Carrollian spacetimes, deriving them from the geometry of the screen bundle. For generic Carrollian structures we specify how to generate the entire algebra of differential invariants, with emphasis on dimension 3, which has special physical relevance. Then, in the framework of jet-spaces, we compute the numerology behind these invariants: the Hilbert and Poincaré functions that govern their numbers according to order. Finally, we compute the Spencer cohomology behind the Carrollian geometry that, in particular, contains the spaces of intrinsic torsion and intrinsic curvature, which are fundamental invariants, important in the equivalence problem and symmetry analysis. Thus, we also discuss symmetry sizes of Carrollian spacetimes.
ER -