Carroll Structures, Null Geometry and Conformal Isometries

TL;DR

The paper builds Carrollian spacetimes as fiber bundles endowed with an Ehresmann connection to implement a clean time–space split and a degenerate metric, enabling a natural description of null hypersurfaces and their intrinsic Carrollian tensors. It derives how Carrollian data on null leaves arise from ambient Lorentzian geometry and analyzes their conformal isometries, showing that for shearless geometries the symmetry algebra is the semi-direct product of the base’s spatial conformal algebra with supertranslations, reproducing BMS in certain dimensions. The results underscore the role of the Ehresmann connection in lifting spatial conformal symmetries to the Carrollian bundle and highlight avenues for extending the framework to nonzero shear and holographic applications.

Abstract

We study the concept of Carrollian spacetime starting from its underlying fiber-bundle structure. The latter admits an Ehresmann connection, which enables a natural separation of time and space, preserved by the subset of Carrollian diffeomorphisms. These allow for the definition of Carrollian tensors and the structure at hand provides the designated tools for describing the geometry of null hypersurfaces embedded in Lorentzian manifolds. Using these tools, we investigate the conformal isometries of general Carrollian spacetimes and their relationship with the BMS group.