# Carroll Structures, Null Geometry and Conformal Isometries

## TL;DR

This paper explores the geometry of Carrollian spacetimes, focusing on their fiber-bundle structure, and investigates their conformal symmetries and relation to the BMS group, providing new tools for null hypersurface analysis.

## Contribution

It introduces a fiber-bundle approach to Carrollian geometry, enabling a detailed study of conformal isometries and their connection to the BMS group.

## Key findings

- Carrollian diffeomorphisms preserve the fiber-bundle structure.
- Defined Carrollian tensors for null hypersurface geometry.
- Established links between Carrollian conformal symmetries and the BMS group.

## 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.