Year: 2026
Type: preprint
Abstract: We introduce, motivated by noncommutative Carrollian geometry, the notion of a Carrollian--Poisson bundle understood as a Carrollian manifold with a compatible Poisson structure. Compatibility is expressed as the inclusion of the Carroll distribution in the image of the Poisson anchor. We explore the geometric consequences of this compatibility and present several simple examples of Carrollian--Poisson bundles, including the (outer) Kerr horizon, the BTZ horizon, and future null infinity. Furthermore, we establish that every Carrollian--Poisson bundle can be equipped with a Vaisman (contravariant) connection that is both metric-compatible and clock-compatible, and thus geometric kinematics can be defined and studied.
Source: arXiv (Cornell University)
Author: Bruce, Andrew James
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211985658