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.
Highlights
The Carroll group was discovered by Levy-Leblond in 1965 [1] as a dual contraction of the Poincaregroup, operating at vanishing rather than infinite velocity of light
Carroll structures consist of a d þ 1-dimensional manifold C equipped with a degenerate metric g and a vector field E, which defines the kernel of the metric, i.e., gðE; :Þ 1⁄4 0
The Carroll group emerges as the isometry group of flat Carrollian structures, whereas general diffeomorphisms are always available
Summary
The Carroll group was discovered by Levy-Leblond in 1965 [1] as a dual contraction of the Poincaregroup, operating at vanishing rather than infinite velocity of light. Subset of diffeomorphisms arises, the Carrollian diffeomorphisms, which preserves this separation Given their defining properties, Carroll structures are expected to arise systematically as geometries on null hypersurfaces of relativistic spacetimes, because the induced metric inherited from the embedding is degenerate.. The BMS group was discovered in 1962 by Bondi, van der Burg, Metzner and Sachs [11,12] as the asymptotic isometry group of asymptotically flat spacetimes towards null infinity (see, e.g., [13,14]) It was in particular proven [3] that the bmsðd þ 2Þ algebra is isomorphic to the conformal Carroll algebra ccarrðd þ 1Þ for d 1⁄4 1; 2. Different such proposals may lead to different algebras that preserve the given structure, along with a related choice of partial gauge fixing
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