Characterize the solution space of conformal Carroll Killing vectors

Characterize the global solution space of conformal Carroll Killing vectors on a general three-dimensional Carroll manifold, including the conditions under which these vectors form the extended BMS algebra.

Background

The paper defines conformal Carroll Killing vectors through the simultaneous preservation of the Carroll clock one-form and spatial metric, up to Weyl and Carroll-boost transformations. Their associated currents are identified with BMS currents, whose non-conservation is controlled by the K-curvatures.

The authors decompose a conformal Carroll Killing vector into temporal and spatial parts and derive a hierarchy of differential equations governing these components. They explain that, locally, the boundary geometry can be brought to a round two-sphere with exact retarded-time form, suggesting the existence of vectors generating the extended BMS algebra. However, the general solution space on an arbitrary Carroll manifold is not characterized.