The gauging procedure and carrollian gravity

We discuss a gauging procedure that allows us to construct lagrangians dictate the dynamics of an underlying Cartan geometry. In sense be made precise in paper, starting datum is Klein pair corresponding homogeneous space. What amounts construction geometry modelled on geometry, with gauge field defining connection. The lagrangian itself consists all gauge-invariant top-forms constructed from connection and its curvature. After demonstrating this produces four-dimensional General Relativity upon Minkowski spacetime, we proceed maximally symmetric carrollian spaces: Carroll, (anti-)de Sitter--Carroll lightcone. For first three these spaces, our generalise earlier first-order lagrangians. resulting theories gravity take same form, which seems manifestation model mutation at level odd one out, lightcone, not reductive means although equations motion form as other cases, geometric interpretation different. obtain analogues Gauss--Bonnet, Pontryagin Nieh--Yan topological terms, well two additional terms are intrinsically seem have no lorentzian counterpart. Since scratch work also provides no-go result for electric theory formulation.