Cartan-like Formulation of Electric Carrollian Gravity

We present a Cartan-like first-order action principle for electric Carrolliangravity. The action is invariant under the local homogeneous Carroll group,albeit in a different representation than the one obtained by gauging theCarroll algebra. Additionally, we show that this first-order action can bederived from a smooth Carrollian limit of the Einstein-Cartan action. Theconnection with the Hamiltonian and metric forms of the action for electricCarrollian gravity, as well as with previous works in the literature, is alsodiscussed.