Formulate the Carrollian construction in relaxed Bondi gauge

Determine whether the Carrollian conformal-dynamics construction can be formulated in relaxed Bondi gauge.

Background

The paper develops an intrinsic Carrollian description of the conformal boundary of four-dimensional asymptotically flat spacetimes and shows that, in a standard BMS frame, its evolution equations reproduce the Bondi mass- and angular-momentum-aspect equations. The construction relies on a particular Bondi gauge and on identifying the undetermined transverse part of the compatible Carrollian connection with the Bondi shear.

The Discussion explicitly raises the question of extending this construction to relaxed Bondi gauge, where the boundary data and residual gauge structure are less restrictive. Such an extension would test the gauge dependence and generality of the Carrollian variational framework.