Ehlers, Carroll, charges and dual charges

We unravel the boundary manifestation of Ehlers' hidden Mobius symmetry present in four-dimensional Ricci-flat spacetimes that enjoy a time-like isometry and are Petrov-algebraic. This is achieved in a designated gauge, shaped in the spirit of flat holography, where the Carrollian three-dimensional nature of the null conformal boundary is manifest and covariantly implemented. The action of the Mobius group is local on the space of Carrollian boundary data, among which the Carrollian Cotton tensor plays a predominent role. The Carrollian and Weyl geometric tools introduced for shaping an appropriate gauge, as well as the boundary conformal group, which is BMS4, allow to define electric/magnetic, leading/subleading towers of charges directly from the boundary Carrollian dynamics and explore their behaviour under the action of the Mobius duality group.

Automated summary

We study the boundary manifestation of Ehlers' hidden Mobius symmetry in four-dimensional Ricci-flat spacetimes with a time-like isometry and Petrov-algebraic property. This is done in a designated gauge inspired by flat holography, where the Carrollian nature of the null conformal boundary is clearly seen and implemented covariantly. The Mobius group acts locally on the space of Carrollian boundary data, with the Carrollian Cotton tensor playing a predominant role. By using Carrollian and Weyl geometric tools and the boundary conformal group BMS4, electric/magnetic, leading/subleading towers of charges can be defined directly from the boundary Carrollian dynamics and their behavior under the Mobius duality group can be explored.