Ehlers, Carroll, charges and dual charges

Abstract

We unravel the boundary manifestation of Ehlers’ hidden Möbius 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 Möbius 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 Möbius duality group.

Dynamics of Carrollian scalar fields

“…but, while (33) is, this statement is not (local and diff) Carroll boost invariant. Under the latter h µν transforms as in (8) and thus δ ij is boost invariant but δ ij is not, as part of the degenerate tensor h µν 6 .…”