Ehlers, Carroll, Charges and Dual Charges

TL;DR

This paper explores the boundary effects of Ehlers' hidden M"obius symmetry in four-dimensional Ricci-flat spacetimes with a time-like isometry, revealing a Carrollian structure at the null boundary and defining related charges.

Contribution

It uncovers the Carrollian geometric structure of the boundary in Ricci-flat spacetimes and formulates the action of the M"obius group on boundary data, including charges and their transformations.

Findings

Identifies Carrollian boundary structure in Ricci-flat spacetimes.

Defines electric/magnetic and leading/subleading charges from boundary dynamics.

Analyzes the behavior of charges under M"obius duality.

Abstract

We unravel the boundary manifestation of Ehlers' hidden M\"obius 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 M\"obius 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 $\text{BMS}_4$, 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 M\"obius duality group.