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 ${\text{BMS}}_4$, 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 Möbius duality group.

V1: Latex 1+46 pages, V2: JHEP version, ammended by a footnote (nb 44) in Appendix B

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Cited by in corpus (7)

• Flat from anti-de Sitter
• Carroll Hawking effect
• Chern-Simons action and the Carrollian Cotton tensors
• Radiation in Fluid/Gravity and the Flat Limit
• Quantization of Carrollian fermions
• Supersymmetric Carroll Galileons in Three Dimensions
• Nonperfect Carrollian Fluids Through Holography