Asymptotic symmetries in Carrollian theories of gravity

TL;DR

This paper classifies asymptotic symmetries for two Carrollian gravities derived from General Relativity: magnetic and electric contractions. Using Regge-Teitelboim and Henneaux-Troessaert parity conditions, it shows that magnetic Carrollian gravity can realize the Carroll group (RT) or a BMS-like extension (HT), while the electric contraction yields only spatial rotations plus translations (RT) or rotations plus parity-odd supertranslations (HT), with no energy generator in either electric case. The analysis relies on a Hamiltonian formulation with well-defined boundary charges and a finite symplectic term, mirroring the GR treatment. A Schwarzschild-like solution in each theory demonstrates the presence or absence of energy charges consistent with the respective parity choices. Overall, the magnetic limit behaves as a smooth GR-like contraction at infinity, whereas the electric limit presents a discontinuity in asymptotic symmetries and eliminates a global energy concept, highlighting a sharp structural difference between the two Carrollian gravities.

Abstract

Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from "magnetic" and "electric" ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For the electric contraction, because the lapse function does not appear in the boundary term needed to ensure a well-defined action principle, the asymptotic symmetry algebra is truncated, for Regge-Teitelboim parity conditions, to the semidirect sum of spatial rotations and spatial translations. Similarly, with Henneaux-Troessaert parity conditions, the asymptotic symmetries are given by the semidirect sum of spatial rotations and an infinite number of parity odd supertranslations. Thus, from the point of view of the asymptotic symmetries, the magnetic contraction can be seen as a smooth limit of General Relativity, in contrast to its electric counterpart.