Asymptotic symmetries in Carrollian theories of gravity

TL;DR

This paper investigates the asymptotic symmetries of Carrollian gravitational theories derived from ultrarelativistic contractions of General Relativity, revealing different symmetry structures depending on the contraction type and boundary conditions.

Contribution

It provides a detailed analysis of asymptotic symmetries in Carrollian gravity, highlighting differences between magnetic and electric contractions and their relation to known symmetry algebras.

Findings

Magnetic contraction yields Carroll and BMS-like symmetries.

Electric contraction results in truncated or extended symmetry algebras.

Magnetic contraction is a smooth limit of General Relativity, unlike the electric case.

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.