  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.
