AdS Carroll Structures from Poincar\'e Isomorphism: Asymptotic Symmetry Analysis

Abstract

Starting from the isomorphism between the AdS Carroll and Poincar\'e algebras, we map the three-dimensional asymptotically flat solutions of Poincar\'e gravity into an AdS Carroll spacetime. We show the mapped solutions satisfy the field equations of the Chern-Simons formulation of AdS Carroll gravity and exhibit a Carroll geometry structure. Despite the presence of a negative cosmological constant in the mapped spacetime, the algebra of the canonical generators of the asymptotic symmetries is given by the $\mathfrak{bms}_3$ algebra.