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AdS Carroll Structures from Poincar\'e Isomorphism: Asymptotic Symmetry Analysis
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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.
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3D Carrollian gravity from 2D Euclidean symmetry
Post-Carroll-Newtonian Chern-Simons gravities are systematically obtained by semigroup-expanding 2D Euclidean B_k algebras, recovering known Carrollian models as subcases.
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