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

TL;DR

This paper explores the relationship between AdS Carroll and Poincaré algebras, mapping asymptotically flat solutions into AdS Carroll spacetime, revealing a Carroll geometry with BMS3 asymptotic symmetry despite a negative cosmological constant.

Contribution

It introduces a novel mapping between AdS Carroll and Poincaré algebras, showing how asymptotically flat solutions translate into AdS Carroll spacetime with consistent symmetry structures.

Findings

Mapped solutions satisfy AdS Carroll gravity field equations

The asymptotic symmetry algebra is BMS3

Negative cosmological constant does not alter the BMS3 symmetry

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.