AdS Carroll structures from Poincaré isomorphism: Asymptotic symmetry analysis

Starting from the isomorphism between the anti–de Sitter (AdS) Carroll and Poincaré algebras, we obtain the magnetic AdS Carroll gravity in three dimensions. Moreover, we derive the first set of asymptotic conditions for the AdS Carroll structure, and we prove that the asymptotic symmetry algebra is given by the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="fraktur">bms</a:mi><a:mn>3</a:mn></a:msub></a:math> algebra. By mapping the three-dimensional asymptotically flat solutions of Poincaré gravity into an AdS Carroll spacetime, we demonstrate that the resulting solutions satisfy the field equations of the Chern-Simons formulation of AdS Carroll gravity, and we note that this solution possesses an infinite set of Killing vectors.