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This work introduces a novel family of boundary conditions for AdS$_3$General Relativity, constructed through a polynomial expansion in negativeinteger powers of the Brown-Henneaux central charge. The associated dynamics isgoverned by the Dym hierarchy of integrable equations. It is shown that theinfinite set of Dym conserved charges generates an abelian asymptotic symmetrygroup. Additionally, these boundary conditions encompass black hole solutions,whose thermodynamic properties are examined.

1/c deformations of AdS$_3$ boundary conditions and the Dym hierarchy