In (super) gravity theories, T-duality relates solutions with an exact isometry which can have wildly different asymptotic behaviors: A well-known example is the duality between BTZ black holes and (non-extremal) three-dimensional black strings. Using this dual pair, we show how the knowledge of a phase space which includes one set of solutions (here, BTZ black holes embedded in the Brown-Henneaux phase space) allows to obtain a phase space for the dual set via an asymptotic notion of T-duality. The resulting asymptotic symmetry algebras can be very different. For our particular example, we find a large algebra of symmetries for the black string phase space which includes as subalgebras bms₂ 𝔟𝔪𝔰2, bms₃ 𝔟𝔪𝔰3, and a twisted warped conformal algebra. On the way, we show that a chiral half of the Brown-Henneaux boundary conditions are dual to the Compère-Song-Strominger ones.
Detournay et al. (Mon,) studied this question.