Most general flat space boundary conditions in three-dimensional Einstein gravity

Abstract

We consider the most general asymptotically flat boundary conditions in three-dimensional Einstein gravity in the sense that we allow for the maximal number of independent free functions in the metric, leading to six towers of boundary charges and six associated chemical potentials. We find as associated asymptotic symmetry algebra an current algebra. Restricting the charges and chemical potentials in various ways recovers previous cases, such as , Heisenberg or Detournay–Riegler, all of which can be obtained as contractions of corresponding AdS3 constructions. Finally, we show that a flat space contraction can induce an additional Carrollian contraction. As examples we provide two novel sets of boundary conditions for Carroll gravity.