Vacuum energy in asymptotically flat spacetimes in 3 dimensions.*

The vacuum energy limit of asymptotically flat spacetimes is calculated, based on the evaluation of the Noether charges. The action formulation used is three-dimensional asymptotically flat gravity based on a Chern–Simons formulation in the Poincaré group, corresponding to an Einstein–Hilbert term in the bulk, plus half of the Gibbons-Hawking term at the boundary. This is required for a well-defined and finite action principle under the conditions adopted. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space. We also comment on an approach based on holonomies of the Chern-Simons connection used to model the solutions being considered.