I will present a gluing theorem for time-symmetric vacuum general relativistic initial data sets with negative cosmological constant in 2 spatial dimensions and sketch the derivation of the mass formulae of the resulting manifolds. Our gluing procedure yields complete manifolds with any mass aspect function, which are smooth except for one or two conical singularities. Near conformal infinity, these glued manifolds exhaust all time-symmetric Banados geometries.
based on joint work with Piotr T. Chruściel, arXiv:2401.04048