BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
Marc Henneaux, Cédric Troessaert
TL;DR
This work introduces new boundary conditions at spatial infinity for asymptotically flat spacetimes that are invariant under the BMS group and yield a finite, well-defined symplectic form. By using mixed parity conditions on leading metric and momentum components, the authors render the Hamiltonian generators of asymptotic symmetries integrable and nontrivial, while still containing Schwarzschild and Kerr solutions and their Poincaré transforms. The resulting charges do not vanish in general, including nonzero supertranslation charges, and the asymptotic symmetry algebra closes to the BMS algebra without a central extension. The approach connects spatial infinity in the ADM formalism to the BMS structure known at null infinity and opens avenues for incorporating matter, superrotations, and alternative sectors like Taub–NUT.
Abstract
New boundary conditions for asymptotically flat spacetimes are given at spatial infinity. These boundary conditions are invariant under the BMS group, which acts non trivially. The boundary conditions fulfill all standard consistency requirements: (i) they make the symplectic form finite; (ii) they contain the Schwarzchild solution, the Kerr solution and their Poincaré transforms, (iii) they make the Hamiltonian generators of the asymptotic symmetries integrable and well-defined (finite). The boundary conditions differ from the ones given earlier in the literature in the choice of the parity conditions. It is this different choice of parity conditions that makes the action of the BMS group non trivial. Our approach is purely Hamiltonian and off-shell throughout.