The BMS group, that arises as the asymptotic symmetry group of Einstein’s gravity, comprises of Lorentz transformations and “supertranslations”. The supertranslations, first discovered at the null infinity of spacetime, have been extensively studied in the context of various physical phenomena such as gravitational radiation, scattering amplitudes, black hole physics, etc. In this talk, I will discuss how the BMS supertranslations appear in the Hamiltonian formulation of gravity, which is crucial for understanding these symmetries at the spatial infinity of spacetime. Starting from the (3+1) ADM formalism, the BMS symmetry can be obtained from the invariance of the ADM action and interpreted as canonical transformations in the phase space. In the second part of the talk, I will focus on an alternative Hamiltonian formulation of gravity, called the (2+2) or double-null formalism, in which these supertranslations may also be understood from the perspective of canonical transformations. Although the two formulations have some apparent differences, the nature of BMS supertranslations inferred from the two approaches are in agreement with each other. I will conclude with some important implications of these two studies and their relevance to real-world physical processes.
