Lie theory for asymptotic symmetries in general relativity: The BMS group

We study the Lie group structure of asymptotic symmetry groups in General Relativity from viewpoint infinite-dimensional geometry. To this end, we review geometric definition simplicity and emptiness due to Penrose coordinate-wise flatness Bondi et al. Then construct Bondi--Metzner--Sachs (BMS) discuss its theoretic properties. find that BMS is regular sense Milnor, but not real analytic. This motivates us conjecture it locally exponential. Finally, verify Trotter property as well commutator property. As an outlook, comment on situation related groups. In particular, much more involved Newman--Unti highlighted, which will be studied future work.