SUPERTRANSLATIONS, ANGULAR MOMENTUM, AND COVARIANCE IN 4D ASYMPTOTICALLY FLAT SPACE I

Abstract

I will give a quick and incomplete introduction of the canonical formalism for the null conformal boundary of asymptotically flat 4D spacetime. The formalism will be used to find the infinite-dimensional isometries of asymptotically flat spacetime and their generators, which define the BMS (Bondi, Metzner, van der Burg, Sachs) algebra. This algebra contains supertranslations, which represent infinite-wavelength gravitational waves as well as the Poincarè algebra. The former can be factored out from dynamics using a classical equivalent of IR factorization, which I will briefly review. The latter is not a normal subalgebra so the generators of Lorentz transformations transform under supertranslations. This ambiguity is the origin of the  “angular momentum problem” in general relativity, which I will review in the last part of the lecture.