Asymptotically flat spacetimes

Abstract

For the next lecture, we consider four-dimensional asymptotically flat spacetimes, which are the solutions of General Relativity with localised energy-momentum sources. We will start with a review of the work of Penrose on the conformal compactification of asymptotically flat spacetimes in order to get a global view on the asymptotic structure. We will then concentrate on the properties of radiative fields by reviewing the work of van der Burg, Bondi, Metzner and Sachs of 1962. One may think at first that the group of asymptotic symmetries of radiative spacetimes is the Poincaré group, but a larger group appears, the BMS group which contains so-called supertranslations. Additional symmetries, known as superrotations, also play a role and we shall briefly discuss them too. Finally, we will give some comments on the scattering problem in General Relativity. We will show that the extended asymptotic group gives conserved quantities once junction conditions are fixed at spatial infinity.