Seminarium KMMF "Teoria Dwoistości"

The Poincaré group is the symmetry group of special relativity. In general relativity, sensible symmetry groups exist only for the so-called asymptotically flat spacetimes. Here mass is concentrated in a compact region and the metric tensor decays to the Minkowski metric when going to infinity. The symmetries then arise as certain diffeomorphisms of the conformal compactification of spacetime. As generalisations of the Poincaré group, the Bondi-Metzner-Sachs (BMS) group and the Newman-Unti (NU) group have been proposed. We will briefly recall these and explain that both are infinite-dimensional groups given by a semidirect product of a finite dimensional group and a function space. For these types of groups, we shall then sketch recent results implying that they are not locally exponential. This means, that the Lie group exponential is bad in so far as it does not yield a local diffeomorphism onto a unit neighbourhood of the group. This is joint work with A. Chirvasitu, R. Dahmen, D. Prinz and K.-H. Neeb.