Poincaré Pseudosymmetries in Asymptotically Flat Spacetimes

Abstract

It is the purpose of this note to point out (or perhaps, more accurately, to argue) that for asymptotically flat spacetimes that are sufficiently close to flat space, there are global vector fields and associated global transformations (arising from the existence of the asymptotic symmetries) that can be identified as nonlinear counterparts of the Poincaré transformations. They are however not symmetries in any obvious sense, and hence the reference to them as “pseudosymmetries.” They are obtained by rigidly pulling the asymptotic symmetries of null infinity into the interior of the spacetime, via the rigid light-cone structure ofthe spacetime. In the limiting flat-space case, when the radiation vanishes, these pseudosymmetries become the exact flat-space symmetries. It thus seems reasonable to think of the pseudosymmetries as being approximate global symmetries for these weak gravitational fields. Presumably this idea can be extended to the associated concept of approximate conservation laws.

Dedicated to Engelbert Schucking, who knows more mathematics and physics than most of us put together.