Towards a proof of a rigidity conjecture for asymptotically flat spacetimes

30 October 2007
Juan Valiente Kroon
I will discuss ongoing work to provide a proof for the following conjecture: if the development of a time symmetric, conformally flat initial data set admits a smooth null infinity, then the initial data is Schwarzschildean in a neighbourhood of infinity. The strategy to construct a proof consists in a detailed analysis of a certain type of expansions that can be obtained using H. Friedrich's "cylinder at infinity" formalism. I will also discuss a toy model for the analysis of the Maxwell field near the spatial infinity of the Schwarzschild spacetime