Workshop From geometry to numerics
IHP, Paris, 20-24 November 2006

Lydia Bieri (ETH Zurich, Switzerland)

Solutions of the Einstein-Vacuum Tending to the Minkowski Spacetime at Infinity

The talk addresses the global, nonlinear stability of solutions of the Einstein equations in General Relativity. In particular, it deals with the initial value problem for the Einstein vacuum equations, generalizing the results of D. Christodoulou and S. Klainerman in 'The global nonlinear stability of the Minkowski space'. Every strongly asymptotically flat, maximal, initial data which is globally close to the trivial data gives rise to a solution which is a complete spacetime tending to the Minkowski spacetime at infinity along any geodesic. We consider the Cauchy problem with more general, asymptotically at initial data. This yields a spacetime curvature which is not continuous any more. In order to show decay of the spacetime curvature and the corresponding geometrical quantities, the Einstein equations are decomposed with respect to adequate foliations of the spacetime. In this work, the main proof is based on a bootstrap argument, that is, an extension of the theorem of Noether.

[slides]

[back to the program]