Appears in collection : General relativity: a celebration of the 100th anniversary

In general it is not possible to localize solutions of the Einstein equations since there are asymptotic conserved quantities such as the total mass which are nonzero for every nontrivial space-time. In this lecture we will describe work with A. Carlotto which achieves a localization in cones which is in a certain sense optimal. The construction leads to a superposition theorem for solutions of the Einstein vacuum equations in such a way that there is no interaction between the solutions for a fixed time. It also leads to some surprising new phenomena for the geometry of initial data sets. https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-richardschoen.pdf