Asymptotic Analysis in General Relativity

General relativity will be 99 years old in 2014. During this near century of research, Einstein's theory has been remarkably successful in terms of the correctness and precision of its predictions.

As years went by, a variety of domains of mathematics have contributed to its development, bringing in techniques that have pushed back the boundaries of our understanding of the theory and, to a certain extent, of the universe.

In the mid 1960's, the method of conformal compactification provided a simple and intuitive description of the Sachs peeling and has since been a powerful geometrical technique of asymptotic analysis. In the 1970's and 1980's, spinor and twistor methods, in addition to simplifying considerably many aspects of the theory, such as the Petrov classification, opened the way for the study of generalized symmetries related to Killing spinors, Killing tensors and Killing-Yano tensors. In the 1990's the first results of global non-linear stability of solutions of the Einstein equations appeared, based on geometric energy estimates, also referred to as vector field methods.

During the last ten years, the understanding of the propagation of waves on black hole backgrounds has made spectacular progress, with fundamental implications for both quantum field theory on black hole spacetimes and the nonlinear stability of such geometries.

This summer school will focus on geometrical and analytical aspects of asymptotic analysis in general relativity.

Organization committee : Thierry Daudé (Cergy-Pontoise), Dietrich Häfner (Grenoble), Jean-Philippe Nicolas (Brest).

All the records of mini-courses and lectures are online at : http://ifmathlive.ujf-grenoble.fr/videos