Relativité générale: solutions exactes stationnaires

Abstract

After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes, corresponding to a special spacetime geometry. Then, we will show that the reformulation of the stationary Einstein-Maxwell equations as a gravitating sigma model provides us with a powerful tool to generate new solutions.

Lectures given at the 3e Ecole de Physique Theorique de Jijel (Algeria), Sept. 2009. 52 pages, in French