Static Spaces and Related Topics in Matematical General Relativity

The aim of this course is to present some classical and more recent results concerning the classification and rigidity properties of static spaces, i.e., Riemannian manifolds arising as spatial cross-sections of static solutions to Einstein's field equations of General Relativity. The topics treated in the course will include the uniqueness theorem for static black holes, the positive mass theorem and some recent uniqueness and rigidity results for static spaces with constant nonzero scalar curvature (corresponding to solutions to the Einstein's field equations with nonzero cosmological constant) and for sub-static spaces, a generalization of the notion of static spaces that has been an active research theme in the last decade.