Mathematics and General Relativity

General relativity is one of the most successful alliances of mathematics and physics. It provides us with a theory of gravity which agrees with all experimentation and observation to date. In addition, there is a great deal of physical evidence for a number of interesting effects predicted by the theory of gravity---black holes, cosmological expansion, gravitational waves, and gravitational lenses. The enabling tool is the language of differential geometry. Throughout its 70-year history, general relativity has significantly stimulated pseudo-Riemannian as well as Riemannian geometry and has also motivated important work in complex geometry, topology, and the study of both elliptic and hyperbolic systems of partial differential equations.