Mathematical problems in general relativity

General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation and is fundamentally rooted in classical mechanics. Its main objective is the understanding of the evolution of gravitational physical systems such as planetary systems, multiple stars, black holes, (a cluster of) galaxies and ultimately the universe as a whole.

The research program will strive to resolve certain fundamental mathematical questions pertaining to the main conjectures in general relativity. Specifically, the project will investigate the stability problem for the so-called extremal and sub-extremal Kerr black holes aiming at establishing the relevance of black holes from a theoretical point of view. It will also develop a scattering theory for the Einstein equations which is expected to provide new insights into the study of the propagation of gravitational waves. Finally, the program will investigate the gluing problem for characteristic initial data of hyperbolic equations. The latter is an extension of the Riemannian gluing problem for elliptic equations and is intensively studied in geometric analysis. The proposal, if successful, will lead to the discovery of genuinely new analytical techniques applicable in a wider spectrum of problems in geometry, analysis, PDEs and mathematical physics, contributing to further strengthening the ties between these communities and pure mathematics.