Global evolution problems in General Relativity
General relativity is a theory of gravity that relates the geometry of space and time to the distribution of matter. In fact, even in the absence of matter it can be viewed as a theory for the evolution of the geometry of space in time, and poses a number of challenging problems in the theory of hyperbolic partial differential equations. In this talk, I will elaborate on two global evolution problems for Einstein's equations: The first is in the regime of a space-time geometry globally close to the flat Minkowski space-time, and can be recast as a scattering problem for nonlinear wave equations (joint with Hans Lindblad). The second relates to models of the expanding universe, and I will describe some of my work on the stability of black hole cosmologies.
Volker Schlue, University of Melbourne