Mathematical Physics seminar: Non-linear stability in GR and related theories
The nonlinear stability of Minkowski space as a solution to the Einstein equations has been known since the pioneering work of Christodoulou and Klainerman in the '90s. However, despite a large literature building on this result, certain important questions remain unanswered. What, precisely, are the structures within the Einstein equations that allow this result to hold? And how can we generalise the techniques developed by Christodoulou and Klainerman so that they can be applied to other (more interesting) spacetimes, such as black holes? In this talk I will give a partial answer to both of these questions, by first situating the Einstein equations within a much broader class of nonlinear wave equations for which I prove a stability result. This stability result is also proved using a new approach which relies on much weaker assumptions about the 'final state' of the spacetime.