The proposed project concerns the study of mathematical aspects of the general theory of relativity. Major unsolved problems in the area include the problem of nonlinear stability of black hole spacetimes and the problem of weak and strong cosmic censorship. Mathematically, these problems concern the global dynamics of solutions to the Einstein equations. Resolution of these problems is of fundamental importance both to our understanding of the nature of the theory of relativity and to our assessment of its validity. In previous work, I have addressed these problems either under symmetry reductions or in linearised settings. These studies have revealed much of the mathematical structure of the dynamics of the Einstein equations in the context of black holes. Further progress extending beyond symmetry or linearised theory now appears possible. A research programme with this as a goal will be outlined in the proposal.
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