Final Report Summary - MPGR (Mathematical Problems in General Relativity) This project concerned the mathematical study of some of the most celebrated open problems in general relativity, regarding the stability of black holes and the nature of spacetime singularities. A complete resolution of these problems still lies in the future, but important progress has been made in the context of this project, achieving and in several case going well beyond the original specific objectives of the proposal. In particular, it has been mathematically proven by the PI and his collaborators that the celebrated Kerr black hole family is indeed stable to linear "scalar" perturbations, except in the extremal case, where a Ph.D. student of the PI has discovered a new instability. This allows in the near future a treatment of the full nonlinear stability problem in the context of Einstein's nonlinear field equations themselves, what would be a milestone result for mathematical analysis in the service of theoretical physics. In parallel, the study of spacetime singularities has also been advanced in the project by work of the PI, his collaborators and students, with further progress on the strong cosmic censorship conjecture of Roger Penrose in various model problems. This promises to open the way for a complete resolution of the conjecture, addressing fundamental questions about nature, such as, "Is the future determined by the present?"
