The evolution problem in general relativity

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Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I (2011, background): “On the other hand, the so-called weak cosmic censorship conjecture suggests that naked singularities are dynamically unstable (see the discussion in [26]).”
Linear and Quasi-Linear Evolution Equations in Hilbert Spaces (2012, background): “, Majda [108], and Nishida [126]); general relativity, and, specifically, the so-called Einstein vacuum equations (Klainerman and Christodoulou [78], and Klainerman and Nicolò [80]); wave maps (Shatah and Struwe [145], and Tao [156]); von Karman type thin plate equations (Cherrier and Milani [26, 27”
Extensions of the Stability Theorem of the Minkowski Space in General Relativity (2009, background): “ver, there are more conditions to be imposed on the data than in [21]. There is a variant for the exterior part of the proof from [21] using a double-null foliation by S. Klainerman and F. Nicolo in [28]. Also a semiglobal result was given by H. Friedrich [23] with initial data on a spacelike hyperb”
The linear stability of the Schwarzschild solution to gravitational perturbations (2016, background): “We note that double null gauges have figured prominently in the nonlinear analysis of the Einstein vacuum equations [11, 56, 46, 42] and thus provide a promising setting for a future full non-linear analysis of the stability problem.”