General Relativity and the Einstein Equations

By Y. Choquet-bruhat. 2009

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Energy conditions in general relativity and quantum field theory (2020, background): “nd on derivatives of the metric, then (30) coupled to Einstein’s equation is a symmetric hyperbolic system of equations. It is well-known that such systems have a well-posed initial value formulation [52, 8, 32, 31], which means that for any initial data (satisfying the problem’s constraint equation”
Hybrid Metric-Palatini Gravity (2015, methodology): “Given initial data on a space-like surface, the associated Cauchy problem is then well-posed in suitable Sobolev spaces [63].”
The Global Nonlinear Stability of Minkowski Space for Self-gravitating Massive Fields (2015, methodology): “We follow [5,26] and work in wave coordinates satisfying, by definition, gx = 0.”