The Cauchy problem in General Relativity

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The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon (2017, background): “A manifestly weaker formulation which has been considered in the literature replaces C with C(2) (see [105]).”
The Cauchy Problem in General Relativity (2009, background): “We omit the details of how these spaces are defined; the interested reader is referred to [19, 20] for the details.”
Energy conditions in general relativity and quantum field theory (2020, unknown): “, energy conditions seem by no means a necessary condition for a classical eld theory to have a well-posed initial value formulation, even though theymay enter as a useful method in the proof of such a property [8].”
A Primer on Energy Conditions (2014, background): “For the AWEC, if Γ contains enough timelike geodesics and the spacetime is well behaved, then there may be null geodesics that are limit curves of subfamilies of Γ ; in this case, the relevant characteristic integral will be nonnegative for those null geodesics, and the AWEC with the fixed Γ can be ”