The idea of cosmic censorship goes back to the work of Roger Penrose; see [62] (reprinted in [64]) and [63]. It comes in two forms: weak and strong. The weak cosmic-censorship conjecture is concerned with isolated systems and essentially states that, generically, singularities should not be visible to an observer at infinity; see [90] for a more precise and extensive discussion. The strong cosmic censorship conjecture is a statement concerning the deterministic nature of the general theory of relativity. This is the form we are interested in here, and we shall phrase it in terms of initial data. Consequently, we need to formulate the initial value (or Cauchy) problem for Einstein’s equations.

4.1 The initial value problem

4.1.1 The vacuum equations

4.1.2 Formulation, intuition

4.1.3 Formulation, formal definition

4.1.4 Existence of a development

4.1.5 Existence of a maximal globally-hyperbolic development

4.2 Strong cosmic censorship

4.2.1 Genericity

4.2.2 Inextendibility

4.3 Curvature blow up

4.4 Pathological examples in the case of Gowdy

4.1.1 The vacuum equations

4.1.2 Formulation, intuition

4.1.3 Formulation, formal definition

4.1.4 Existence of a development

4.1.5 Existence of a maximal globally-hyperbolic development

4.2 Strong cosmic censorship

4.2.1 Genericity

4.2.2 Inextendibility

4.3 Curvature blow up

4.4 Pathological examples in the case of Gowdy

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