# Penrose cosmic censorship

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A (future) singularity in a space-time corresponds to a causal geodesic $\gamma$ (cf. also Geodesic line) which is future inextensible and whose affine parameter remains finite (cf. Naked singularity). Penrose's weak (respectively, strong) cosmic censorship hypothesis states that any "physically realistic" space-time with a future-inextensible incomplete geodesic $\gamma$ that lies in the past of future infinity (respectively, of a point of space-time) is unstable with respect to a (still to be specified) natural topology of space-times [a9], [a10]. Here, "future infinity" refers to the conformal future boundary of a weakly asymptotically flat space-time in the sense of Penrose [a5] or a variant thereof. The meanings of "physically realistic" and "stable" are not specified. This is due to the existence of counter-examples which are not entirely unrealistic from a physical point of view but still have properties which seem to be very special (see, for instance, [a6]). There are various variants for both the weak and the strong cosmic censorship hypothesis. An especially important version of strong cosmic censorship is the hypothesis that any physically reasonable and qualitatively stable space-time is globally hyperbolic. The deepest general result on weak cosmic censorship has been obtained by R.P.A.C. Newman [a7], [a8], who shows that "persistent curvature" enforces a version of weak cosmic censorship. A more direct version of the cosmic censorship theorem, which is, however, only applicable for space-times very close to $4$-dimensional flat Lorentzian space, has been obtained by D. Christodoulou and S. Klainerman [a4]. Christodoulou has also investigated subclasses of spherically symmetric scalar field space-times and has obtained very detailed results with regard to cosmic censorship in these classes of space-times [a1], [a2], [a3].