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The weak and the strong Cosmic Censorship Hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity.
Singularities that arise in the solutions of Einstein's equations are typically hidden within event horizons, and therefore cannot be seen from the rest of spacetime. Singularities which are not so hidden are called naked. The weak cosmic censorship hypothesis conjectures that no naked singularities other than the Big Bang singularity exist in the universe. The hypothesis was conceived by Roger Penrose in 1969. Cosmic censorship hypotheses should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation.[1]
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Since the physical behavior of singularities is unknown, if singularities can be observed from the rest of spacetime, causality may break down, and physics may lose its predictive power. The issue cannot be avoided, since according to the PenroseHawking singularity theorems, singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe is deterministic — it's possible to predict the entire evolution of the universe (possibly excluding some finite regions of space hidden inside event horizons of singularities), knowing only its condition at a certain moment of time (more precisely, everywhere on a spacelike 3dimensional hypersurface, called the Cauchy surface). Failure of the cosmic censorship hypothesis leads to the failure of determinism, because it is yet impossible to predict the behavior of spacetime in the causal future of a singularity. Cosmic censorship is not merely a problem of formal interest; some form of it is assumed whenever black hole event horizons are mentioned.
The hypothesis was first formulated by Roger Penrose in 1969, and it is not stated in a completely formal way. In a sense it is more of a research program proposal: part of the research is to find a proper formal statement that is physically reasonable and that can be proved to be true or false (and that is sufficiently general to be interesting).^{[1]}
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