Naked Singularities and the Cosmic Censorship Hypothesis

While spacetime singularities in general are frequently viewed with suspicion, physicists often offer the reassurance that we expect most of them to be hidden away behind the event horizons of black holes. Such singularities therefore could not affect us unless we were actually tojump into the black hole. A “naked” singularity, on the other hand, is one that is not hidden behind an event horizon. Such singularities appear much more threatening because they are uncontained, accessible to vast areas of spacetime.

The heart of the worry is that singular structure would seem to signify some sort of breakdown in the fundamental structure of spacetime to such a profound depth that it could wreak havoc on any region of universe that it were visible to. Because the structures that break down in singular spacetimes are required for the formulation of our known physical laws in general, and of initial-value problems for individual physical systems in particular, one such fear is that determinism would collapse entirely wherever the singular breakdown were causally visible. As Earman (1995, pp. 65-6) characterizes the worry, nothing would seem to stop the singularity from “disgorging” any manner of unpleasant jetsam, from TVs showing Nixon's Checkers Speech to old lost socks, in a way completely undetermined by the state of spacetime in any region whatsoever, and in such a way as to render strictly indeterminable all regions in causal contact with what it spews out.

One form that such a naked singularity could take is that of a white hole, which is a time-reversed black hole. Imagine taking a film of a black hole forming, and various astronauts, rockets, etc. falling into it. Now imagine that film being run backwards. This is the picture of a white hole: one starts with a naked singularity, out of which might appear people, artifacts, and eventually a star bursting forth. Absolutely nothing in the causal past of such a white hole would determine what would pop out of it (just as items that fall into a black hole leave no trace on the future). Because the field equations of general relativity do not pick out a preferred direction of time, if the formation of a black hole is allowed by the laws of spacetime and gravity, then white holes will also be permitted by these laws.
Roger Penrose famously suggested that although naked singularties are comaptible with general relativity, in physically realistic situations naked singularities will never form; that is, any process that results in a singularity will safely deposit that singularity behind an event horizon. This suggestion, titled the “Cosmic Censorship Hypothesis,” has met with a fair degree of success and popularity; however, it also faces several difficulties.

Penrose's original formulation relied on black holes: a suitably generic singularity will always be contained in a black hole (and so causally invisible outside the black hole). As the counter-examples to various ways of articulating the hypothesis in terms of this idea have accumulated over the years, it has gradually been abandoned.

More recent approaches either begin with an attempt to provide necessary and sufficient conditions for cosmic censorship itself, yielding an indirect characterization of a naked singularity as any phenomenon violating those conditions, or else they begin with an attempt to provide a characterization of a naked singularity and so conclude with a definite statement of cosmic censorship as the absence of such phenomena. The variety of proposals made using both approaches is too great to canvass here; the interested reader is referred to Joshi (2003) for a review of the current state of the art, and to Earman (1995, ch. 3) for a philosophical discussion of many of the proposals.


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