In newtonian gravity, an axially symmetric cylindrical uniform dust cloud obviously collapses into a line segment singularity. If the cylinder does not contain too much mass per unit length, then it probably does not become a black hole in general relativity. Could it be that in general relativity, too, there is a singularity there, and the singularity is naked since it is not hidden behind an event horizon?
Shapiro and Teukolsky (1991)
Stewart Shapiro and Saul Teukolsky (1991) used a computer program to calculate a dust collapse where the dust spheroid is elongated (prolate). The results suggested that a "spindle" singularity forms without an apparent horizon.
The example is contrived, though. Nature does not contain infinitely fine dust particles. If we assume classical point particles, then each particle is a tiny black hole. In principle, we can order these tiny black holes on a straight line, and their horizons do not touch. Thus, at a microscopic level, our cylinder would not be a cylinder at all, but a string of tiny beads.
Division of classical matter into elementary particles prevents naked singularities?
We can extend our argument in the previous section to all naked singularities which are supposed to contain infinitely dense matter. If each elementary particle is a tiny black hole, then infinitely dense matter presumably contains many such black holes which have merged together. The singularity, if any, is behind their event horizon. It is not naked.
Is a naked singularity a problem at all in classical physics?
People have done a lot of general relativity calculations with "domain walls", which are assumed to be infinitely thin massive walls. Classically, there is nothing pathological in such a hypothetical structure.
Some people assume that the center of a (classical) Schwarzschild black hole contains a point which contains all the matter in the black hole. Is there anything wrong with such a model in classical physics? As long as it is a point which is solely characterized by it mass M, there should be no problem.
In quantum mechanics, infinitely dense objects may be problematic, though.
Conclusions
If classical matter consists of elementary particles, then there seem to be no classical naked singularities.
If there exists infinitely fine dust, then, for example, the Shapiro and Teukolsky setup may create a naked singularity. However, there probably is nothing contradictory or problematic in such an object.
In quantum mechanics, an electron is often thought of as a point particle which is not a black hole, though. Quantum mechanics does not play well together with objects which are infinitely dense. The existence of singularities or naked singularities in quantum gravity is a subject which we will not touch here.
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