From Scientific American: Do Naked Singularities Break the Rules of Physics?
In this article, Dr. Pankaj Joshi at the Tata Institute of Fundamental Research in Mumbai discusses the possibility of naked singularities. (I know that sounds a little naughty, but bear with me, because it actually is thrilling in its own way.) Naked singularities are basically black holes, without an event horizon. So, there would be a point of infinity density without the same effect on gravity; there would not be the same "point of no return" as there is with black holes. In addition, if naked singularities do exist, it would be possible for them to be observed directly. Theoretical models seem to show that with a certain inhomogeneity of density in a star, this type of singularity could be formed.