Just found this wonderful little snipplet from an article/lecture by S. W. Hawking. Citation: Hawking, S.W. "The Event Horizon", from Black Holes: Les Astres Occlus Ed. C DeWitt, B.S. DeWitt; 1972, Gordon and Breach, New York.

On the topic of stability of black holes, Hawking posed three questions: 1) Whether the occurence of singularities is a stable feature of general relativity 2) Whether the form of the singularity is stable and 3) Whether the fact that the singularity cannot be seen from infinity is stable. (All three are features of Schwarzchild and Kerr black holes, so the question to ask is that whether they are generic for all black holes.)

After answering yes to the first (by using general well posedness of initial data) and no to the second (Schwarzchild with a small perterbation in the form of electric charge becomes Reissner-Nordström), he proceeds to be undecided about the third.

Yet he is convinced that the third proposition should be true, based on two bits of evidence. Firstly, linearized gravity calculations show such stability. (Of course, the calculation is so far from the full non-linear problem that such calculations are only meaningful in really restricted settings.) And secondly, he says thus:

The second ground for believing that the singularities are hidden is that Penrose and Gibbons have tried and failed to devise situations in which they are not. The idea was to try and obtain a contradiction with the result that the area of the event horizon increases which is a consequence of the assumption that the singularities are hidden. However they failed.

Being a good scientist, he goes on to clarify:

Of course their failure does not prove anything but it does strengthen my personal conviction that the singularities in gravitational collapse will not be visible from infinity.

(Just to give a reason why we care about such questions as stability of black holes, Hawking says:

If there are non-trivial singularities which are naked, i.e. which can be seen from infinity, we may as well all give up. Once cannot predict the future in the presence of a space-time singularity since the Einstein equations and all the known laws of physics break down there. This does not matter so much if the singularities are all safely hidden inside black holes but if they are not we should be in for a shock every time a star in the galaxy collapsed. People working in General Relativity have a strong vested interest in believing that singularities are hidden.

So... this is what I am working on at the moment and why I am getting funding from the NSF.)

Just a thought: Hawking likes to write really really really long sentences. I didn't notice so much when I was reading the article, but in transcription it really sticks out to me.