If you read Einstein’s little book “The Meaning of Relativity” Appendix II, you will come across a most interesting remark (by Einstein). With regard to his General Theory of Relativity he poses the following two questions:
1) Should one admit the appearance of singularities?
2) Should one postulate boundary conditions?
Einstein gives the following answer regarding singularities. “As to the first question, it is my opinion that singularities must be excluded. It does not seem reasonable to me to introduce into a continuum theory (my bold/italics) points (or lines, etc.) for which the field equations do not hold. Moreover, the introduction of singularities is equivalent to postulating boundary conditions (which are arbitrary from the point of view of the field equations) on ‘surfaces’ which closely surround the singularities. Without such a postulate the theory is much too vague.”
Whoops – that’s a biggy, did you see it? Einstein says that his continuum theory (the General Theory of Relativity) shouldn’t allow the existence of Black-Holes. Bit odd that he was to work on Black-Hole theory not too many years later, but that is by the by 🙂 What is more to the point is that, yes, his General Theory of Relativity IS a continuum theory, it is not a Quantum theory. As such, although it gives extremely good agreement with observation, it is undoubtedly “incorrect” in the fine detail, maybe even where Black-Holes are concerned. Interesting!