In the case of quantum singularities…such as black holes or the cosmic egg which sprang forth the Big Bang…are hard to describe due to the break down of Relativity and Quantum mechanics in their immediate vicinity.
Since the superstring theory known as M-theory seems to integrate GR and QM, has any previously unknown new insights been discovered in singularity phenomenae?
[nitpick]The plural of phenomenon is phenomena, not phenomenae.[/nitpick]
I don’t know the answer to your quest, except that, as far as I’m aware, M-theory suggests that it’s not really a singularity; that is to say, it’s not a point object, but rather exists in three dimensions.
The results from models of black holes are actually possibly the single clearest achievement of M-theory to date. There’s a lot of interest in this area.
Underlying this all is a sort of technical trick: you can create black holes by “stitching” branes together. What you get is a pretty crude approximation to anything like an everyday black hole, but it’s still a model of some sort of black hole. For instance, for a particular mass, the hole has to have a particular charge. The neat thing, however, is that you can take this simplified/restricted model and start calculating. You can thus get some good answers for a black hole. Nobody can yet use these methods to extend these results to black holes in general, but what’s been seen so far makes sense. Being able to get numbers out at all is a major step forward.
The biggie so far has been the stuff on entropy. There are the long-known “semi-classical” results about black hole thermodynamics, with Hawking radiation as the famous one. But these are all derived by talking about what happens outside the event horizon. Still, they imply that a black hole has an entropy. Which, in turn, suggests that it must have some set of internal states. But that’s very difficult to conceive of classically. There everything that falls in winds up in the singularity. Which has no structure, so how can you talk about it being in different states? Stuff crushed together into a point is just stuff crushed together into a point. That’s all there is to say about it.
String theory models of black holes turn out to have exactly the entropy that would be needed. Yet they don’t have that central singularity. That’s pretty damn tantalising.
Lee Smolin’s Three Roads to Quantum Gravity (2000) discusses some of this, particularly at the end of chapter 13. He (naturally) describes how this ties into similar progress in loop quantum gravity.