I've been reading Kip Thorne's Black Holes and Time Warps and got curious about extreme states of degenerate matter; a little research reveals that since the book was written quark and preon degenerate matter has been hypothesized (with corresponding types of stars.) I have also run across the notion of string degenerate matter and the corresponding star --a fuzzball --but am having less luck in finding out whether, as in the case of less exotic kinds of degenerate matter (neutron, i.e.) it's possible to calculate a degeneracy pressure for string degenerate matter, and whether it's possible in theory to overcome it and cause a sufficiently massive collapsing star to form a singularity (or whether in the context of string theory "singularity" in the GR sense even makes sense any more.) Any pointers on where to find more info on the subject welcome (as are comments on why the question makes sense or not!)
The point of the fuzzball conjecture is that spacetime is geometrically altered at the black hole horizon. Rather than having an interior, the extra dimensions pinch off at the horizon and encode the complicated data from incoming particles in complicated geometry. This resolves 2 issues
- There's no singularity because the black hole effectively doesn't have an interior.
- There's no information paradox because the horizon geometry encodes the data.
So if you accept the fuzzball proposal, then you must give up on the idea of singularities associated with black holes.
One interesting issue is how fuzzballs form. The traditional argument is that there are so many possible fuzzball configurations that a black hole will inevitably quantum tunnel into one of them. Unfortunately I don't know in detail the calculations which support this!
If you want to get the nitty gritty on the current state of fuzzball research, I suggest you take a look at some of Mathur's recent papers.