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!)

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    $\begingroup$ String theorists can't even calculate at what time five o'clock tea is being served in the common room. Seriously, I think the correct question is not one of degeneracy and the equation of state, because both are assuming that spacetime has the same dimensionality before and after the collapse. General relativity suggests that this is not the case (the "density" of black holes decreases as masses increase). The thermodynamics of black holes suggests that we are not dealing with hot objects that are being held up by internal pressure, at least not in the description of the outside observer. $\endgroup$
    – CuriousOne
    Dec 28, 2014 at 18:15
  • $\begingroup$ Thank you very much for that clarification, which seems to connect well with the answer below. $\endgroup$
    – JForster
    Dec 29, 2014 at 1:19

1 Answer 1


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

  1. There's no singularity because the black hole effectively doesn't have an interior.
  2. 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.

  • $\begingroup$ Thank you very much for this clarification --I won't lie, the math looks horrible (I have a life sciences not a physics background.) So a fuzzball black hole is in every way (Hawking radiation, calculation of spacetime curvature from total mass/energy) is indistinguishable from a classical GR black hole? Will read further. Trying to imagine some way of experimentally verifying the fuzzball model. $\endgroup$
    – JForster
    Dec 29, 2014 at 1:25
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    $\begingroup$ I believe the idea is that a fuzzball looks indistinguishable from a classical black hole from sufficiently far away. The black hole will gradually evaporate due to Hawking radiation. At small scales on the horizon, this evaporation corresponds to the geometry simplifying as information flows away from the black hole again. $\endgroup$ Dec 29, 2014 at 13:10
  • $\begingroup$ Thank you again. Are singularities generally forbidden under string theory then, or is there some generalization of the Hawking-Penrose result applicable to string theory? $\endgroup$
    – JForster
    Dec 29, 2014 at 17:02

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