Laura Mersini-Houghton and Harald Pfeiffer published a paper with numerical results suggesting that black holes may not really exist (see also this earlier result). As one would expect, several pop. sci. webpages have already picked this story up.
The paper is of course not a general proof, but describes a particular model using certain assumptions; it considers the spherically symmetric collapse of pressure-less dust and it makes simplifying assumptions about the Hawking radiation: The energy tensor for the Hawking radiation is taken from earlier calculations for (static) black holes, proportional to 1/R^2, and I don't think this is justified if one wants to prove that black holes do not exist. Further it is assumed that most of the radiation is generated by the collapsing body itself (*) and finally assumptions are made about the heat transfer function C which I cannot follow (yet).
The resulting differential equations are numerically integrated until a shell-crossing singularity appears, in other words a naked singularity (presumably an artifact of the model assumptions, i.e. perfect spherical symmetry, so it is only slightly embarrassing in a paper which wants to remove black hole singularities).
The behavior of the dust suggests a rebound near the horizon, but it is too bad the full evolution is unknown, because it raises interesting questions.
What happens to the pressure-less dust in the long run? Will it collapse again after the rebound, perhaps infinitely often?
What does the final state (including Hawking radiation and the "influx" of negative energy) actually look like?
I am sure this paper will generate several responses and eventually more realistic calculations will follow.
Until then I remain skeptical that this result will actually hold in general.
(*) I admit that I do not understand this passage in the earlier paper: "Hawking radiation is produced by the changing gravitational field of the collapsing star, i.e. prior to the black hole formation [..]. Otherwise the surface gravity of the black hole κ, and the temperature of Hawking radiation would increase with time..."
I thought the standard picture is that the "influx" is at the event horizon (not the collapsing body) and the temperature does indeed increase with time...
added later: Supposedly William Unruh was more direct and he thinks that the paper is nonsense.