In their papers, Laura Mersini-Houghton and her collaborator Harald Pfeiffer have taken into account the backreaction from the emitted Hawking radiation on the collapsing mass which is normally neglected. They claim to have shown that the mass loss is so large that black holes never form to begin with.
To make sense of this, note that black hole radiation is produced by the dynamics of the background and not by the presence of a horizon. The horizon is why the final state misses information, but the particle creation itself does not necessitate a horizon. The radiation starts before horizon formation, which means that the mass that is left to form the black hole is actually less than the mass that initially collapsed.
Physicists have studied this problem back and forth since decades, and the majority view is that this mass loss from the radiation does not prevent horizon formation. This shouldn’t be much of a surprise because the temperature of the radiation is tiny and it’s even tinier before horizon formation. You can look eg at this paper 0906.1768 and references [3-16] therein to get an impression of this discussion. Note though that this paper also mentions that it has been claimed before every now and then that the backreaction prevents horizon formation, so it’s not like everyone agrees. Then again, this could be said about pretty much every topic.
Now what one does to estimate the backreaction is to first come up with a time-dependent emission rate. This is already problematic because the normal Hawking radiation is only the late-time radiation and time-independent. What is clear however is that the temperature before horizon formation is considerably smaller than the Hawking-temperature and it drops very quickly the farther away the mass is from horizon formation. Incidentally, this drop was topic of my master’s thesis. Since it’s not thermal equilibrium one actually shouldn’t speak of a temperature. In fact the energy spectrum isn’t quite thermal, but since we’re only concerned with the overall energy the spectral distribution doesn’t matter here.
Next problem is that you will have to model some collapsing matter and take into account the backreaction during collapse. Quite often people use a collapsing shell for this (as I did in my master’s thesis). Shells however are pathological because if they are infinitely thin they must have an infinite energy-density and are by themselves already quantum gravitational objects. If the shell isn’t infinitely thin, then the width isn’t constant during collapse. So either way, it’s a mess and you best do it numerically.
What you do next is take that approximate temperature which now depends on some proper time in which the collapse proceeds. This temperature gives via Stefan-Bolzmann’s law a rate for the mass loss with time. You integrate the mass-loss over time and subtract the integral from the initial mass. Or at least that’s what I would have done. It is not what Mersini-Houghton and Pfeiffer have done though. What they seem to have done is the following.
Hawking radiation has a negative energy-component. Normally negative energies are actually anti-particles with positive energies, but not so in the black hole evaporation. The negative energy particles though only exist inside the horizon. Now in Laura’s paper, the negative energy particles exist inside the collapsing matter, but outside the horizon. Next, she doesn’t integrate the mass loss over time and subtracts this from the initial mass, but integrates the negative energies over the inside of the mass and subtracts this integral from the initial mass. At least that is my reading of Equation IV.10 in 1406.1525, and equation 11e in 1409.1837 respectively. Note that there is no time-integration in these expressions which puzzles me.
The main problem I have with this calculation is that the temperature that enters the mass-loss rate for all I can see is that of a black hole and not that of some matter which might be far from horizon crossing. In fact it looks to me like the total mass that is lost increases with increasing radius, which I think it shouldn’t. The more dispersed the mass, the smaller the gravitational tidal force, and the smaller the effect of particle production in curved backgrounds should be. This is for what the analytical estimate is concerned. In the numerical study I am not sure what is being done because I can’t find the relevant equation, which is the dependence of the luminosity on the mass and radius.
In summary, the recent papers by Mersini-Houghton and Pfeiffer contribute to a discussion that is decades old, and it is good to see the topic being taken up by the numerical power of today. I am skeptic that their treatment of the negative energy flux is consistent with the expected emission rate during collapse. Their results are surprising and in contradiction with many previously found results. It is thus too early to claim that is has been shown black holes don’t exist.