Ciao,
Ho trovato un paper che dovrebbe trattare l'argomento, magari lo avevi gia visto.
https://arxiv.org/pdf/1801.00272.pdfDevo essere sincero, al momento non me la sento di leggerlo a fondo

...
Riporto un breve estratto:
In a recent article in this journal,1 Aste and Trautmann discussed the radial fall of a test particle onto a black hole evaporating by Hawking radiation. They did so in terms of what they admit to be a toy model, an approximation the validity of which is, in their own words, “dubious at best” near the event horizon of the black hole. Nevertheless, they believe their model to be a good approximation far from the horizon and consider their major qualitative result to be correct, i.e., that the black hole will evaporate under an infalling particle or observer before the latter can cross the horizon. Such a result would call into
question that a black hole can form at all,2 because any piece of infalling matter should hover above the nascent horizon, accumulating time dilation, while the incipient
black hole is already busy evaporating. The purpose of this paper is to show that a slightly more realistic approach, still a toy model, but at least one using a time coordinate that does not become singular at the Schwarzschild radius, leads to a diametrically opposed prediction: an observer falling towards an evaporating black hole will normally cross the “horizon” without noticing anything dramatic happening and, unfortunately, hit the central singularity the same way as with an eternal black hole. Rather precise timing of the fall, approaching the black hole near the end of its lifetime, when its mass has gotten small, would be necessary to avoid hitting it before it evaporates.
...
In this paper, it was shown that there is no a priori reason to believe that Hawking radiation will make a
black hole evaporate from under an observer, before she
can fall in...
As it turns out, in this model the Schwarzschild radius
is as easily crossed by a particle for an evaporating black
hole as for an eternal one, and the crossing happens in
finite time.
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