A simple quantum test for smooth horizons, with Kyriakos and Pushkal.
https://arxiv.org/abs/1910.02992
We use the short distance behaviour of the two-point function to set out some very general necessary conditions for a quantum state of the fields to be smooth at any null surface. In the case of black holes with both an inner and an outer horizon, where we apply our test, these conditions require that the degrees of freedom near both horizons be occupied at just the right temperature and also be entangled with partners just behind the horizons.
There is an interesting story here. If you talked to me a couple of months ago, I would have explained to you (as I did explain to several people!) that this meant that quantum mechanical effects always imposed strong cosmic censorship regardless of all the recent classical discussions on the subject. Note how tricky it is for all the conditions above to be satisfied. The modes near the outer horizon have to be automatically “heated” by the geometry to attain the temperature of the inner horizon when they reach there. Moreover, in attempting to cross the inner horizon, we have the problem of the monogamy of entanglement: since the modes between the inner and outer horizon are entangled with partners outside the outer horizon they cannot be entangled with fresh modes behind the inner horizon. So, surely, one would be unable to extend the field into that region?
This intuition is right in higher dimensions. But for the BTZ black hole, this naive conclusion is just wrong! In that case (and, as far as we know, only in that case) the geometry does magically heat the field by just the right amount as they reach the inner horizon; and the existing degrees of freedom can then be cleverly juggled to extend the field behind the inner horizon.
Does this mean that strong cosmic censorship is violated for the BTZ black hole as Dias, Reall and Santos argued a few months back? What would this mean for AdS/CFT? We think that quantum effects could still have a few tricks up their sleeve at very late times, but I now think this is a very interesting question.