What happens at the center of a black hole according to holographic theory?

As far as I understand, the AdS/CFT correspondence proposed by Maldacena is an exact duality to a four-dimensional theory, which interpolates between one well-defined conformal field theory in the UV and another conformal field theory in the IR. So holographic renormalization is in one-to-one correspondence with renormalization in the four-dimensional theory. Or, in simpler terms, according to this theory, dynamical phenomena occurring in a curved space-time like black holes can be described by a theory on a flat space-time, just as a hologram can record the information of 3D objects on a plane

The web is full of popular science articles about this correspondence, but the only "detailed" results that I found about Maldacena's theory is that it has been sucessfully tested by calculating the relationship between the mass and the temperature of a black hole on a computer.

My specific question is: has anybody calculated the predictions of holographic theory at a point that corresponds to the center of a black hole (singularity?) in the 4D theory, and if not, why? If yes were could I find more details? Thanks!

Answer

The AdS/CFT duality is a weak-strong duality which basically implies that when gravity is weak (and its only then you can talk about general relativity as an effective theory and therefore talk about black holes) the dual CFT is strongly coupled. As such it is very hard to calculate things in the CFT to get results for the AdS theory. So even though it is possible in principle to use the CFT to read off results for quantum gravity that is rarely done and most results of AdS CFT use gravity calculations to predict something about strongly coupled CFTs.

So the short answer is no, not much has been claimed about the interior of black holes using AdS/CFT (for some efforts in this direction see http://arxiv.org/abs/hep-th/0212277 for instance and references therein). There have been some claims that the CFT shows the interior of the black hole may need to be modified (http://arxiv.org/abs/1405.6394) or not exist at all (http://arxiv.org/abs/1307.4706).