Starting in September 2023, I will be working at Princeton University to explore new techniques for solving the black hole information paradox, including the recent formalization of the AdS/CFT correspondence.
Image taken from scientific illustrator Alan Stonebraker
Since the beginning of the 20th century, general relativity and quantum mechanics have each proved incredibly useful in making predictions about large and small scale objects, respectively. General relativity holds dear a principle called Lorentz covariance, which states that the laws of physics are the same for anyone in an inertial reference frame. Quantum mechanics, on the other hand, espouses the principle of unitarity, stating that information cannot be created nor destroyed. In normal situations, both of these ideas (seem) to remain true without conflict. However, black holes introduce tension.
General relativity predicts that nothing entering a black hole will ever be able to exit it. But then, if I write down information on an object and toss it into the black hole, where did that information go? This violates unitarity. The information cannot come back out: that would violate Lorentz covariance. This is the black hole information paradox. One popular path toward resolving this paradox states that the Hawking radiation generated by the black hole must be (quantum) entangled with the information in the black hole interior. But since the Hawking radiation seems to be generated at the black hole surface, this would imply that all of the information in the interior of the black hole in fact can be found on its surface!
This is the essence of the AdS/CFT correspondence. It hypothesizes that the interior of a black hole, which can be described in general relativity as Anti-de Sitter space (AdS) is dual to its surface, on which can ascribe a quantum mechanical conformal field theory (CFT). The dualism is such that any quantity one would want to measure in the AdS interior can in fact be measured by only looking at the CFT surface, and vice versa. Thus, the information does not disappear, nor does matter escape the black hole. Current efforts on this front are directed towards trying to specify precisely what kinds of interior AdS spaces can be dual to what kinds of boundary CFTs, and how measurements in one might be made in the other.
The figure above shows an artistic styling of the AdS/CFT correspondence at a black hole. The dark interior is an AdS space, but the information contained in it (the 1s and 0s) actually lives on its CFT surface.