Starting in August 2023, I have been working with Prof. Herman Verlinde at Princeton University to explore new holographic techniques for solving the black hole information paradox. Our work resulted in the following publication:
AS and Herman Verlinde, Baby Universe in a Coupled SYK Model, 2605.05291.
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 brings us to the AdS/CFT correspondence. It hypothesizes that the interior of a special class of spacetimes which can be described in general relativity as Anti-de Sitter space (AdS) is dual to its surface, on which we 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. The CFT is unitary, so no information disappears. And in the semiclassical limit, where we recover bulk GR, no matter escapes from black holes.
My own research focuses on realizing an analogous holographic correspondence for different kinds of spacetimes that might be more relevant for learning about our own universe. Inferences from accelerating cosmic expansion lead us to believe that our own universe may bear more resemblance to de Sitter space (dS) than to AdS space. The primary obstacle to applying the same logic of AdS/CFT to such a system is the lack of a timelike spatial boundary. I am working on resolving this issue in lower dimensional situations where more tractable boundary theories have been successful in the past.
The figure above shows an artistic styling of the AdS/CFT correspondence. The dark interior is an AdS space, but the information contained in it (the 1s and 0s) actually lives on its CFT surface.