We have (in my unbiased opinion :-) ) an interesting paper out today: https://arxiv.org/pdf/2012.04671 with Hao Geng, Andreas Karch, Carlos Perez-Pardavila, Lisa Randall, Marcos Riojas, and Sanjit Shashi. One of the significant problems we managed to solve was to “how to set up multiple Zoom meetings across four time zones on opposite sides of the world.”
More seriously, there has been a lot of recent activity on computing the entropy of “Hawking radiation” using entanglement islands. However, the precise computations actually deal with black holes that are rather different from black holes in our world. More specifically, they generally consider an entire holographic system that has an asymptotic AdS region of its own, which is then coupled to a nongravitational bath. As several of us have pointed out, it is not clear if the lessons learned from such setups hold when gravity is everywhere dynamical, as it is in our world.
So the idea of today’s paper was to turn on gravity in the bath itself. This can be done elegantly in the braneworld scenarios that have been used for higher-dimensional computations (and that were studied by Andreas and Lisa long ago) by just introducing a second brane into the geometry. And, lo and behold, when we do this, the Page curve disappears!
So we find that the nongravitational bath is not just a calculational device, but it modifies the physics in a significant way. This is also precisely what one would expect from our previous work on black holes in asymptotically flat space: we pointed out that when gravity is dynamical, information about the black-hole interior is always available outside, and so there should be no Page curve for the fine-grained entropy of radiation. On the other hand, there might be other questions one could ask that might yield a Page curve.
And indeed, even in the setup of today’s paper, there is still a codimension 2 boundary that is nongravitational. On this nongravitational boundary, we can divide the Hilbert space into two parts. If we ask about the entanglement between these two parts, we recover a Page curve. This Page curve has many interesting properties, and islands play a role provided the branes obey some interesting geometric constraints.
This Page curve is answering a nongravitational question, that can nevertheless be studied by analyzing minimal surfaces in a dual geometry. It is not a Page curve that describes how information “emerges” from a black hole.
I think this is also how previous Page-curve computations should be interpreted. One takes a nongravitational theory, maybe N=4 SYM, and divides it into two parts. Or maybe one takes a SYK model and couples it to a CFT. There is no gravity in sight. But when the theories have a bulk dual, it is still possible to compute the entanglement between these two subsystems using bulk extremal surfaces.
So the Page curves that have been computed should not be interpreted as telling us the rate at which information is transferred from the black hole into the radiation; rather they are telling us about how information is transferred from one nongravitational region to another.
