State counting in gravity and maximal entropy principle
Juan Hernandez, Mikhail Khramtsov
TLDR
This paper shows that black hole state counting and the Page curve are equivalent in semiclassical gravity, resolving the information loss paradox.
Key contributions
- Demonstrates the equivalence between black hole state counting and the Page curve in semiclassical gravity.
- Resolves Hawking's information loss puzzle by using a compatible basis of black hole microstates.
- Introduces a convex optimization problem to relate the von Neumann entropy of Hawking radiation.
Why it matters
This paper unifies two fundamental quantum aspects of gravity: black hole entropy and the Page curve. By showing their equivalence, it provides a solution to Hawking's information loss puzzle, advancing our understanding of quantum gravity.
Original Abstract
It is known that the semiclassical approximation to the gravity path integral can be leveraged to explain certain inherently quantum aspects of gravity. One such aspect is the state-counting interpretation of the Bekenstein-Hawking entropy of black holes. A second aspect is the Page curve for the entanglement entropy of Hawking radiation, which agrees with expectations from unitarity. We show that these two questions are equivalent from the gravity path integral point of view. In particular, the Hawking's information loss puzzle gets resolved automatically by considering any (over)complete basis of black hole microstates which is compatible with black hole entropy. The tool which relates the two questions is a convex optimization problem for the von Neumann entropy of Hawking radiation.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.