Abstract
The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number n → 1, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these replica wormholes explicitly in two-dimensional Jackiw-Teitelboim gravity coupled to matter.
Highlights
A useful diagnostic for information loss is the fine-grained entropy of the Hawking radiation, SR = −Tr ρR log ρR, where ρR is the density matrix of the radiation
We show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral
Even though the radiation lives in a region where the gravitational effects are small, the fact that we are describing a state in a theory of gravity implies that we should use the gravitational formula for the entropy, including the island rule
Summary
We begin by reviewing the recent progress on the information paradox in AdS/CFT [4, 5]. The discrepancy in the Page curve is a large, O(1/GN ), effect This classic version of the information paradox can be embedded into AdS/CFT by coupling AdS to an auxiliary system that absorbs the radiation, allowing the black hole to evaporate [4, 5] (see [7, 36, 37]). ΡR is the density matrix of the region R in the full theory coupled to quantum gravity, and ρI∪R is the density matrix of the state prepared via the semi-classical path integral on the Euclidean black hole saddle This is equal to (1.1), since the quantum fields are pure on the full Cauchy slice I ∪ B ∪ R. In this paper we explain how the surprising island rule (1.2) follows from the standard rules for computing gravitational fine-grained entropy, without appealing to higher dimensional holography
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
