Entanglement wedge reconstruction and the information paradox
- PDF / 2,971,107 Bytes
- 84 Pages / 595.276 x 841.89 pts (A4) Page_size
- 9 Downloads / 182 Views
Springer
Received: May 27, 2020 Accepted: July 13, 2020 Published: September 1, 2020
Entanglement wedge reconstruction and the information paradox
Stanford Institute for Theoretical Physics, Stanford University, 450 Jane Stanford Way, Stanford, CA 94305, U.S.A.
E-mail: [email protected] Abstract: When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum RyuTakayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/2π log SBH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox. Keywords: AdS-CFT Correspondence, Black Holes, Black Holes in String Theory ArXiv ePrint: 1905.08255
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)002
JHEP09(2020)002
Geoffrey Penington
Contents 1 Introduction
1 9 15 18 25 32
3 State dependence 3.1 State dependence in entanglement wedge reconstruction 3.2 State dependence in evaporating black holes 3.3 Approximation to the rescue 3.4 Large diaries 3.5 Minimal state dependence
41 41 45 49 50 55
4 Discussion 4.1 Summary of results 4.2 Entanglement wedge reconstruction in toy models 4.3 The post evaporation state and the bulk-to-boundary map 4.4 The peak of the Page curve 4.5 Explicit interior reconstruction 4.6 The information paradox beyond AdS/CFT
57 57 61 61 65 66 67
A Cut-offs in Rindler space
68
B Finite temperature infalling modes
69
C Minimal state dependence in the SYK model
74
1
Introduction
By di
Data Loading...
