Islands and Page curves for evaporating black holes in JT gravity
- PDF / 684,781 Bytes
- 39 Pages / 595.276 x 841.89 pts (A4) Page_size
- 64 Downloads / 194 Views
Springer
Received: June 9, 2020 Accepted: July 18, 2020 Published: August 20, 2020
Timothy J. Hollowood and S. Prem Kumar Department of Physics, Swansea University, Swansea, SA2 8PP, U.K.
E-mail: [email protected], [email protected] Abstract: The effect of a CFT shockwave on the entanglement structure of an eternal black hole in Jackiw-Teitelboim gravity, that is in thermal equilibrium with a thermal bath, is considered. The shockwave carries energy and entropy into the black hole and heats the black hole up leading to evaporation and the eventual recovery of equilibrium. We find an analytical description of the entire relaxational process within the semiclassical high temperature regime. If the shockwave is inserted around the Page time then several scenarios are possible depending on the parameters. The Page time can be delayed or hastened and there can be more than one transition. The final entropy saddle has a quantum extremal surface that generically starts inside the horizon but at some later time moves outside. In general, increased shockwave energy and slow evaporation rate favour the extremal surface to be inside the horizon. The shockwave also disrupts the scrambling properties of the black hole. The same analysis is then applied to a shockwave inserted into the extremal black hole with similar conclusions. Keywords: Black Holes, 2D Gravity, AdS-CFT Correspondence, Conformal Field Theory ArXiv ePrint: 2004.14944
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)094
JHEP08(2020)094
Islands and Page curves for evaporating black holes in JT gravity
Contents 1
2 Review: islands and the eternal black hole 2.1 The geometry 2.2 The dilaton 2.3 The quantum state 2.4 Entanglement dynamics 2.5 Resolving the entropy paradox via replica wormholes 2.6 The island
2 3 3 4 5 6 8
3 Shockwaves 3.1 Shockwave production 3.2 Shockwaves in the AdS region 3.3 The equilibrium state 3.4 Effect of shockwave 3.5 The exact solution 3.6 High temperature limit 3.7 Stress tensor 3.8 Vacuum coordinates 3.9 Dilaton 3.10 Entropy of the evaporating black hole
9 9 11 11 12 13 14 16 16 17 18
4 Entropy saddles 4.1 No Islands 4.2 Island with QES in front of shockwave 4.3 Island with QES behind the shockwave 4.4 Left/right independence
19 19 20 22 24
5 Page curves 5.1 Entanglement dynamics 5.2 Scrambling time 5.3 QES: inside or outside the horizon?
25 25 26 28
6 Shockwaves and the extremal black hole 6.1 The extremal black hole 6.2 The solution with a shockwave 6.3 QES in front of shockwave 6.4 QES behind shockwave
28 28 29 30 31
7 Conclusions
33
–i–
JHEP08(2020)094
1 Introduction
A Coordinate systems
33
B Exact solution for f (t)
34
C High temperature limit
35
1
Introduction
1
The notation here refers to a Hawking mode B emitted by an old black hole. It must be entangled with its partner mode A behind the horizon but also with a mode in the early part of the Hawking radiation so that the final state of the radiation, after the black has evaporated, is pur
Data Loading...
