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.
S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
R. Jackiw, Lower dimensional gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. 126B (1983) 41 [INSPIRE].
E. Sharon and D. Mumford, 2D-shape analysis using conformal mapping, Int. J. Computer Vision 70 (2006) 55.
P. Hayden and G. Penington, Approximate quantum error correction revisited: introducing the alpha-bit, arXiv:1706.09434.
S.W. Hawking, Quantum coherence down the wormhole, Phys. Lett. B 195 (1987) 337 [INSPIRE].
G.V. Lavrelashvili, V.A. Rubakov and P.G. Tinyakov, Disruption of quantum coherence upon a change in spatial topology in quantum gravity, JETP Lett. 46 (1987) 167 [INSPIRE].
S.B. Giddings and A. Strominger, Axion induced topology change in quantum gravity and string theory, Nucl. Phys. B 306 (1988) 890 [INSPIRE].
S.R. Coleman, Black holes as red herrings: topological fluctuations and the loss of quantum coherence, Nucl. Phys. B 307 (1988) 867 [INSPIRE].
S.B. Giddings and A. Strominger, Loss of incoherence and determination of coupling constants in quantum gravity, Nucl. Phys. B 307 (1988) 854 [INSPIRE].
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
ArXiv ePrint: 1911.12333
About this article
Cite this article
Almheiri, A., Hartman, T., Maldacena, J. et al. Replica wormholes and the entropy of Hawking radiation. J. High Energ. Phys. 2020, 13 (2020). https://doi.org/10.1007/JHEP05(2020)013
- 2D Gravity
- Black Holes
- Models of Quantum Gravity