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Replica wormholes and the entropy of Hawking radiation. (English) Zbl 1437.83084

Summary: 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 \( n \rightarrow 1 \), 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.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C45 Quantization of the gravitational field
83C80 Analogues of general relativity in lower dimensions
83C57 Black holes
81P17 Quantum entropies
81S40 Path integrals in quantum mechanics
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