Replica wormholes and the entropy of Hawking radiation

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.

Gravity/ensemble duality

“…The bulk path integral derivation of the Page curve has been interpreted as a resolution of the firewall paradox [5,13,16,17]. This seems plausible, since the bulk geometry involved in the calculation of the Page curve (top of Fig.…”

“…It is obtained as the analytic continuation to n ¼ 1 of the n-th Renyi entropies of the radiation, which can be computed from a path integral using the replica trick. After the Page time, one finds that the dominant saddle point has wormholes connecting the replicas [15,16]; see Ref. [17] for a pedagogical review.…”

“…After the Page time, one finds that the dominant saddle point has wormholes connecting the replicas [15,16]; see Ref. [17] for a pedagogical review.…”

“…II. Another compelling argument for gravity/ensemble duality comes from the fact that the partition function on multiple copies of a boundary need not factorize when it is computed from a bulk gravity dual, because connected geometries can contribute [15,16]. It would be interesting to understand the detailed relation between these arguments.…”

$$ T\overline{T} $$ and EE, with implications for (A)dS subregion encodings

“…Finally, we note some potential connections to other recent developments in quantum gravity. Recently, important progress has been made in another direction by deriving the Page curve for black hole evaporation using entanglement wedge reconstruction (for instance, see [75][76][77][78][79][80][81]). It would be very interesting to understand if these results generalize to the deformed theories which characterize finite bulk patches of spacetime.…”