Replica Wormholes and the Entropy of Hawking Radiation

TL;DR

The paper addresses the black hole information paradox by showing that replica wormholes—non-perturbative gravitational saddles in the replicated path integral—alter the computation of fine-grained entropy and realize the island rule. By explicit analysis in two-dimensional JT gravity coupled to a CFT, it derives how the replicated action near n ≈ 1 reduces to the generalized entropy and how quantum extremal surfaces arise, yielding a Page-curve consistent entropy for single and two-interval setups. The work demonstrates that replica wormholes reproduce island contributions, connect to entanglement wedge ideas, and imply a bulk mechanism for interior reconstruction while preserving global purity. It provides a non-holographic bulk derivation of the island prescription, highlighting cosmic branes, conical defects, and conformal welding as essential tools in constructing these saddles and understanding their entropy implications. Overall, the results strengthen the case that non-perturbative gravitational effects are essential for unitarity in black hole evaporation and offer a concrete framework for analyzing information flow in gravity-dominated spacetimes.

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 $n \to 1$, 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.

Figures (16)

• Figure 1: We display an evaporating black hole. The vertical line separates a region on the left where gravity is dynamical from a region on the right where we can approximate it as not being dynamical. The black hole is evaporating into this second region. In red we see the regions associated to the computation of the entropy of radiation and in green the regions computing the entropy of the black hole. (a) Early times. (b) Late times, where we have an island.
• Figure 2: We prepare the combined thermofield double state of the black hole and radiation using a Euclidean path integral. These are two pictures for the combined geometry. In (b) we have represented the outside cylinder as the outside of the disk. By cutting along the red dotted line, we get our desired thermofield double initial state that we can then use for subsequent Lorentzian evolution (forwards or backwards in time) to get the diagram in figure \ref{['fig:eternalBH-lorentzian']}.
• Figure 3: Eternal black hole in AdS$_2$, glued to Minkowski space on both sides. Hawking radiation is collected in region $R$, which has two disjoint components. Region $I$ is the island. The shaded region is coupled to JT gravity.
• Figure 4: (a) Growing entropy for the radiation for an eternal black hole plus radiation in the thermofield double state. We draw two instants in time. The particles with the same color are entangled. They do not contribute to the entanglement of the radiation region (indicated in red) at $t=0$ but they do contribute at a later value of $t$. (b) When the island is included the entanglement ceases to grow, because now both entangled modes mentioned above are included in $I \cup R$.
• Figure 5: Page curve for the entropy of the radiation, for the model in fig. \ref{['fig:eternalBH-lorentzian']}. The dotted line is the growing result given by the Hawking computation, and the entropy calculated from the other saddle is dashed. The minimum of the two is the Page curve for this model.