The entropy of Hawking radiation

TL;DR

The paper addresses the black hole information paradox by extending gravitational fine-grained entropy concepts to Hawking radiation. It introduces the island formula and quantum extremal surfaces, showing how the entropy of radiation can follow a Page curve consistent with unitarity, aided by replica wormholes that connect different spacetime topologies. The central results demonstrate that including interior regions (islands) in the entropy computation resolves the paradox at a coarse-grained level and that the entanglement wedge structure explains how interior information becomes accessible to radiation. This work provides a coherent framework connecting quantum information, gravity, and holography, with implications for the nature of spacetime and the recovery of information in black hole evaporation.

Abstract

In this review, we describe recent progress on the black hole information problem that involves a new understanding of how to calculate the entropy of Hawking radiation. We show how the method for computing gravitational fine-grained entropy, developed over the past 15 years, can be extended to capture the entropy of Hawking radiation. This technique reveals large corrections needed for the entropy to be consistent with unitary black hole evaporation.

Figures (25)

• Figure 1: Left: Penrose diagram of a black hole formed by gravitational collapse. Right: Zoomed-in view of the flat near-horizon region, with the trajectory of a uniformly accelerated observer at $\rho = a^{-1}$.
• Figure 2: The Euclidean Schwarzschild black hole. The Euclidean time and radial directions have the geometry of a cigar, which is smooth at the tip, $r=r_s$. At each point we also have a sphere of radius $r$.
• Figure 3:
• Figure 4: Penrose diagram for the formation and evaporation of a black hole. Spatial slices $(a)$-$(d)$ correspond to the slices drawn in fig. \ref{['fig:evap-stages']}.
• Figure 5: The skeptics' view: The diagram of an evaporating black hole is conceptually similar to one where we split off a baby universe, so that in the future we have two regions, the future region of the original universe, and the future of the interior, which is singular.