The entropy of Hawking radiation

2020/06/11 by Ahmed Almheiri, Thomas Hartman, Juan Maldacena +2 · 27 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #gr-qc #hep-th

paper · pdf · doi:10.1103/revmodphys.93.035002

published as Rev. Mod. Phys. 93, 35002 (2021) · 40 pages, many figures

arxiv created 2020/06/11 · openalex publication_date 2021/07/21 · arxiv updated 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• The four laws of black hole mechanics
• Particle creation by black holes
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Holes and Entropy
• Cool horizons for entangled black holes
• The Large-N Limit of Superconformal Field Theories and Supergravity
• Entanglement Wedge Reconstruction via Universal Recovery Channels
• JT gravity as a matrix integral
• Entanglement wedge reconstruction and the information paradox
• The Formation of Black Holes in General Relativity
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Replica Wormholes and the Entropy of Hawking Radiation
• ER = EPR revisited: On the Entropy of an Einstein-Rosen Bridge
• Page Curve and the Information Paradox in Flat Space
• Microscopic Models of Linear Dilaton Gravity and Their Semi-classical Approximations
• Entanglement Wedge Reconstruction and the Information Paradox

Cited by

• Quenched free energy from spacetime D-branes
• Quantum aspects of spacetime: A quantum optics view of acceleration radiation and black holes
• The black hole information puzzle and the quantum de Finetti theorem
• Black holes to white holes I. A complete quasi-classical model
• Real-time gravitational replicas: Low dimensional examples
• A reverse black hole information problem
• Models of Hidden Purity
• Small corrections to semiclassical gravity and their role in information paradoxes
• Future Boundaries and the Black Hole Information Paradox
• Three Impossible Theories
• Evaporating Black Holes Coupled to a Thermal Bath
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Surface gravity and the information loss problem
• Quantum entanglement in cosmology
• Could Planck Star Remnants be Dark Matter?
• No Future in Black Holes
• Quantum Information Theory of the Gravitational Anomaly
• Hawking radiation with pure states
• An algebra of observables for de Sitter space
• Concerns about the replica wormhole derivation of the island conjecture
• Globally hyperbolic evaporating black hole and the information loss issue
• Interpreting the Bulk Page Curve: A Vestige of Locality on Holographic Screens
• Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Inverted c-functions in thermal states
• A new look at the entanglement entropy of a single interval in a 2d CFT
• Euclidean wormhole in the Sachdev-Ye-Kitaev model

Related

• Entropy/information flux in Hawking radiation
• Entropy budget for Hawking evaporation
• Gravitational correlation, black hole entropy and information conservation
• Information storage and near horizon quantum correlations
• Black hole entropy and the semiclassical approximation