The entropy of Hawking radiation

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.

40 pages, many figures

References in corpus (13)

• Black holes as mirrors: quantum information in random subsystems
• Causality & holographic entanglement entropy
• Deriving covariant holographic entanglement
• JT gravity as a matrix integral
• Eigenstate Thermalization and Disorder Averaging in Gravity
• Nonperturbative black hole entropy and Kloosterman sums
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• The ghost in the radiation: Robust encodings of the black hole interior
• Page Curve and the Information Paradox in Flat Space
• ER = EPR revisited: On the Entropy of an Einstein-Rosen Bridge
• The Formation of Black Holes in General Relativity
• Recovering Infalling Information via String Spreading
• Microscopic Models of Linear Dilaton Gravity and Their Semi-classical Approximations

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