An order-unity correction to Hawking radiation

Abstract

When a black hole first forms, the properties of the emitted radiation as measured by observers near future null infinity are very close to the 1974 prediction of Hawking. However, deviations grow with time, and become of order unity after a time $t\sim M_i^{7/3}$, where $M_i$ is the initial mass in Planck units. After an evaporation time the corrections are large: the angular distribution of the emitted radiation is no longer dominated by low multipoles, with an exponential fall off at high multipoles. Instead, the radiation is redistributed as a power law spectrum over a broad range of angular scales, all the way down to the scale $\Delta \theta \sim 1/M_i$, beyond which there is exponential falloff. This effect is is a quantum gravitational effect, whose origin is the spreading of the wavefunction of the black hole's center of mass location caused by the kicks of the individual outgoing quanta, discovered by Page in 1980. The modified angular distribution of the Hawking radiation has an important consequence: the number of soft hair modes that can effectively interact with outgoing Hawking quanta increases from the handful of modes at low multipoles $l$, to a large number of modes, of order $\sim M_i^2$. We argue that this change unlocks the Hawking-Perry-Strominger mechanism for purifying the Hawking radiation.

arXiv comment5 pages, no figures; v2 minor corrections; v3 minor clarifications and figure added

References in corpus (19)

• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• The Page curve of Hawking radiation from semiclassical geometry
• Soft Hair on Black Holes
• The entropy of Hawking radiation
• Jerusalem Lectures on Black Holes and Quantum Information
• Local subsystems in gauge theory and gravity
• Asymptotic symmetries and subleading soft graviton theorem
• Superrotation Charge and Supertranslation Hair on Black Holes
• Conserved charges of the extended Bondi-Metzner-Sachs algebra
• New symmetries for the Gravitational S-matrix
• Superboost transitions, refraction memory and super-Lorentz charge algebra
• The Black Hole information problem: past, present, and future
• Local phase space and edge modes for diffeomorphism-invariant theories
• Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
• Continuity bounds for entanglement
• HPS meets AMPS: How Soft Hair Dissolves the Firewall
• Decoherence of black hole superpositions
• Soft black hole information paradox: Page curve from Maxwell soft hair of a black hole

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• The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity
• Tunneling of Hawking radiation for BTZ black hole revisited
• Evaporating black holes and late-stage loss of soft hair
• The classical dynamics of gauge theories in the deep infrared