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Soft Hair on Black Holes

Stephen W. Hawking, Malcolm J. Perry, and Andrew Strominger
Phys. Rev. Lett. 116, 231301 – Published 6 June 2016
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Abstract

It has recently been shown that Bondi–van der Burg–Metzner–Sachs supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian spacetimes. These laws require black holes to carry a large amount of soft (i.e., zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This Letter gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of the horizon. Charge conservation is used to give an infinite number of exact relations between the evaporation products of black holes which have different soft hair but are otherwise identical. It is further argued that soft hair which is spatially localized to much less than a Planck length cannot be excited in a physically realizable process, giving an effective number of soft degrees of freedom proportional to the horizon area in Planck units.

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  • Received 15 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.231301

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsGravitation, Cosmology & Astrophysics

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The Work of Stephen Hawking in Physical Review

To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters. They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."

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Black Holes Have Soft Quantum Hair

Published 6 June 2016

A black hole may carry “soft hair,” low-energy quantum excitations that release information when the black hole evaporates.

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Authors & Affiliations

Stephen W. Hawking1, Malcolm J. Perry1, and Andrew Strominger2

  • 1DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
  • 2Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 116, Iss. 23 — 10 June 2016

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