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.
Highlights
Forty years ago, one of the authors argued [1] that information is destroyed when a black hole is formed and subsequently evaporates [2, 3]
In this paper we show that soft hair has a natural description as quantum pixels in a holographic plate
We show that this assertion fails in a predictable manner due to soft hair
Summary
One of the authors argued [1] that information is destroyed when a black hole is formed and subsequently evaporates [2, 3]. When the black hole has fully evaporated, the net supertranslation charge in the outgoing radiation must be conserved This will force correlations between the early and late time Hawking radiation, generalizing the correlations enforced by overall energy-momentum conservation. The combination of the uncertainty principle and cosmic censorship requires all physical particles to be larger than the Planck length, effectively setting a minimum spatial size for excitable pixels This gives an effective number of soft hairs proportional to the area of the horizon in Planck units and hints at a connection to the area-entropy law.
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