Soft Hair on Black Holes

TL;DR

This paper explores how soft hair, associated with supertranslation symmetries, encodes black hole information on the horizon, linking quantum states, conservation laws, and the horizon area.

Contribution

It provides an explicit description of soft hair in terms of soft gravitons and photons, and relates it to black hole information and evaporation processes.

Findings

Soft hair encodes quantum information on the horizon.

Infinite conservation laws relate black hole evaporation outcomes.

Soft degrees of freedom scale with horizon area in Planck units.

Abstract

It has recently been shown that BMS 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 paper 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.