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Soft Hair on Black Holes
Stephen W Hawking1, Malcolm J Perry1, Andrew Strominger2
1DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
Physical Review Letters
|June 25, 2016
Summary
Black holes possess infinite soft hair due to supertranslation symmetries, influencing their evaporation. This hair stores quantum information holographically, leading to conservation laws between black hole evaporation products.
Area of Science:
- Theoretical Physics
- Gravitational Theory
- Black Hole Physics
Background:
- Supertranslation symmetries in gravitational theories lead to infinite conservation laws.
- These laws necessitate black holes possessing soft (zero-energy) supertranslation hair.
- Maxwell fields imply the existence of soft electric hair.
Purpose of the Study:
- To provide an explicit description of soft hair.
- To demonstrate holographic information storage of soft hair quantum states.
- To explore implications for black hole evaporation and conservation laws.
Main Methods:
- Describing soft hair using soft gravitons and photons on the black hole horizon.
- Utilizing charge conservation to derive relations between black hole evaporation products.
- Analyzing the physical realizability of localized soft hair.
Main Results:
- Soft hair is explicitly described in terms of soft gravitons/photons at the black hole horizon.
- Complete quantum state information of soft hair is stored on a holographic plate at the future boundary of the horizon.
- Infinite exact relations are found between evaporation products of black holes with different soft hair.
Conclusions:
- Soft hair degrees of freedom are proportional to the horizon area in Planck units.
- Spatially localized soft hair below a Planck length is not physically realizable.
- The study offers new insights into black hole thermodynamics and information paradox.
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