Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective

TL;DR

This paper shows that infalling particles create soft graviton hair on a Schwarzschild black hole horizon using a quantum field theory approach with gravitational Wilson lines, linking classical and quantum descriptions.

Contribution

It introduces a quantum field theoretical method to construct gravitational Wilson line dressings that encode supertranslation hair on black hole horizons, extending classical proposals.

Findings

Infalling particles induce soft graviton hair on the horizon.

Supertranslation charges can be labeled by particle properties and contact points.

Zero modes of gravitons are identified as canonical partners of horizon charges.

Abstract

We demonstrate within the quantum field theoretical framework that an asymptotic particle falling into the black hole implants soft graviton hair on the horizon, conforming with the classical proposal of Hawking, Perry and Strominger. A key ingredient to this result is the construction of gravitational Wilson line dressings of an infalling scalar field, carrying a definite horizon supertranslation charge. It is shown that a typical Schwarzschild state is degenerate, and can be labeled by different soft supertranslation hairs parametrized for radial trajectories by the mass and energy of the infalling particle and its asymptotic point of contact with the horizon. The supertranslation zero modes are also obtained in terms of zero-frequency graviton operators, and are shown to be the expected canonical partners of the linearized horizon charge that enlarge the horizon Hilbert space.