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.
Highlights
One main consequence of this development is that the usual Fock vacuum in a gauge or gravity theory is degenerate, and any non-trivial scattering process induces a transition between the degenerate vacua
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
This idea was recently adopted in [79] for QED in a Rindler wedge, to show that a Wilson line along the geodesic of a massive particle near the future Rindler horizon implements soft photon hair at the point where the geodesic meets the horizon. This was interpreted as soft photon hair of Schwarzschild black hole in the near-horizon limit. We use these ideas to demonstrate that asymptotic particles falling into the black hole leave behind a soft graviton hair on the horizon, by constructing gravitational dressings on the black hole horizon in the context of perturbative quantum gravity in a Schwarzschild background
Summary
We review the gravitational FK dressings in flat spacetime [43] and its Wilson line representation [77, 78]. We review how the dressings carry a definite supertranslation charge [28, 29]. These results will be central to our construction of dressings on the Schwarzschild horizon
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