Comments on Lorentz Transformations, Dressed Asymptotic States and Hawking Radiation

TL;DR

This paper explores how infrared dynamics factorization affects Lorentz transformations and particle creation near black holes, revealing that soft graviton clouds induce phase shifts but do not alter particle fluxes.

Contribution

It introduces a redefinition of Lorentz transformations to commute with supertranslations and analyzes the impact of soft graviton clouds on Hawking radiation.

Findings

Soft photon clouds do not affect particle creation.

Soft graviton clouds induce a phase shift in Bogolyubov coefficients.

Particle flux remains unaffected by soft graviton clouds.

Abstract

We consider two applications of the factorization of infrared dynamics in QED and gravity. The first is a redefinition of the Lorentz transformations that makes them commute with supertranslations. The other is the process of particle creation near a black hole horizon. For the latter we show that the emission of soft particles factors out of the S-matrix in the fixed-background approximation and to leading order in the soft limit. The factorization is implemented by dressing the incoming and outgoing asymptotic states with clouds of soft photons and soft gravitons. We find that while the soft photon cloud has no effect, the soft graviton cloud induces a phase shift in the Bogolyubov coefficients relating the incoming and outgoing modes. However, the flux of outgoing particles, given by the absolute value of the Bogolyubov coefficient, is insensitive to this phase.