Shaving off Black Hole Soft Hair

TL;DR

The paper analyzes whether soft hair arising from asymptotic symmetries can resolve the black hole information paradox. It employs Weinberg's soft theorems to factorize the S-matrix into a hard component and soft dressings, and recasts states in a basis of dressed hard+soft states. The main result is that soft dynamics decouples from the hard sector, yielding no cross-talk between early and late radiation and implying that soft hair cannot encode evaporation information. This clarifies limitations of soft-hair-based resolutions and guides future efforts toward mechanisms beyond soft symmetry charges. The work provides a precise S-matrix framework in which memory effects do not supply additional information about black hole evolution.

Abstract

A recent, intriguing paper by Hawking, Perry and Strominger suggests that soft photons and gravitons can be regarded as black hole hair and may be relevant to the black hole information paradox. In this note we make use of factorization theorems for infrared divergences of the S-matrix to argue that by appropriately dressing in and out hard states, the soft-quanta-dependent part of the S-matrix becomes essentially trivial. The information paradox can be fully formulated in terms of dressed hard states, which do not depend on soft quanta.

Figures (1)

• Figure 1: In the presence of a classical black hole, the Cauchy surface is $I^+\cup H$, but the charge ${\mathscr Q}$ is an asymptotic quantity, as it can be written as a boundary integral at $I^+_-$. However, ${\mathscr Q}=0$ for classical stationary black holes unless $\varepsilon = {\rm constant}$, in which case it is a multiple of the black hole electric charge.