Dressed Hard States and Black Hole Soft Hair

A recent, intriguing Letter 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 Letter 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.