Black-Hole Microstate Hair Requires a Horizon Measurement

Abstract

Can a smooth horizon hide its microstates? At fixed classical and superselected data, the exterior distinguishability $D_{\max }$ of same-sector infalling states and the departure $\epsilon$ from isometric infall obey $D_{\max }^2+(1-2\epsilon {)}^2\le 1$, and every point is realized. Below maximal disruption, the boundary is reached only by which-state measurements: the distinguished pair crosses undisturbed while the exterior records which one fell in. The least a horizon can do to have microstate hair is measure what falls in. Classically hairy black holes are labeled backgrounds, not microstate hair.

arXiv comment8+8 Pages. Currently under review at Phys. Rev. Lett