The Quantum Black Hole as a Hydrogen Atom: Microstates Without Strings Attached

Abstract

Applying an expansion in spherical harmonics, turns the black hole with its microstates into something about as transparent as the hydrogen atom was in the early days of quantum mechanics. It enables us to present a concise description of the evolution laws of these microstates, linking them to perturbative quantum field theory, in the background of the Schwarzschild metric. Three pieces of insight are obtained: One, we learn how the gravitational back reaction, whose dominant component can be calculated exactly, turns particles entering the hole, into particles leaving it, by exchanging the momentum- and position operators; two, we find out how this effect removes firewalls, both on the future and the past event horizon, and three, we discover that the presence of region II in the Penrose diagram forces a topological twist in the background metric, culminating in antipodal identification. Although a cut-off is required that effectively replaces the transverse coordinates by a lattice, the effect of such a cut-off minimizes when the spherical wave expansion is applied. This expansion then reveals exactly how antipodal identification restores unitarity - for each partial wave separately. We expect that these ideas will provide new insights in some highly non-trivial topological space-time features at the Planck scale.