Membrane paradigm realized?

Abstract

Are there any degrees of freedom on the black hole horizon? Using the `membrane paradigm' we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need `real' degrees of freedom at the horizon, which can modify Hawking's evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.

Figures (3)

• Figure 1: Schematic depiction of phase space in the black hole: there is a large phase space near the horizon from the microstate solutions of Einstein's equations.
• Figure 2: Schematic description of a microstate solution of Einstein's equations. There are 'local ergoregions' with rapidly changing direction of frame dragging near the horizon. The geometry closes off without having an interior horizon or singularity due to its peculiar topological structure.
• Figure 3: A circular elastic band in flat space will shrink to a point under its tension, but rapid oscillations maintain a nonzero average radius for the loop.