Membrane Paradigm from Near Horizon Soft Hair

TL;DR

This paper demonstrates that the soft hair paradigm, involving zero-energy charges near black hole horizons, naturally leads to the membrane paradigm, providing a new formulation that accounts for black hole entropy through near horizon degrees of freedom.

Contribution

It shows how near horizon soft hair charges imply the membrane paradigm, linking horizon symmetries to black hole microstates and entropy.

Findings

Soft hair charges form a Heisenberg algebra near the horizon

The algebra accounts for black hole entropy

Provides a new formulation of the membrane paradigm

Abstract

The membrane paradigm posits that black hole microstates are dynamical degrees of freedom associated with a physical membrane vanishingly close to the black hole's event horizon. The soft hair paradigm postulates that black holes can be equipped with zero-energy charges associated with residual diffeomorphisms that label near horizon degrees of freedom. In this essay we argue that the latter paradigm implies the former. More specifically, we exploit suitable near horizon boundary conditions that lead to an algebra of `soft hair charges' containing infinite copies of the Heisenberg algebra, associated with area-preserving shear deformations of black hole horizons. We employ the near horizon soft hair and its Heisenberg algebra to provide a formulation of the membrane paradigm and show how it accounts for black hole entropy.