Membrane Paradigm from Near Horizon Soft Hair

TL;DR

The work connects the near-horizon soft hair program to the membrane paradigm by showing that soft hair charges form a Heisenberg algebra conjugate to area-preserving deformations. This structure yields a soft, area-based first law that reproduces the Bekenstein-Hawking entropy and identifies a membrane tension of 1/(4G), with the membrane action accounting for entropy. The Kerr black hole example illustrates microstate labeling by soft hair independent of the classical conserved charges, and the authors outline a path to quantize the membrane and introduce a spectral cutoff to count microstates. The approach offers a semi-classical route to black hole microstate counting and suggests connections to holographic entanglement entropy and firewall discussions.

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.