Membrane paradigm from near-horizon soft hair

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 paper 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.