An Action for Black Hole Membranes

TL;DR

The paper provides an action-based derivation of the black hole membrane paradigm by adding appropriate boundary surface terms to the external action, yielding a dynamical, dissipative 2+1D membrane on the stretched horizon that reproduces electromagnetic and gravitational boundary dynamics. It extends the framework to axidilaton and dyonic sectors, and connects the membrane to thermodynamics through Euclidean path integrals, including a derivation of the Bekenstein–Hawking entropy via the interior action. A Hamiltonian formulation then yields a minimum-heat-production principle, linking dissipation to horizon boundary conditions and extracting membrane equations for both electromagnetic and gravitational sectors. The approach provides conceptual unification, a path toward quantization, and a systematic avenue to study back-reaction effects on black-hole thermodynamics.

Abstract

The membrane paradigm is the remarkable view that, to an external observer, a black hole appears to behave exactly like a dynamical fluid membrane, obeying such pre-relativistic equations as Ohm's law and the Navier-Stokes equation. It has traditionally been derived by manipulating the equations of motion. Here we provide an action formulation of this picture, clarifying what underlies the paradigm, and simplifying the derivations. Within this framework, we derive previous membrane results, and extend them to dyonic black hole solutions. We discuss how it is that an action can produce dissipative equations. Using a Euclidean path integral, we show that familiar semi-classical thermodynamic properties of black holes also emerge from the membrane action. Finally, in a Hamiltonian description, we establish the validity of a minimum entropy production principle for black holes.