An Action for Black Hole Membranes

TL;DR

This paper develops an action-based framework for the black hole membrane paradigm, clarifying its foundations, deriving known results, extending to dyonic black holes, and connecting to thermodynamics and dissipation.

Contribution

It introduces an action formulation of the membrane paradigm, simplifying derivations and extending results to dyonic black holes, while linking to thermodynamics and dissipation principles.

Findings

Derived membrane results from the action framework

Extended membrane paradigm to dyonic black holes

Connected membrane dynamics to thermodynamic properties

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.