Testing the membrane paradigm with holography

TL;DR

This paper critically examines the membrane paradigm in holography, showing it fails to capture certain quasinormal modes and long-wavelength responses unless replaced by true horizon boundary conditions, revealing new insights into black hole physics.

Contribution

It demonstrates the limitations of the membrane paradigm in holography and proposes that true horizon boundary conditions are necessary for accurate quasinormal mode and response spectrum analysis.

Findings

Membrane paradigm fails to capture massive quasinormal modes.

Spurious long-wavelength excitations are removed with true horizon boundary conditions.

An additional Goldstone boson arises due to symmetry breaking at the stretched horizon.

Abstract

One version of the membrane paradigm states that as far as outside observers are concerned, black holes can be replaced by a dissipative membrane with simple physical properties located at the stretched horizon. We demonstrate that such a membrane paradigm is incomplete in several aspects. We argue that it generically fails to capture the massive quasinormal modes, unless we replace the stretched horizon by the exact event horizon, and illustrate this with a scalar field in a BTZ black hole background. We also consider as a concrete example linearized metric perturbations of a five-dimensional AdS-Schwarzschild black brane and show that a spurious excitation appears in the long-wavelength response that is only removed from the spectrum when the membrane paradigm is replaced by ingoing boundary conditions at the event horizon. We interpret this excitation in terms of an additional Goldstone boson that appears due to symmetry breaking by the classical solution ending on the stretched horizon rather than the event horizon.