Non-equilibrium thermodynamics near the horizon and holography

TL;DR

This paper explores non-equilibrium thermodynamics near black hole horizons using a membrane paradigm approach, deriving hydrodynamic properties of dual gauge theories via holography without relying on boundary conditions.

Contribution

It introduces a novel method to evaluate classical solutions slightly away from the horizon, linking horizon boundary stress tensors to dual theory viscosities and confirming quasinormal modes align with the membrane paradigm.

Findings

Boundary stress tensor at the horizon satisfies conservation laws.

Shear and bulk viscosities of the dual theory are directly obtained.

Quasinormal modes are consistent with the membrane paradigm.

Abstract

Small perturbations of a black brane are interpreted as small deviations from thermodynamic equilibrium in a dual theory with the AdS/CFT correspondence. In this paper, we calculate hydrodynamics of the dual Yang-Mills theory in the gravity side using membrane paradigm. This method is different from the usual AdS/CFT correspondence and evaluate classical solutions not at boundaries but at the place slightly away from a horizon. There are sound modes or shear modes for gravity perturbation. For sound modes, such calculation at the horizon has not yet been done. Then, we find that boundary stress tensor at the horizon satisfies conservation law in flat space and can represent dissipative parts of stress tensor in the dual theory by holography. Using them, we can read off directly shear and bulk viscosity of the dual theory. Quasinormal modes are solutions to linearized equations obeyed by classical fluctuations of a gravitational background subject to specific boundary conditions and are also gauge-invariant quantities. We use solutions for each fluctuation that compose such quantities and show that quasinormal modes are consistent with the membrane paradigm.