Non-equilibrium thermodynamics near the horizon and holography

TL;DR

This work addresses how non-equilibrium thermodynamics near black-brane horizons can be understood holographically by the membrane paradigm. By constructing a deformed Brown-York quasi-local stress tensor on the stretched horizon and enforcing flat-space conservation, it directly extracts dissipative hydrodynamic coefficients for the dual Yang-Mills theory. Through explicit quasi-normal mode analysis and horizon-centered fluctuations, it obtains the shear viscosity coefficient via $\gamma_\eta=1/(4\pi T)$, the sound velocity $v_s^2=(5-p)/(9-p)$, and the bulk viscosity relation $\gamma_\zeta=2(3-p)^2/(p(9-p))\gamma_\eta$, thereby linking horizon data to IR hydrodynamics. The results corroborate the membrane paradigm as a consistent, horizon-based route to holographic hydrodynamics and complement the traditional AdS/CFT boundary approach.

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.