Non-equilibrium thermodynamics near the horizon and holography

Small perturbations of a black brane are interpreted as small deviations from thermodynamic equilibrium in a dual theory with the AdS/CFT correspondence. 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 give analytic solutions for each fluctuation that compose such quantities. Then, in a place slightly away from the horizon Brown and York boundary stress tensor is calculated. Using them, we make conserved stress tensor near the horizon which can represent dissipative parts of stress tensor in the dual theory by holography. Thus, we propose gravitational counterparts of sound modes in the membrane paradigm. 1 E-mail address : [email protected]