Relativistic CFT Hydrodynamics from the Membrane Paradigm

TL;DR

This paper demonstrates that the dynamics of horizons in certain spacetimes can be described by relativistic conformal field theory (CFT) hydrodynamics, connecting gravitational horizon behavior with fluid dynamics and thermodynamics.

Contribution

It establishes a novel link between horizon dynamics in AdS and Minkowski spacetimes and relativistic CFT hydrodynamics, including the non-relativistic limit leading to Navier-Stokes equations.

Findings

Horizon dynamics follow relativistic CFT hydrodynamics equations.

The second law of thermodynamics maps to the area increase theorem.

Non-relativistic limit yields incompressible Navier-Stokes equations.

Abstract

We use the membrane paradigm to analyze the horizon dynamics of a uniformly boosted black brane in a (d+2)-dimensional asymptotically Anti-de-Sitter space-time and a Rindler acceleration horizon in (d+2)-dimensional Minkowski space-time. We show that in these cases the horizon dynamics is governed by the relativistic CFT hydrodynamics equations. The fluid velocity and temperature correspond to the normal to the horizon and to the surface gravity, respectively. The second law of thermodynamics for the fluid is mapped into the area increase theorem of General Relativity. The analysis is applicable, in general, to perturbations around a stationary horizon, when the scale of variations of the macroscopic fields is much larger than the inverse of the temperature. We show that the non-relativistic limit of our analysis yields the incompressible Navier-Stokes equations.