Hydrodynamics of spacetime and vacuum viscosity

Abstract

It has recently been shown that the Einstein equation can be derived by demanding a non-equilibrium entropy balance law dS = dQ/T + dS_i hold for all local acceleration horizons through each point in spacetime. The entropy change dS is proportional to the change in horizon area while dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. The internal entropy production term dS_i is proportional to the squared shear of the horizon and the ratio of the proportionality constant to the area entropy density is \hbar/4π. Here we will show that this derivation can be reformulated in the language of hydrodynamics. We postulate that the vacuum thermal state in the Rindler wedge of spacetime obeys the holographic principle. Hydrodynamic perturbations of this state exist and are manifested in the dynamics of a stretched horizon fluid at the horizon boundary. Using the equations of hydrodynamics we derive the entropy balance law and show the Einstein equation is a consequence of vacuum hydrodynamics. This result implies that \hbar/4πis the shear viscosity to entropy density ratio of the local vacuum thermal state. The value \hbar/4πhas attracted much attention as the shear viscosity to entropy density ratio for all gauge theories with an Einstein gravity dual. It has also been conjectured as the universal lower bound on the ratio. We argue that our picture of the vacuum thermal state is consistent with the physics of the gauge/gravity dualities and then consider possible applications to open questions.