  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/4\pi. 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/4\pi is the shear
viscosity to entropy density ratio of the local vacuum thermal state. The value
\hbar/4\pi has 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.
