  It has been conjectured, on the basis of the gauge-gravity duality, that the
ratio of the shear viscosity to the entropy density should be universally
bounded from below by 1/ 4 pi in units of the Planck constant divided by the
Boltzmann constant. Here, we prove the bound for any ghost-free extension of
Einstein gravity and the field-theory dual thereof. Our proof is based on the
fact that, for such an extension, any gravitational coupling can only increase
from its Einstein value. Therefore, since the shear viscosity is a particular
gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show
that the entropy density can always be calibrated to its Einstein value. Our
general principles are demonstrated for a pair of specific models, one with
ghosts and one without.
