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We discuss corrections to the ratio of shear viscosity to entropy density$\eta/s$ in higher-derivative gravity theories. Generically, these theoriescontain ghost modes with Planck-scale masses. Motivated by generalconsiderations about unitarity, we propose new boundary conditions for theequations of motion of the graviton perturbations that force the amplitude ofthe ghosts modes to vanish. We analyze explicitly four-derivative perturbativecorrections to Einstein gravity which generically lead to four-derivativeequations of motion, compare our choice of boundary conditions to previousproposals and show that, with our new prescription, the ratio $\eta/s$ remainsat the Einstein-gravity value of $1/4\pi$ to leading order in the corrections.It is argued that, when the new boundary conditions are imposed on six andhigher-derivative equations of motion, $\eta/s$ can only increase from theEinstein-gravity value. We also recall some general arguments that support thevalidity of our results to all orders in the strength of the corrections toEinstein gravity. We then discuss the particular case of Gauss-Bonnet gravity,for which the equations of motion are only of two-derivative order and thevalue of $\eta/s$ can decrease below $1/4\pi$ when treated in a nonperturbativeway. Our findings provide further evidence for the validity of the KSS boundfor theories that can be viewed as perturbative corrections to EinsteinGravity.

Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity