Higher Derivative Corrections to Locally Black Brane Metrics

In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the Gauss-Bonnet term (with coefficient ${\alpha }^{\mathrm{\prime }}$) as a toy example. We find the solution to the ${\alpha }^{\mathrm{\prime }}$ corrected Einstein equations to first order in the boundary derivative expansion. This allows us to find the ${\alpha }^{\mathrm{\prime }}$ corrections to the boundary stress tensor in the presence of the Gauss-Bonnet term in the bulk action. We therefore obtain the ratio of shear viscosity to entropy which agrees with other methods of computation in the literature.