Higher Derivative Corrections to Locally Black Brane Metrics

TL;DR

This paper extends the construction of locally boosted black brane spacetimes to include higher derivative corrections, specifically Gauss-Bonnet terms, and computes their effects on boundary stress tensors and viscosity ratios.

Contribution

It introduces a first-order correction to black brane solutions in higher derivative gravity, providing new insights into holographic transport properties.

Findings

Derived the $ ext{α'}$-corrected boundary stress tensor.

Calculated the shear viscosity to entropy ratio with Gauss-Bonnet corrections.

Confirmed the ratio matches previous results in the literature.

Abstract

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 $\alpha'$) as a toy example. We find the solution to the $\alpha'$ corrected Einstein equations to first order in the boundary derivative expansion. This allows us to find the $\alpha'$ 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.