Fluid/gravity correspondence: second order transport coefficients in compactified D4-branes

Abstract

We develop the boundary derivative expansion (BDE) formalism of fluid/gravity correspondence to nonconformal version through the compactified, nearextremal black D4-brane. We offer an explicit calculation of 9 second order transport coefficients, i.e., the τπ , τπ∗, τΠ, λ1,2,3 and ξ1,2,3 for the strongly coupled, uncharged and nonconformal relativistic fluid which is the holographic dual of compactified, near extremal black D4-brane. We also show that the nonconformal fluid considered in this work is free of causal problem and admits the Haack-Yarom relation 4λ1 − λ2 = 2ητπ.