The dynamical second-order transport coefficients of smeared Dp-brane

TL;DR

This paper calculates the second-order transport coefficients of the fluid dual to smeared Dp-branes, establishing their equivalence to compactified Dp-branes and revisiting stability conjectures within the fluid/gravity framework.

Contribution

It explicitly computes the seven dynamical second-order transport coefficients for smeared Dp-branes and demonstrates their equivalence to those of compactified Dp-branes, advancing the understanding of their fluid duals.

Findings

Explicit calculation of 7 second-order transport coefficients.

Proof of equivalence between smeared and compactified Dp-branes.

Reassessment of the Correlated Stability Conjecture for smeared Dp-branes.

Abstract

The smeared Dp-brane is constructed by having the black Dp-brane uniformly smeared over several transverse directions. After integrating the spherical directions and the smeared directions, the smeared Dp-brane turns out to be a Chamblin-Reall model with one background scalar field. Within the framework of the fluid/gravity correspondence, we not only prove the equivalence between the smeared Dp-brane and the compactified Dp-brane by explicitly calculating the 7 dynamical second-order transport coefficients of their dual relativistic fluids, but also revisit the Correlated Stability Conjecture for the smeared Dp-brane via the fluid/gravity correspondence.