Relativistic viscous hydrodynamics, conformal invariance, and holography

Comment on "Viscous hydrodynamics relaxation time from AdS/CFT correspondence"

“…In order to avoid the confusion which comes from the power counting, it is best to consider a plasma whose deviations are small from equilibrium. In this case, the naive counting does work and we obtain the exactly the same value (8).…”

“…Just before we submitted this comment, a number of interesting papers appeared[7,8,9,10], which study the similar problem as ours. In particular, our point was made independently in Ref [7]…”

Fluid/gravity correspondence: A nonconformal realization in compactified D4 branes

“…Following [36], the authors of [39,40] calculated the first order transport coefficients in near extremal D3 brane background and found that, in the long-distance and low-frequence limit, these correlators turn into hydrodynamical forms. Second order transport coefficients of this system were calculated in [41]. The framework that investigates transport properties of a fluid via its corresponding gravity is called the fluid/gravity correspondence, and the most notable feature in above works [39][40][41] is the use of Green-Kubo formula, thus one may call it the Green-Kubo formalism of fluid/gravity correspondence.…”

Near Horizon Analysis of Extremal AdS5 Black Holes

“…Incorporating electric charges and working in the global AdS rather than the Poincaré patch, the corrections in the fluid mechanics could be matched against corresponding corrections to the near horizon equations we obtained in this paper. The systematic derivative expansion developed in [44,45,46,47,48] would be helpful in such an attempt. We hope to return to some of these questions in the near future.…”

“… 45). Equations(3.42) can be solved for (e r , e t ) in a closed form, though the answer is rather complicated.…”