Non-conformal Hydrodynamics in Einstein-dilaton Theory

TL;DR

This paper explores non-conformal hydrodynamics via Einstein-dilaton black holes, analyzing thermodynamics, gauge theory duals, and charge transport, revealing how parameters influence stability, conductivity, and mode lifetimes.

Contribution

It introduces a new black hole solution in Einstein-dilaton theory and studies its dual non-conformal hydrodynamics, including transport properties and stability conditions.

Findings

Black hole is thermodynamically stable for 0 ≤ η < 2.

Charge diffusion constant decreases with η.

DC conductivity increases with temperature in the dual gauge theory.

Abstract

In the Einestein-dilaton theory with a Liouville potential parameterized by $\eta$, we find a Schwarzschild-type black hole solution. This black hole solution, whose asymptotic geometry is described by the warped metric, is thermodynamically stable only for $0 \le \eta < 2$. Applying the gauge/gravity duality, we find that the dual gauge theory represents a non-conformal thermal system with the equation of state depending on $\eta$. After turning on the bulk vector fluctuations with and without a dilaton coupling, we calculate the charge diffusion constant, which indicates that the life time of the quasi normal mode decreases with $\eta$. Interestingly, the vector fluctuation with the dilaton coupling shows that the DC conductivity increases with temperature, a feature commonly found in electrolytes.