Holography of Charged Dilaton Black Holes in General Dimensions

TL;DR

This paper explores the properties of charged dilaton black holes in higher dimensions, analyzing their thermodynamics, AC conductivity, and Gauss-Bonnet corrections to viscosity-to-entropy ratio, extending previous four-dimensional studies.

Contribution

It generalizes the understanding of charged dilaton black holes to arbitrary dimensions and includes new results on conductivity and Gauss-Bonnet effects.

Findings

AC conductivity scales as  with frequency, depending on dilaton coupling and dimension.

Thermodynamics of near-extremal black holes is characterized.

Gauss-Bonnet corrections modify the s/s ratio in five dimensions.

Abstract

We study several aspects of charged dilaton black holes with planar symmetry in $(d+2)$-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schr\"{o}dinger equation and find that the AC conductivity behaves like $\omega^{\delta}$, where the exponent $\delta$ is determined by the dilaton coupling $\alpha$ and the spacetime dimension parameter $d$. Moreover, we also study the Gauss-Bonnet corrections to $\eta/s$ in a five-dimensional finite-temperature background.