Black holes in 4D Einstein-Maxwell-Gauss-Bonnet gravity coupled with scalar fields

TL;DR

This paper explores four-dimensional Einstein-Maxwell-Gauss-Bonnet gravity coupled with scalar fields, deriving dyonic black hole solutions, analyzing shear viscosity ratios, and examining violations of the KSS bound at low temperatures.

Contribution

It introduces a novel four-dimensional dyonic black hole solution with higher derivative terms and studies shear viscosity behavior, revealing bound violations similar to higher-dimensional cases.

Findings

Shear viscosity to entropy density ratio violates KSS bound at low temperature.

Ratio remains nearly unchanged in 4D, characterized by (T/Δ)^2.

Uncharged black holes exhibit similar viscosity behavior as in 5D.

Abstract

Einstein-Maxwell-Gauss-Bonnet-axion theory in $4$-dimensional spacetime is investigated in this paper through a "Kaluza-Klein-like" process. Dual to systems at finite temperature with background magnetic field on three dimensions, the four-dimensional dyonic black hole solution coupled with higher derivative terms is obtained. After the tensor-type perturbation is added, the shear viscosity to entropy density ratio is calculated at high temperature and low temperature separately. The behaviour of shear viscosity to entropy density ratio of uncharged black holes is found to be similar with that in $5$-dimensional spacetime, violating the Kovtun-Starinets-Son bound as well when temperature becomes lower. In addition, the main feature of this ratio remains almost unchanged in $4$ dimensions, which is characterised by $(T/\Delta)^2$ at low temperature $T$, with $\Delta$ proportional to the coefficient $\beta$ from scalar fields. The difficulty in causal analysis is also discussed, which is mainly caused by the vanishing momentum term in equations of motion.