Axionic black branes in the k-essence sector of the Horndeski model

TL;DR

This paper introduces new black brane solutions within Horndeski gravity's K-essence sector, analyzing their thermodynamics and holographic conductivity, thus expanding the understanding of scalar-tensor theories in higher dimensions.

Contribution

It presents the first exact analytic black brane solutions with axion fields in Horndeski gravity's K-essence sector, including thermodynamic and holographic properties.

Findings

Found neutral and charged solutions in D-dimensions

Analyzed thermodynamics of 4D solutions

Computed dual holographic DC conductivity

Abstract

We construct new black brane solutions in the context of Horndeski gravity, in particular in its K-essence sector. These models are supported by axion scalar fields that depend only on the horizon coordinates. The dynamics of these fields is determined by a K-essence term that includes the standard kinetic term $X$ and a correction of the form $X^{k}$. We find both neutral and charged exact and analytic solutions in $D$-dimensions, which are asymptotically anti de Sitter. Then, we describe in detail the thermodynamical properties of the four-dimensional solutions and we compute the dual holographic DC conductivity.