Planar black holes configurations and shear viscosity in arbitrary dimensions with shift and reflection symmetric scalar-tensor theories

TL;DR

This paper investigates higher-dimensional planar black holes with scalar hair in a special class of Horndeski theories, deriving new solutions, analyzing their thermodynamics, and showing potential violations of the shear viscosity bound.

Contribution

It introduces new time-dependent and independent scalar field solutions in shift and reflection symmetric Horndeski theories and computes their shear viscosity, revealing bound violations.

Findings

Derived new scalar hairy black hole solutions in higher dimensions.

Confirmed thermodynamic consistency via Wald formalism.

Found conditions under which the shear viscosity bound is violated.

Abstract

In higher dimensions, we explore planar hairy black hole configurations for a special subclass of the Horndeski theory, defined by two coupling functions depending on the kinetic term and enjoying shift symmetry and reflection symmetry. For this analysis, we derive a set of new solutions, given by time-dependent as well as time independent scalar field configurations. Additionally, we calculate their thermodynamic quantities by using Wald formalism, satisfying the First Law of Thermodynamics as well as a Smarr relation. Together with the above, the Wald procedure allows us to compute the shear viscosity, showing that for a suitable choice of the coupling functions the Kovtun-Son-Starinets bound is violated.