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

In higher dimensions, we explore planar hairy black hole configurations in a special subclass of the Horndeski theory, which possesses shift symmetry and reflection symmetry, constructed by two coupling functions depending on the kinetic term. For this analysis, we derive a set of new solutions, given by the linear time dependence or the time-independence for the scalar field. Additionally, we calculate their thermodynamic parameters by using Wald formalism, satisfy the First Law of Thermodynamics as well as a Smarr relation. Together with the above, the Wald procedure allows to compute the shear viscosity, showing that for a suitable choice of the coupling functions the Kovtun-Son-Starinets bound does not fulfill.