Shear viscosity from black holes in generalized scalar-tensor theories in arbitrary dimensions

TL;DR

This paper investigates black hole solutions in higher-dimensional scalar-tensor theories, computes their thermodynamics, and explores how shear viscosity in the dual field theory can violate the KSS bound.

Contribution

It derives new black hole solutions in generalized scalar-tensor theories and calculates shear viscosity, showing potential violations of the KSS bound in higher dimensions.

Findings

Black hole solutions resemble Schwarzschild-AdS in higher dimensions

Shear viscosity can violate the KSS bound with specific couplings

Thermodynamics satisfy the First Law and Smarr relation

Abstract

In higher dimensions, we study Degenerate-Higher-Order-Scalar-Tensor theories and we derive solutions that resemble the Schwarzschild Anti-de Sitter black holes. We compute their thermodynamic quantities following the Wald formalism, satisfying the First Law of Thermodynamics and a higher dimensional Smarr relation. Constructing a Noether charge with a suitable choice of a space-like Killing vector, we obtain the shear viscosity of the non-gravitational dual field theory, where for a suitable choice of the couplings functions, the Kovtun-Son-Starinets bound is violated. These results are corroborated by the calculation of the Green's functions following the Kubo formalism.