Global Scaling Symmetry, Noether Charge and Universality of Shear Viscosity

TL;DR

This paper extends the understanding of the shear viscosity to entropy ratio in various gravity theories, linking it to black hole thermodynamics and demonstrating its universality across different models.

Contribution

It generalizes the relation between shear viscosity and black hole thermodynamics to Einstein gravity with various matter couplings, including non-minimal scalar fields.

Findings

Established the boundary dual of the Smarr relation in Einstein gravity with matter.

Demonstrated the universality of the viscosity/entropy ratio in different gravity models.

Provided explicit examples confirming the theoretical relations.

Abstract

Recently it was established in Einstein-Maxwell-Dilaton gravity that the KSS viscosity/entropy ratio associated with AdS planar black holes can be viewed as the boundary dual to the generalized Smarr relation of the black holes in the bulk. In this paper we establish this relation in Einstein gravity with general minimally-coupled matter, and also in theories with an additional non-minimally coupled scalar field. We consider two examples for explicit demonstrations.