Holographic equation of state in fluid/gravity duality

TL;DR

This paper derives a detailed relation between boundary conditions of scalar fields in AdS spacetimes and the equation of state of the dual fluid, focusing on five-dimensional cases and scalar fields at the Breitenlohner-Freedman bound.

Contribution

It provides a precise derivation of the connection between mixed boundary conditions and fluid equations of state in the context of fluid/gravity duality, especially for five-dimensional scalar fields.

Findings

Established a relation between boundary conditions and fluid equations of state.

Derived the relation explicitly for five-dimensional scalar fields at the Breitenlohner-Freedman bound.

Discussed scalar-tensor theories with constant speed of sound.

Abstract

We establish a precise relation between mixed boundary conditions for scalar fields in asymptotically anti de Sitter spacetimes and the equation of state of the dual fluid. We provide a detailed derivation of the relation in the case of five bulk-dimensions for scalar fields saturating the Breitenlohner-Freedman bound. As a concrete example, we discuss the five dimensional scalar-tensor theories describing a constant speed of sound.