Holographic Constraints on Generalised Rivlin-Ericksen Fluid

TL;DR

This paper derives a generalized non-relativistic Rivlin-Ericksen fluid from relativistic Weyl invariant fluids and explores holographic constraints, revealing universal relations among second order transport coefficients.

Contribution

It introduces a relativistic origin for the Rivlin-Ericksen fluid and computes holographic values of second order transports, identifying universal constraints.

Findings

Rivlin-Ericksen fluid is a subclass of a generalized non-relativistic system.

Holographic calculations yield specific second order transport coefficients.

Three transport coefficients satisfy a universal constraint relation.

Abstract

The Rivlin-Ericksen model is one of the oldest models in fluid dynamics to describe non-Newtonian properties. The model comes with two independent transports at second order. In this paper, we study the relativistic origin of the Rivlin-Ericksen fluid. Starting from a relativistic Weyl invariant uncharged fluid in $3+1$ dimensions, we reduce it over light-cone directions and obtain a generic non-relativistic uncharged fluid in one lower dimension with all possible second order terms in the constitutive relations. We observe that the Rivlin-Ericksen fluid is a subclass of our generalised non-relativistic system. We also compute the holographic values of all the non-relativistic second order transports and find that three of them satisfy a universal constraint relation.