Fields and fluids on curved non-relativistic spacetimes

TL;DR

This paper develops a generalized geometric framework for non-relativistic fluids on curved spacetimes, introducing a Galilean spin connection with a boost component, and explores its implications for fluid dynamics and response coefficients.

Contribution

It introduces a new geometric structure with a Galilean spin connection including a boost component, extending previous models of non-relativistic fluids on curved backgrounds.

Findings

Derived the most general dissipative fluid theory consistent with the second law.

Found significant differences in transport coefficients compared to previous models.

Presented Kubo formulas for all response coefficients.

Abstract

We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group. This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility. As an example we write down the most general theory of dissipative fluids consistent with the second law in curved non-relativistic geometries and find significant differences in the allowed transport coefficients from those found previously. Kubo formulas for all response coefficients are presented. Our approach also immediately generalizes to systems with independent mass and charge currents as would arise in multicomponent fluids. Along the way we also discuss how to write general locally Galilean invariant non-relativistic actions for multiple particle species at any order in derivatives. A detailed review of the geometry and its relation to non-relativistic limits may be found in a companion paper [arXiv:1503.02682].