Causal first-order hydrodynamics from kinetic theory and holography

TL;DR

This paper derives causal relativistic hydrodynamics from kinetic theory and holography, ensuring causality through specific zero modes, and applies this to non-conformal fluids with conserved currents.

Contribution

It introduces a method to obtain causal hydrodynamics from kinetic theory and holography by selecting appropriate zero modes, extending causal hydrodynamics to more complex fluids.

Findings

Causal relativistic Navier-Stokes equations derived from Boltzmann equation.

Application of the method to non-conformal fluids with U(1) symmetry.

Demonstration of causality preservation via zero mode choices.

Abstract

We show how causal relativistic Navier-Stokes equations arise from the relativistic Boltzmann equation: the causality is preserved via a judicious choice of the zero modes of the collision operator. A completely analogous procedure may be used to extract causal hydrodynamics from the fluid-gravity correspondence: again, causality of the hydrodynamic equations is preserved by a suitable choice of zero modes of the corresponding differential operators in the bulk. We give examples of zero modes which give rise to causal hydrodynamic equations for non-conformal fluids with a conserved U(1) global symmetry current.