Relativistic hydrodynamics from projection operator method

TL;DR

This paper derives relativistic hydrodynamic equations using Mori's projection operator method, clarifying the distinction between frames and showing the equivalence of slow dynamics in Landau and Eckart frames.

Contribution

It provides a novel derivation of relativistic hydrodynamics in both frames using the projection operator method, clarifying the nature of frame ambiguity.

Findings

Derived linearized Landau equation from the projection operator method.

Showed that Eckart frame dynamics are described by Landau frame variables.

Clarified that frame differences are due to variable choice, not rest frame.

Abstract

We study relativistic hydrodynamics in the linear regime, based on Mori's projection operator method. In relativistic hydrodynamics, it is considered that ambiguity about the fluid velocity occurs from a choice of a local rest frame: the Landau and Eckart frames. We find that the difference of the frames is not the choice of the local rest frame, but rather that of dynamic variables in the linear regime. We derive hydrodynamic equations in the both frames by the projection operator method. We show that natural derivation gives the linearized Landau equation. Also, we find that, even for the Eckart frame, the slow dynamics is actually described by the dynamic variables for the Landau frame.