A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics

TL;DR

This paper introduces a novel variational framework for relativistic dissipative fluid dynamics that extends existing principles to include multiple dissipation channels without relying on equilibrium assumptions.

Contribution

The work develops a covariant action principle for dissipative fluids using matter spaces and extended volume forms, advancing the theoretical foundation of relativistic fluid dynamics.

Findings

Derived relativistic Navier-Stokes equations

Demonstrated non-symmetric dissipative stress tensors

Extended variational formalism to heat flow models

Abstract

We present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients in the construction are i) the use of a lower dimensional matter space for each fluid component, and ii) an extended functional dependence for the associated volume forms. In an effort to make the concepts clear, the formalism is developed in steps with the model example of matter coupled to heat considered at each level. Thus we discuss a model for heat flow, derive the relativistic Navier-Stokes equations and discuss why the individual dissipative stress tensors need not be spacetime symmetric. We argue that the new formalism, which notably does not involve an expansion away from an assumed equilibrium state, provides a conceptual breakthrough in this area of research and provide an ambitious list of directions in which one may want to extend it in the future. This involves an exciting set of problems, relating to both applications and foundational issues.