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

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 step-by-step with model examples considered at each level. Thus we consider 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. We also 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.