Causality and stability in relativistic hydrodynamic theory -- a choice to be endured

TL;DR

This paper explores how causality and stability in relativistic hydrodynamics can be maintained through frame transformations and the inclusion of appropriate degrees of freedom, linking different theoretical formalisms.

Contribution

It demonstrates that a generic fluid frame transformation can convert a stable-causal hydrodynamic theory into a pathology-free one, highlighting the importance of frame choice and degrees of freedom.

Findings

Frame transformations can recast hydrodynamic theories for causality and stability.

A stable theory in one frame may require additional degrees of freedom in another.

Causality and stability are interconnected through the choice of frame and degrees of freedom.

Abstract

In this work, it has been indicated that the key features requisite for preserving causality and stability of the popularly existing relativistic hydrodynamic theories, can be translated into each other. It has been shown here, that a generic `fluid frame transformation' including all orders of gradient corrections can recast a stable-causal hydrodynamic theory that (i) only includes fundamental fluid variables (velocity and temperature) but requires to be in a general hydrodynamic frame other than the Landau or Eckart, to a theory that is (ii) pathology free in Landau frame but needs newer degrees of freedom. Since frame choice provides the first principle field definitions and degrees of freedom indicate the number of conserved quantities, the causality and stability of a theory seem to require a consensus between the two unless the derivative correction goes to infinity. The key finding of this work is to indicate a connection between these different formalisms, that lead to a causal and stable hydrodynamic theory.