Causality and Stability in Relativistic Hydrodynamics

TL;DR

This paper demonstrates that causality and stability in relativistic hydrodynamics require either additional degrees of freedom or a non-Landau/Eckart frame, with all-order derivative resummation being essential for a consistent theory.

Contribution

It shows that finite-order derivative corrections lead to acausality, and that an exact, all-order resummation from microscopic theory ensures causality and stability in relativistic hydrodynamics.

Findings

Finite truncations cause acausality.

All-order derivative resummation restores causality.

New degrees of freedom are necessary for a consistent theory.

Abstract

The causality and stability of a relativistic hydrodynamic theory is shown to require a consensus between, either (i) newer degrees of freedom apart from the fundamental fluid fields, or (ii) a general hydrodynamic frame other than the Landau or Eckart compromising the field's first principle definition, unless the non-equilibrium derivative correction goes to infinity. Any finitely truncated derivative correction (no matter how high it is) is shown to lead to an acausal theory, unless the corrections are infinitely summed up to include all orders. From an underlying microscopic theory, an exact form of relativistic hydrodynamics has been derived which establishes that the resummation of all order temporal derivatives is essential for causality, which finally 'integrated in' as newer degrees of freedom.