Modification of Eckart theory of relativistic dissipative fluid by introducing extended matching conditions

TL;DR

This paper introduces extended matching conditions into Eckart's relativistic dissipative fluid theory, deriving stable and causal equations of motion by ensuring thermodynamic stability of the entropy current.

Contribution

It proposes a novel extension to matching conditions in relativistic hydrodynamics, ensuring stability and causality within Eckart's framework.

Findings

Derived stable equations of motion for the extended model

Established the relation between stability and causality

Demonstrated linearized stability against perturbations

Abstract

We deal with a novel approach to formulation of the relativistic dissipative hydrodynamics by extending the so-called matching conditions widely used in the literature. The form of the non-equilibrium entropy current can be determined by requiring thermodynamical stability of the entropy current under extended matching conditions. We derive equations of motion for the relativistic dissipative fluid based on the Eckart theory and show that linearized equations obtained from them are stable against small perturbations. It is also shown that the required fluid stability conditions are related to the causality of the model.