A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics

TL;DR

This paper develops a Lagrangian effective theory for relativistic hydrodynamics, incorporating dissipative effects like viscosity and relaxation times, and justifies the Israel-Stewart formalism from fundamental principles.

Contribution

It introduces a Lagrangian formulation of relativistic hydrodynamics that naturally includes dissipative terms, providing a theoretical basis for the Israel-Stewart approach.

Findings

Derivation of relativistic hydrodynamics as a Lagrangian effective theory.

Inclusion of shear and bulk viscosity, and Israel-Stewart relaxation terms.

Justification of Israel-Stewart terms from energy-momentum considerations.

Abstract

We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear viscosity, and the requirement of a bounded energy-momentum "vacuum", forces the inclusion of the Israel-Stewart term into the theory, thereby providing a justification for the origin and uniqueness of these terms.