Generalized Eulerian Coordinates for Relativistic Fluids: Hamiltonian Rest-Frame Instant Form, Relative Variables, Rotational Kinematics

TL;DR

This paper introduces a novel Hamiltonian formulation of relativistic perfect fluids using generalized Eulerian coordinates, separating center of mass and relative variables, and defining dynamical body frames and multipoles.

Contribution

It presents a new Hamiltonian rest-frame instant form for relativistic fluids with generalized Eulerian coordinates and dynamical body frames, advancing the understanding of relativistic fluid kinematics.

Findings

Separation of relativistic center of mass from relative variables.

Definition of orientational and shape variables for relativistic fluids.

Introduction of Dixon's multipoles for the fluid.

Abstract

We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on the Wigner hyper-planes, we define orientational and shape variables for the fluid, viewed as a relativistic extended deformable body, by introducing dynamical body frames. Finally we define Dixon's multipoles for the fluid.