Variational Principle for Relativistic Fluid Dynamics

TL;DR

This paper develops a variational principle framework for relativistic fluid dynamics, enabling derivation of approximate solutions and specific models like relativistic spherical droplet motion using effective Lagrangians.

Contribution

It introduces a variational approach for relativistic hydrodynamics and derives effective Lagrangians for specific dynamical variables, including a relativistic spherical droplet model.

Findings

Derived a relativistic version of the spherical droplet motion equation.

Presented a general Lagrangian for spherically symmetric relativistic systems.

Showed how to obtain approximate solutions using variational principles.

Abstract

The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable ansatz for the dynamical variables such as density profile of the system. As an example, the relativistic version of spherical droplet motion (Rayleigh-Plesset equation) is derived from a simple Lagrangian. For the general relativistic case the most general Lagrangian for spherically symmetric systems is given.