Variational principle for relativistic fluid dynamics

The variational principle for the special and general relativistic hydrodynamics is discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable ansatze for the dynamical variables such as the 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.