Thursday 17 September 2009
to 11:00 at
Gregory L. Comer (Department of Physics & Center for Fluids at All Scales, Saint Louis University )
We present an overview of a fully relativistic treatment for systems (such as neutron stars) that contain one or more, dynamically independent fluids. The approach is that originally due to Brandon Carter, which takes as its fundamental fields the individual particle fluxes (including also entropy). While an action principle exists for the conservative case, we will use a more "pedestrian" presentation that starts with the standard, perfect fluid, and then builds up to multi-fluid systems. Perhaps the single most important aspect of Carter's approach is a clear recognition of the so-called chemical potential covector, i.e. the fluid momentum. It is both dynamically and thermodynamically conjugate to the particle flux. In a multi-fluid context, this construction readily incorporates the entrainment effect, whereby the momentum of a given fluid is in general a linear combination of all the particle fluxes. It can also immediately accomodate electromagnetism, via the addition of the usual gauge- coupling four-vector. The final goal of the talk is to outline the complexity associated with dissipation for multi-fluid systems, and briefly discuss some recent progress (but in the Newtonian limit).