Go to previous page Go up Go to next page

6 An Overview of the Perfect Fluid

There are many different ways of constructing general relativistic fluid equations. Our purpose here is not to review all possible methods, but rather to focus on a couple: (i) an “off-the-shelve” consistency analysis for the simplest fluid a la Eckart [39Jump To The Next Citation Point], to establish some key ideas, and then (ii) a more powerful method based on an action principle that varies fluid element world lines. The ideas behind this variational approach can be traced back to Taub [108Jump To The Next Citation Point] (see also [101]). Our description of the method relies heavily on the work of Brandon Carter, his students, and collaborators [19Jump To The Next Citation Point36Jump To The Next Citation Point37Jump To The Next Citation Point2829Jump To The Next Citation Point67Jump To The Next Citation Point9091Jump To The Next Citation Point]. We prefer this approach as it utilizes as much as possible the tools of the trade of relativistic fields, i.e. no special tricks or devices will be required (unlike even in the case of our “off-the-shelve” approach). One’s footing is then always made sure by well-grounded, action-based derivations. As Carter has always made clear: When there are multiple fluids, of both the charged and uncharged variety, it is essential to distinguish the fluid momenta from the velocities, in particular in order to make the geometrical and physical content of the equations transparent. A well-posed action is, of course, perfect for systematically constructing the momenta.

 6.1 Rates-of-change and Eulerian versus Lagrangian observers
 6.2 The single, perfect fluid problem: “Off-the-shelf” consistency analysis

  Go to previous page Go up Go to next page