Variational theory of non-perfect relativistic fluids

A basic question in General Relativity from the point of view of the general field theory is to obtain the Einstein equations coupled with the stress-energy-momentum tensor of a dissipative fluid from a variational principle. We believe that this problem, whose solution for perfect fluids is well known, has not been faced in a systematic way, maybe by the thought of a possible nonsense, for the concept of dissipation is believed to be incompatible with the essentially conservative character of the calculus of variations. In this talk, we shall deal with this topic by discussing a variational problem which generalizes in a natural way to this kind of fluids the Einstein-Taub formalism for the perfect fluids. We shall start by summarizing this formalism looking ahead to this generalization. Next, we shall show the generalization restricting ourselves, for simplicity, to relativistic fluids with just bulk viscosity. Finally, we shall see some simple examples that illustrate very well the essential points of the theory that has just been displayed