equation of state relating the pressure and density of the fluid; we assume only that we have one simple and one triple eigenvalue. In the case of a dust solution (vanishing pressure), these conditions simplify considerably: or In tensor gymnastics notation, this can be written using the Ricci scalar as: In the case of a radiation fluid, the criteria become or In using these criteria, one must be careful to ensure that the largest eigenvalue belongs to a timelike eigenvector, since there are Lorentzian manifolds, satisfying this eigenvalue criterion, in which the large eigenvalue belongs to a spacelike eigenvector, and these cannot represent radiation fluids. The coefficients of the characteristic will often appear very complicated, and the traces are not much better; when looking for solutions it is almost always better to compute components of the Einstein tensor with respect to a suitably adapted frame and then to kill appropriate combinations of components directly. However, when no adapted frame is evident, these eigenvalue criteria can be sometimes be useful, especially when employed in conjunction with other considerations. These criteria can often be useful for spot checking alleged perfect fluid solutions, in which case the coefficients of the characteristic are often much simpler than they would be for a simpler imperfect fluid. Examples Noteworthy individual dust solutions are listed in the article on dust solutions. Noteworthy perfect fluid solutions which feature positive pressure include various radiation fluid models from cosmology, including FRW radiation fluids, often referred to as the radiation-dominated FRW models. In addition to the family of static spherically symmetric perfect fluids, noteworthy rotating fluid solutions include Wahlquist fluid, which has similar symmetries to the Kerr vacuum, leading to initial hopes (since dashed) that it might provide the interior solution for a simple model of a rotating star. See also Dust solution, for the important special case of dust solutions, Exact solutions in general relativity, for exact solutions in general, Lorentz group Perfect fluid, for perfect fluids in physics in general, Relativistic disks, for the interpretation of relativistic disks in terms of perfect fluids. References Gives many examples of exact perfect fluid and dust solutions. . See Chapter 8 for a discussion of relativistic fluids and thermodynamics. . This review article surveys static spherically symmetric fluid solutions known up to about 1995. . This article describes one of several schemes recently found for obtaining all the static spherically symmetric perfect