Invariant construction of solutions to Einstein's field equations - LRS perfect fluids II

The properties of LRS class II perfect fluid spacetimes are analysed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the plane and hyperbolic analogues to the spherical symmetric case. For spherically symmetric static models the set of equations is reduced to the Tolman-Oppenheimer-Volkoff equation only. Some new non-stationary and inhomogeneous solutions with shear, expansion and acceleration of the fluid are presented. Among these are some of temporally self-similar solutions with equation of state given by p = ( - 1)µ, 1 < < 2 and a class of solutions characterized by = -(1/6). We give an example of a geometry where the Riemann tensor and the Ricci rotation coefficients are not sufficient to give a complete description of the geometry. Using an extension of the method, we find the full metric in terms of curvature quantities.