Transforming the Einstein static Universe into physically acceptable static fluid spheres II: A two - fold infinity of exact solutions

Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas the entire class of solutions can be considered as generalizations of the familiar Tolman IV solution, no member of the class can be written explicitly in isotropic coordinates. Further, except for a set of measure zero, no member of the class can be written explicitly in curvature coordinates either.Comment: 6 pages, 6 figures, revtex4,improved figures. To appear in Phys. Rev.

Generalized Swiss-cheese cosmologies: Mass scales

We generalize the Swiss-cheese cosmologies so as to include nonzero linear momenta of the associated boundary surfaces. The evolution of mass scales in these generalized cosmologies is studied for a variety of models for the background without having to specify any details within the local inhomogeneities. We find that the final effective gravitational mass and size of the evolving inhomogeneities depends on their linear momenta but these properties are essentially unaffected by the details of the background model.Comment: 10 pages, 14 figures, 1 table, revtex4, Published form (with minor corrections

Generalized Swiss-Cheese Cosmologies II: Spherical Dust

The generalized Swiss - cheese model, consisting of a Lema\^itre - Tolman (inhomogeneous dust) region matched, by way of a comoving boundary surface, onto a Robertson-Walker background of homogeneous dust, has become a standard construction in modern cosmology. Here we ask if this construction can be made more realistic by introducing some evolution of the boundary surface. The answer we find is no. To maintain a boundary surface using the Darmois - Israel junction conditions, as opposed to the introduction of a surface layer, the boundary must remain exactly comoving. The options are to drop the assumption of dust or allow the development of surface layers. Either option fundamentally changes the original construction.Comment: 5 pages revtex 4.1 Final form to appear in Phys. Rev.