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

Understand

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.