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

Abstract

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.

6 pages, 6 figures, revtex4,improved figures. To appear in Phys. Rev. D

References in corpus (6)

• Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations
• Gravitational Energy in Spherical Symmetry
• All static spherically symmetric perfect fluid solutions of Einstein's Equations
• The Ultimate Energy Density of Observable Cold Matter
• Buchdahl-like transformations for perfect fluid spheres
• Transforming the Einstein static Universe into physically acceptable static fluid spheres

Cited by in corpus (8)

• Stability of the Einstein static Universe in $f(R,T)$ gravity
• Einstein static universes are unstable in generic f(R) models
• Isotropic stars in general relativity
• Generating static spherically symmetric anisotropic solutions of Einstein's equations from isotropic Newtonian solutions
• Modelling anisotropic fluid spheres in general relativity
• Holes in the static Einstein universe and the model of the cosmological voids
• Anisotropic compact star with a linear pressure-density relationship
• Generating Static Fluid Spheres by Conformal Transformations