  Starting with a static, spherically symmetric spacetime incorporating
critical (unstable) closed null geodesics, a family of models for equilibrium
states of non-isolated compact objects is obtained by solving the Einstein
equations for an energy-momentum tensor featuring a perfect fluid with
ideal-gas equation of state, dark energy, and a magnetic field. All of these
source fields are described by simple, monotonically decreasing mathematical
functions. No ansatz is made for either of the two unknown metric elements;the
null curve geometry yields one, and the other follows from a simplification of
the magnetic field vector. The metric elements are free of singularities and
horizons everywhere, although their inverses are singular at the origin. The
entire metric assumes its Lorentzian form at infinity. The geometry of this
model, as well as fundamental quantum considerations, require that the radial
coordinate must always be greater than zero, thereby obviating the physical
singularity at the origin.

General Relativity and Quantum Cosmology