  In the process of protostar formation, astrophysical gas clouds undergo
thermodynamically irreversible processes and emit heat and radiation to their
surroundings. Due the emission of this energy one can envision an idealized
situation in which the gas entropy remains nearly constant. In this setting, we
derive in this paper interior solutions to the Einstein equations of General
Relativity for spheres which consist of isentropic gas. To accomplish this
objective we derive a single equation for the cumulative mass distribution in
the protostar. From a solution of this equation one can infer readily the
coefficients of the metric tensor. In this paper we present analytic and
numerical solutions for the structure of the isentropic self-gravitating gas.
In particular we look for solutions in which the mass distribution indicates
the presence of shells, a possible precursor to solar system formation. Another
possible physical motivation for this research comes from the observation that
gamma ray bursts are accompanied by the ejection of large amounts of
thermodynamically active gas at relativistic velocities. Under these conditions
it is natural to use the equations of general relativity to inquire about the
structure of the ejected mass.
