Regular exact models for a nonstatic gas sphere in general relativity.
Abstract
Some new exact models for an expanding or a contracting “gaseous” sphere (i.e., the densityϱ is to vanish at the outer boundary together with the pressurep) are given. The physical properties of the models are investigated, and it is found that both the pressure and the density are positive inside the outer boundary of the sphere, and their respective gradients are negative. The density is increasing for contracting spheres, and it is decreasing for expanding spheres. It is also shown that this is the case for the pressure at any moment for the layers close to the boundary of the spheres. For these layers it is further shown that the adiabatic speed of sound is less than the speed of light, and the trace of the energymomentum tensor is positive. The rate of change of the circumference as measured by an observer riding on the boundary of the sphere is increasing for expanding spheres and it is decreasing for collapsing spheres. We also find that the “physical radius” is an increasing function of comoving radial coordinate. The mass function is further shown to be positive.
 Publication:

General Relativity and Gravitation
 Pub Date:
 December 1985
 DOI:
 10.1007/BF00773619
 Bibcode:
 1985GReGr..17.1121K
 Keywords:

 Astronomical Models;
 Gas Dynamics;
 Relativity;
 Supernovae;
 Abundance;
 Density Distribution;
 Gravitational Collapse;
 Mass Distribution;
 Pressure Distribution;
 Spheres;
 Astrophysics;
 Gaseous Spheres:General Relativity;
 General Relativity:Gaseous Spheres