On the spherical symmetry of static stars in general relativity.
Abstract
From Einstein's field equation and the second law of thermodynamics it follows that in nonmagnetic thermally conducting static fluids, isobaric surfaces and isothermal surfaces coincide with isopotential surfaces. By symmetry these surfaces must be surfaces of constant curvature. To keep the energy content of the star finite, these surfaces must be closed; that is, positively curved, hence spherical. Since the energy flux divided by the speed of light is small compared with the restenergy density, spherical symmetry is imposed only on the evolutionary time scale, so that observed stars may depart from perfect spherical symmetry by factors of the order of the ratio of the fluid velocity compared to the speed of light.
 Publication:

The Astrophysical Journal
 Pub Date:
 January 1977
 DOI:
 10.1086/154927
 Bibcode:
 1977ApJ...211..266M
 Keywords:

 Einstein Equations;
 Relativity;
 Stellar Structure;
 Thermodynamics;
 Cosmology;
 Spheres;
 Stellar Evolution;
 Stress Tensors;
 Symmetry;
 Thermal Conductivity;
 Astrophysics