The pressurevolume relation of isothermal gas spheres within the framework of general relativity
Abstract
The equation of state p = qp is adopted, where p and p denote pressure and energydensity, respectively, and q is a constant, and the conditions of hydrostatic equilibria within the framework of general relativity are used to obtain the relation between the radius of a gas sphere and the pressure which it exerts at the boundary. It is shown that for given total energy, the pressure volume relation is similar to the corresponding relation for isothermal gas spheres calculated in the Newtonian theory. In particular there exists a maximum pressure which the gas sphere can withstand. Hence, if the relativistic gas sphere is surrounded by an envelope, and if the envelope exerts at the boundary a pressure greater than the maximum pressure, the gas sphere cannot be in static equilibrium.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 1973
 DOI:
 10.1093/mnras/165.1.11
 Bibcode:
 1973MNRAS.165...11Y