Abstract
It is well known and generally accepted, that the temperature of matter in thermal equilibrium in curved space time is proportional to the inverse square root of the tt-component of the metric. During a gravitational collapse, the ordinary matter radius of the star approaches the corresponding Schwarzschild radius. Thereby the value of this metric component on the surface of the star is approaching zero and correspondingly the temperature on the surface rises quite sharply. Therefore the matter on the surface can no longer be modeled as an ideal fluid or as a degenerated Fermi gas. Instead, above some critical temperature, it behaves like an ideal gas. Pressure is rising proportional to the temperature and therefore the matter is pressed away from the surface of the star, which on the other side changes the metric. A equilibrium state is emerging. Some numerical calculations using Mathematica have been carried out and thereby for simplicity a pure ideal gas model has been used. The calculated functions for pressure , energy density, particle density as well as the spherically symmetric metric are shown. In such a model, matter is distributed on a spherical shell, the radius of which is the Schwarzschild radius. The ring is thicker for high temperatures of the matter and thinner for low temperature matter.
Johann Weiser