EXISTENCE AND PROPERTIES OF SPHERICALLY SYMMETRICAL STATIC FLUID BODIES WITH A GIVEN EQUATION OF STATE

It is shown that for a given equation of state and a given value of the central pressure there exists a unique global solution of the Einstein equations representing a spherically symmetric static fluid body. For the proof a new theorem on singular ordinary differential equations is established which is of interest in its own right. For a given equation of state and central pressure, the fluid will either fill the entire space or be finite in extent with a vacuum exterior. Criteria are given which allow one to decide for certain equations of state which of these two cases occurs. This generalizes well known results in Newtonian theory and is proved by showing that the relativistic model inherits the property of having a finite radius from a Newtonian model. Parameter-dependent families of relativistic solutions are constructed which have a Newtonian limit in a rigorous sense. The relationship between relativistic and Newtonian equations of state is examined by looking at the example of a degenerate Fermi gas.