Relativistic Stellar Dynamics

In this paper the theory of stellar dynamics is developed within the framework of general relativity for time-independent, spherically symmetric systems in which collisions are ignored, and a criterion is ob- tained for the applicability of this theory. It is shown how the distribution function may be found for systems with an isotropic pressure if either the energy density of the system is given as a function of the radius or an "equation of state" is assumed. The non-existence of isotropic models with constant energy density is demonstrated by showing that the distribution function so found is negative over an essential part of its range Explicit distribution functions are found for systems corresponding to Tooper's general relativistic polytropes of indices n = 1 0(0 5)3 0 For a given polytropic index the relativity parameter o defined as the ratio of the pressure to the energy density at the center of the system is found to have an upper limit O~ set by the requirement that the distribution function should be non-negative. In every case examined o~ <n/(n + 1), so that the speed of propagation of small disturbances in these systems is always less than the speed of light, and furthermore 2GM/c2R is always less than unity, so that the Schwarzschild singularity never occurs in these system