The Appearance of Relativistic Stellar Systems

Abstract

A formula is derived for the projected density distribution on a photographic plate which would arise from a given static spherically-symmetric relativistic stellar system. For weak gravitational fields, a corresponding post-Newtonian expression is derived which is relatively simple to use once a particular proper stellar number density has been specified for the relativistic system under consideration. For application to the outer regions of such a system, this post-Newtonian formula simplifies considerably, and it is possible to solve von Zeipel's problem explicitly for these outer regions to obtain an expression for the proper number density of stars in such a system from the projected density on a photographic plate. We find that, if Newtonian theory alone were used to calculate the stellar number density in a relativistic system from the projected density, the system so constructed would appear to be less centrally condensed than it really is.