The Exterior Solution for Radiating Spheres with Zero Limb Darkening in General Relativity
Abstract
Zero limb darkening is defined as the case where a freely falling observer sees a uniformly illuminated disk, and the field equations in Bondi's radiation coordinates are presented. By expanding the non vanishing components of the metric tensor in powers of hr a solution to these field equations is obtained; the first seven terms are worked out explicitly. In particular we find that the entire solution is generated by the asymptotic solution. The asymptotic solution, characterized by two functions of the timelike co ordinate, is that solution which holds when cos Z 1  ~Z2, where Z is onehalf of the angular diameter of the observed stellar disk. The complete solution requires all the higherorder derivatives of these two functions. Thus all the parameters of the radiation field, such as the radiative flux and the radiation pressures, are determined once the solution at large distances for the star is specified
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1969
 DOI:
 10.1086/149962
 Bibcode:
 1969ApJ...156..257K