Beyond the Small-Angle Approximation For MBR Anisotropy from Seeds
  In this paper we give a general expression for the energy shift of massless particles travelling through the gravitational field of an arbitrary matter distribution as calculated in the weak field limit in an asymptotically flat space-time. It is {\it not} assumed that matter is non-relativistic. We demonstrate the surprising result that if the matter is illuminated by a uniform brightness background that the brightness pattern observed at a given point in space-time (modulo a term dependent on the oberver's velocity) depends only on the matter distribution on the observer's past light-cone. These results apply directly to the cosmological MBR anisotropy pattern generated in the immediate vicinity of of an object like a cosmic string or global texture. We apply these results to cosmic strings, finding a correction to previously published results for in the small-angle approximation. We also derive the full-sky anisotropy pattern of a collapsing texture knot. 
Albert Stebbins and Shoba Veeraraghavan