Iterative approach to gravitational lensing theory - art. no. 104007

We develop an iterative approach to gravitational lensing theory based on a pproximate solutions of the null geodesic equations. The approach can be em ployed in any space-time which is "close" to a space-time in which the null geodesic equations can be completely integrated, such as, Minkowski space- rime, Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To il lustrate the method, we construct the iterative gravitational lens equation s and time of arrival equation for a single Schwarzschild lens. This exampl e motivates a discussion of the relationship between the iterative approach , the standard thin lens formulation, and an exact formulation of gravitati onal lensing.