Exact general relativistic lensing versus thin lens approximation: the
  crucial role of the void
  We have used an exact general relativistic model structure within a FRW
cosmological background based on a LTB metric to study the gravitational
lensing of a cosmological structure. The integration of the geodesic equations
turned out to be a delicate task. We realized that the use of the rank 8(7) and
10(11) Runge-Kutta numerical method leads to a numerical effect and is
therefore unreliable. The so-called semi-implicit Rosenbrock method, however,
turned out to be a viable integration method for our problem. The deviation
angle calculated by the integration of the geodesic equations for different
density profiles of the model structure was then compared to those of the
corresponding thin lens approximation. Using the familiar NFW density profile,
it is shown that independent of the truncation details the thin lens
approximation differ substantially from the exact relativistic calculation. The
difference in the deflection angle for different impact parameters may be up to
about 30 percent. However, using the modified NFW density profile with a void
before going over to the FRW background, as required by an exact general
relativistic model, the thin lens approximation coincides almost exactly with
the general relativistic calculation.
