Exact general relativistic lensing versus thin lens approximation: the crucial role of the void

Understand

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.