Using a cosmological black hole model proposed recently, we have calculated the quasi-local mass of a collapsing structure within a cosmological setting due to different definitions put forward in the last decades to see how similar or different they are. It has been shown that the mass within the horizon follows the familiar Brown-York behavior. It increases, however, outside the horizon again after a short decrease, in contrast to the Schwarzschild case. Further away, near the void, outside the collapsed region, and where the density reaches the background minimum, all the mass definitions roughly coincide. They differ, however, substantially far from it. Generically, we are faced with three different Brown-York mass maxima: near the horizon, around the void between the overdensity region and the background, and another at cosmological distances corresponding to the cosmological horizon. While the latter two maxima are always present, the horizon mass maxima is absent before the onset of the central singularity.

We use an exact general relativistic model structure within an FRW cosmological background based on a LTB metric to study the gravitational lensing by a cosmological and dynamical structure. Using different density profiles for the model structure, the deviation angle and the time delay through the gravitational lensing has been studied by solving the geodesic equations. The results of these exact calculations have been compared to the thin lens approximation. We have shown that the result for the thin lens approximation based on a modified NFW density profile with a void before going over to the FRW background matches very well with the exact general relativistic calculations. However, the thin lens approximation based on a normal NFW profile does differ from the exact relativistic calculation. The difference is more the less compact the structure is. We have also looked at the impact of our calculation on the observational interpretation of arcs in the case of strong lensing and also the reduced shear in the case of weak lensing. No significant difference has been seen in the data available.PACS numbers: 98.80. Jk, 98.62.Js, 98.62.Ck , 95.35.+d