SIGNATURE WORK
CONFERENCE & EXHIBITION 2022

Einstein’s theory of general relativity predicts the phenomenon of gravitational lensing – the effect that light rays are bent when passing by a massive object in spacetime. This can be studied in various ways: one approach is optical geometry, defined such that geodesics correspond to spatial light rays, thus providing the proper differential geometry for gravitational lensing. Another approach is the standard thin lens approximation often used in astronomy. In this thesis, both approaches are applied. First, I give an exposition introducing the basic theory of differential geometry and general relativity, including an application to the lensing of a Schwarzschild black hole as an example. Then I dive into optical geometry and apply it to the Levi-Civita solution. After explicitly confirming that this is a cylindrically symmetric vacuum solution of Einstein’s field equation, I derive its geodesics and compute the Gaussian curvature of its optical geometry. Hence, the deflection angle of gravitational lensing in this cylindrical solution is obtained using the Gauss-Bonnet theorem. From the astronomical perspective, this thesis also investigates weak lensing by the cylindrically symmetric structures of galaxy filaments. Since such filaments are composed primarily of dark matter, which reveals itself largely through gravity, weak lensing is an excellent tool to study them. Using real observational data, the lensed signals around two nearby galaxies are stacked, resulting in the profile of an average statistical filament. The relationship between mean convergence and filament width is shown, which turns out to match results from previous simulations. The redshift and mass dependence of the filament is discussed as well.