Gravitational Lensing with a Large Deflection Angle as a Probe of General Relativity and the Galactic Center

Gravitational lensing is an important tool for the study of gravity. In this thesis, we use gravitational lensing in the strong field to study a variety of phenomena. We begin with an overview of gravitational lensing in the weak and strong deflection limits, including a formalism for the study of light that passes close enough to a black hole to loop around it several times before reaching the observer. We move on to discuss recent developments in the study of braneworld" models which present an interesting framework for the effect of extra dimensions on gravity. We also discuss several potential black hole metrics in the Randall-Sundrum II braneworld model. We then numerically study a variety of lensing scenarios involving braneworld black holes, including a new form of the tidal Reissner-Nordstrom" metric and find that a braneworld metric will produce results theoretically differentiable from a Schwarzschild black hole. The analytical formalism we review is found to be an accurate reproduction of the numerical results. We outline a test for the application of this analytical formalism to an arbitrary static, spherically symmetric spacetime. We then study the effects of gravitational lensing on the S stars orbiting Sgr A* in the galactic center. We show that modifying the metric for the black hole at Sgr A* will produce different image properties for the lensed S stars. We catalogue these image properties as a function of the metric and comment on the observational prospects for these images and the specifics of their properties. Finally, we suppose that the dark mass at the galactic center is a boson star and offer evidence that this will create observationally significant lensing events for nearby stars.