Black holes are one of the most interesting predictions of general relativity. One of their most interesting features is that they bend and distort any beams of light that pass them. The recent image of the black hole from April 2019 showed one feature of this distortion of light - the "shadow" of the black hole - which is really the distortion of light that was emitted from the accretion disk around the black hole. This project will further examine how light is distorted near black holes by tracing millions of light ray bundles in this region of highly distorted space-time.
In general relativity, the Kerr solution represents an isolated, rotating black hole. My recent research has involved tracing light rays near the black hole, and forming images and movies of the wave-fronts of those light rays. Individual light rays are governed by ordinary differential equations (so that integrating one light ray usually corresponds to simultaneously integrating roughly 10 first order ODEs, which I do with self-written C++ code implementing adaptive stepsize ideas. Currently, I organize my code to examine wave-fronts where a group of light rays is emitted from one place with an initially equal distribution at the single emission point. Due to the lensing, this initially equal distribution of rays expanding from one point will spread into an distorted (and unequally distributed) wave front. As a next step, I will investigate the lensing problem from a different angle - specifically, I want to examine all the light rays that reach a given point from an evenly distributed set of sources. This requires additional computational capabilities, as I will need to compute which light rays connect two separate points, which is the equivalent problem of solving for the mappings from one two dimensional space into a second. This mapping is not one to one, and due to the highly non-linear ODEs which generate the map, strong computational (parallelization) methods are required.