In 2016 I spent a little time exploring x-ray reverberation with colleagues from the University of Southampton. We’re interested in modeling flares in accreting black hole systems. Initially we’re considering a simplified lamppost model where the flare takes place along the symmetry axis of the system. Our goal is to calculate the difference in the time of arrival of the photons that travel directly from the flare to the observer (us on Earth) and the photons that reverberate around the black hole + accretion disk system (this includes photons that are bent around the black hole and photons that ‘reflect’ off the accretion disk).
The project, which is still in its infancy, involves ray-tracing a black hole spacetime with an accretion disk. This involves solving the null geodesic equations, working out where and when the photons interact with the accretion disk and calculating the time of arrival. As well as the time of arrival we’re interested in the intensity of the emission and its spectrum. Currently the first of these (time of arrival) is implemented for a Schwarzschild black hole with a simple accretion disk.
The code is written in Mathematica and uses semi-analytic methods to calculate the path of the light. Using the code I made a few short animations which can be found here: http://nielswarburton.net/ray_tracing/ray_trace_Schwarz.html. The page describes what each animation depicts.