Tracing Geodesics in General Relativity and Modified Theories of Gravity

Ayush Roy 

Tracing trajectories of particles in a given space time is a fun and educational way of inferring information about the geometry of its geodesics. More importantly, for a black hole or black hole mimicker, backward photon tracing is an efficient method to create its shadow. To understand the tools required for ray tracing, re-creating trajectories in Schwarzschild and Kerr space times is discussed. Then, the novel solutions studied in this project, Kerr black holes with two scalar fields is introduced, focusing on the main ingredients required for ray tracing. This is still a stationary and axisymmetric space time, but the non-availability of analytical metric functions leads to the use of bicubic spline interpolation, a useful tool used in analysis of 2-dimensional data. Finally, different schemes to integrate the equations of motion are presented, and examples of similar work done previously are shown.