Numerical Simulation of Black Hole Images from photon trajectories in Schwarzschild Geometry
With the arrival of advanced telescopes such as the Event Horizon Telescope (EHT), direct imaging of a black hole's shadow became a reality. Simulations play an important role in reproducing their appearance and constraining physical parameters of the black hole. We present a simple framework of simulating images of Schwarzschild black holes surrounded by thin, rotating accretion disks, accounting for gravitational and Doppler redshifts. A ray tracing algorithm based on integrating the photon geodesic equations with a 4th-order Runge-Kutta scheme is used for imaging. The accuracy of the numerical method is verified by convergence tests. A brief discussion of the validity of the weak field approximation is included and a qualitative comparison between the simulated images and the EHT image of M87* is presented.