Implementing covariant Monte Carlo radiation transfer in Athena++

With the development of computational astrophysics, theoretical study and modeling of astronomical objects has become a leading field in astronomy. An important advancement came with the ability to study black holes and other compact objects by creating mock images and spectra that can be compared to observations, facilitating the study of these bodies, most of which cannot be directly imaged with the current technology. Athena++ is an astrophysical magnetohydrodynamics (MHD) code written in C++, which coupled with a Monte Carlo radiation transfer, can be used to create and postprocess snapshots of numerical simulations and generate spectra. For the simulation of accretion disks around black holes, we need to account for the strong gravity generated by the massive central object. We implemented a geodesic integration algorithm in the Athena++ code to solve the covariant radiation algorithm. The method works for a general choice of coordinates and spacetime metric and tests are presented for several choices of coordinates and spacetimes: Kerr-Schild, spherical-polar, and cylindrical.