  Intense flaring events in the near-infrared and X-ray wavebands of our
Galactic Center have been the subject of research for decades. In recent years,
the GRAVITY instrument of the Very Large Telescope captured the motion and
polarimetric signature of such a flare in close proximity to the supermassive
black hole. This study aims to investigate a broad parameter space for hot spot
motion in the vicinity of Sgr$A*$ and reproduce the observed flaring behavior.
To this end, we have developed a General Relativistic Radiative Transfer code
and conducted a parameter study including both planar and ejected hot spot
configurations around supermassive black holes. Super-Keplerian orbital
frequencies are favored by circular equatorial, cylindrical and parabolic
models, whereas conical hot spot trajectories provide a better fit for orbital
frequencies below the Keplerian value. Additionally, a distant observer cannot
effectively differentiate between Schwarzschild and Kerr black holes, as well
as face-on orbits at different observation angles.
