Testing alternative theories of gravity by fitting the hot-spot data of
  Sgr A*
  We are fitting dynamics of electrically neutral hot-spot orbiting around Sgr
A* source in Galactic center, represented by various modifications of the
standard Kerr black hole (BH), to the three flares observed by the GRAVITY
instrument on May 27, July 22, July 28, 2018. We consider stationary,
axisymmetric and asymptotically flat spacetimes describing charged BHs in
general relativity (GR) combined with non-linear electrodynamics, or reflecting
influence of dark matter (DM), or in so called parameterized dirty Kerr
spacetimes. We distinguish the spacetimes having different orbital frequencies
from the standard Kerr BH, and test various BH spacetimes using the hot-spot
data. We show that the orbital frequencies and positions of the hot-spots
orbiting the considered BHs, fit the observed positions and periods of the
flare orbits and give relevant constrains on the parameters of the considered
BH spacetimes and the gravity or other theories behind such modified
spacetimes.
